DesignofaSubmarineVehicleforHigherNaturalFrequency Using...
9
Research Article DesignofaSubmarineVehicleforHigherNaturalFrequency Using U ∗ IndexTheoryApproach WeiyanShang 1 andQingguoWang 2 1 Department of Mechanical Engineering, Ningbo University of Technology, Ningbo, Zhejiang 315016, China 2 Department of Mechanical Engineering, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2 Correspondence should be addressed to Qingguo Wang; [email protected] Received 22 June 2018; Revised 15 September 2018; Accepted 18 September 2018; Published 23 October 2018 Academic Editor: Marco Gherlone Copyright © 2018 Weiyan Shang and Qingguo Wang. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. e natural frequency of a vehicle structure should be far higher than the road excitation frequency in order to avoid dynamic problems caused by structural resonance. Submarine vehicles or robots are facing the same issue as mentioned above. is paper proposed a means to effectively increase the natural frequency of submarine vehicles or robots by using U ∗ index approach. e U ∗ theory was originally introduced to investigate load transfer paths within a structure. It is a new design paradigm for vehicle structures. In this study, the U ∗ index theory was applied to evaluate the internal stiffness distribution of a submarine vehicle structure and then a modified design was achieved based on the U ∗ analysis. Compared to the original design, the natural frequency of the modified vehicle structure was increased by more than 40% while the weight of the modified vehicle was only raised by 4.6%. 1.Introduction Recently, ocean engineering technologies have increasingly been focused by many countries and areas of the world. Submarine vehicles or robots are important to the in- vestigation of ocean ecosystem, exploration of ocean energy, and heath monitoring of ocean platform and submarine pipelines. However, compared to ground vehicles, the de- velopment of design and manufacturing techniques of submarine vehicles are still in their primary stage [1]. Structural vibration and control is always one of the prin- cipal problems in vehicle design which significantly affects structural performance such as structural strength, dura- bility, kinematic accuracy, and dynamic stability [2, 3]. To minimize the dynamic problems caused by the road exci- tation, natural frequency of ground vehicles needs to be far higher than 10–20Hz which is a typical road excitation frequency [3]. To avoid the resonance phenomena, rea- sonable matching of stiffness between different parts or assemblies is also necessary in vehicle design [2]. Although road excitation data from the seabed are limited to date, a means to design submarine vehicles or robots with higher natural frequencies is imperative. Structural stiffness is a determinant of modal shapes and frequencies of a structure. However, traditional finite ele- ment analysis (FEA) only gives structural stresses and dis- placements instead of a stiffness distribution. U ∗ index theory which was firstly introduced by Takahashi in 2005 is a method to investigate stiffness distribution of a structure [4]. e original purpose for proposing the U ∗ theory method is to calculate load transfer paths of a load-bearing structure. Load paths analysis is essential for designing better engineering structures in both mechanical performance and weight efficiency [5]. e U ∗ index theory was initially proposed to solve static and linear elastic problems. Re- cently, the U ∗ index theory has been extended to dynamic loads [6], nonlinear elasticity, composite materials [7], and six degrees of freedom systems [8]. Load paths analysis based on the U ∗ index theory is a new design paradigm because it can provide useful information for decision-making which cannot be achieved from traditional finite element analysis (FEA) [9]. e U ∗ theory has been applied in vehicle design Hindawi Shock and Vibration Volume 2018, Article ID 9496026, 8 pages https://doi.org/10.1155/2018/9496026
Transcript of DesignofaSubmarineVehicleforHigherNaturalFrequency Using...
Research ArticleDesign of a Submarine Vehicle for Higher Natural FrequencyUsing Ulowast Index Theory Approach
Weiyan Shang1 and Qingguo Wang 2
1Department of Mechanical Engineering Ningbo University of Technology Ningbo Zhejiang 315016 China2Department of Mechanical Engineering University of Manitoba Winnipeg Manitoba Canada R3T 2N2
Correspondence should be addressed to Qingguo Wang qingguowang1984gmailcom
Received 22 June 2018 Revised 15 September 2018 Accepted 18 September 2018 Published 23 October 2018
Academic Editor Marco Gherlone
Copyright copy 2018 Weiyan Shang and Qingguo Wang is is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in anymedium provided the original work isproperly cited
e natural frequency of a vehicle structure should be far higher than the road excitation frequency in order to avoid dynamicproblems caused by structural resonance Submarine vehicles or robots are facing the same issue as mentioned above is paperproposed a means to effectively increase the natural frequency of submarine vehicles or robots by using Ulowast index approach eUlowast theory was originally introduced to investigate load transfer paths within a structure It is a new design paradigm for vehiclestructures In this study the Ulowast index theory was applied to evaluate the internal stiffness distribution of a submarine vehiclestructure and then a modified design was achieved based on the Ulowast analysis Compared to the original design the naturalfrequency of the modified vehicle structure was increased by more than 40 while the weight of the modified vehicle was onlyraised by 46
1 Introduction
Recently ocean engineering technologies have increasinglybeen focused by many countries and areas of the worldSubmarine vehicles or robots are important to the in-vestigation of ocean ecosystem exploration of ocean energyand heath monitoring of ocean platform and submarinepipelines However compared to ground vehicles the de-velopment of design and manufacturing techniques ofsubmarine vehicles are still in their primary stage [1]Structural vibration and control is always one of the prin-cipal problems in vehicle design which significantly affectsstructural performance such as structural strength dura-bility kinematic accuracy and dynamic stability [2 3] Tominimize the dynamic problems caused by the road exci-tation natural frequency of ground vehicles needs to be farhigher than 10ndash20Hz which is a typical road excitationfrequency [3] To avoid the resonance phenomena rea-sonable matching of stiffness between different parts orassemblies is also necessary in vehicle design [2] Althoughroad excitation data from the seabed are limited to date
a means to design submarine vehicles or robots with highernatural frequencies is imperative
Structural stiffness is a determinant of modal shapes andfrequencies of a structure However traditional finite ele-ment analysis (FEA) only gives structural stresses and dis-placements instead of a stiffness distribution Ulowast indextheory which was firstly introduced by Takahashi in 2005 isa method to investigate stiffness distribution of a structure[4] e original purpose for proposing the Ulowast theorymethod is to calculate load transfer paths of a load-bearingstructure Load paths analysis is essential for designing betterengineering structures in both mechanical performance andweight efficiency [5] e Ulowast index theory was initiallyproposed to solve static and linear elastic problems Re-cently the Ulowast index theory has been extended to dynamicloads [6] nonlinear elasticity composite materials [7] andsix degrees of freedom systems [8] Load paths analysis basedon the Ulowast index theory is a new design paradigm because itcan provide useful information for decision-making whichcannot be achieved from traditional finite element analysis(FEA) [9] e Ulowast theory has been applied in vehicle design
HindawiShock and VibrationVolume 2018 Article ID 9496026 8 pageshttpsdoiorg10115520189496026
by automotive manufacturers like Honda and Nissan[10 11]
In this paper instead of load paths analysis theUlowast indextheory was applied as a means to increase the natural fre-quency of submarine vehicles or robots to reduce the dy-namic problems caused by excitations with lower frequenciesA submarine vehicle designed by our research group was usedas the sample structure to demonstrate the effectiveness of theproposed method Firstly the internal relative stiffness dis-tribution of the submarine vehicle structure was computed bythe Ulowast index theory en a Ulowast-based design criterion wasemployed to improve the overall stiffness of the submarinevehicle structure by only adding a small amount of massFinally due to the improvement of the stiffness distributionthe natural frequency of the submarine vehicle structure wasraised by 435while the structural weight was only increasedby 46
In the following parts of the paper the Ulowast index theoryand theUlowast-based design criterion are presented in Section 2the computational design method of the submarine vehiclestructure is introduced in Section 3 the computationalresults of both original and modified designs are comparedin Section 4 and the conclusion of the paper is drawn inSection 5
2 Theoretical Preliminary Ulowast Index Theory
Figure 1(a) shows a linear elastic body with the loading pointA supporting point B and an arbitrary point C e beamsrepresent the internal stiffness between any two points of thesystem e internal stiffness is the coupling stiffness be-tween two specific points whose meaning is totally differentfrom the stiffness matrix in FEA e following equationdescribes the force-displacement relationship among pointsA B and C
FAFBFCMA
MB
MC
⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣
⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦
KTAA middot middot middot KT
AC KTRAA middot middot middot KTR
AC
⋮ ⋱ ⋮ ⋮ ⋱ ⋮
KTCA middot middot middot KT
CC KTRCA middot middot middot KTR
CC
KRTAA middot middot middot KRT
AC KRAA middot middot middot KR
AC
⋮ ⋱ ⋮ ⋮ ⋱ ⋮
KRTCA middot middot middot KRT
CC KRCA middot middot middot KR
CC
⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣
⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦
DA
DB
DC
RA
RB
RC
⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣
⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦
(1)
where Fi(iABC) Mi(iABC) Di(iABC) and Ri(iABC) areall three-dimensional vectors representing forces bend-ing moments translations and rotations respectivelyKT
ij(iABCjABC) KRij(iABCjABC) KTR
ij(iABCjABC) andKRT
ij(iABCjABC) are the internal stiffness tensors and theyrespectively characterize the relationships between forcesand translations moments and rotations forces and rota-tions and moments and translations
In Figure 1(a) since point B is fixed (DB RB 0)
FA KTAADA + KT
ACDC + KTRAARA + KTR
ACRC (2)
MA KRTAADA + KRT
ACDC + KRAARA + KR
ACRC (3)
e external work of the system caused by the force FAand the bending moment MA is presented in Equations (4)and (5) respectively
WF 12FA middot DA
12
KTAADA + KT
ACDC + KTRAARA + KTR
ACRC1113872 1113873 middot DA
(4)
WM 12MA middot RA
12
KRTAADA + KRT
ACDC + KRAARA + KR
ACRC1113872 1113873 middot RA
(5)
Figure 1(b) shows the arbitrary point C (DC RC 0) ofthe system is restrained while same displacements DA andRA are applied at point A Equations (6) and (7) indicate theexternal work of the constrained system induced by the forceFAprime and the bending moment MAprime respectively
WFprime 12FAprime middot DA
12
KTAADA + KTR
AARA1113872 1113873 middot DA (6)
WMprime 12MAprime middot RA
12
KRTAADA + KR
AARA1113872 1113873 middot RA (7)
e Ulowast index under six DOFs is defined as
Ulowast
1minusU
Uprime 1minus
WF + WM
WFprime + WMprime (8)
where U is the total strain energy of the original system(Figure 1(a)) and Uprime is the total strain energy of theconstrained system (Figure 1(b)) Here the total strainenergy of the system is transformed from the externalwork [12]
Equation (8) can be rewritten as
1minusWF + WM
WFprime + WMprime minus
WFprime + WMprime
WF + WM( 1113857minus WFprime + WMprime( 11138571113890 1113891
minus1
(9)
By subtracting 1 and then adding 1 Equation (9) equalsto
minusWFprime + WMprime
WF + WM( 1113857minus WFprime + WMprime( 1113857minus
WF + WM( 1113857minus WFprime + WMprime( 1113857
WF + WM( 1113857minus WFprime + WMprime( 1113857+ 11113890 1113891
minus1
1minusWF + WM
WF + WM( 1113857minus WFprime + WMprime( 11138571113890 1113891
minus1
(10)
By substituting Equations (4)ndash(7) into Equation (10) weget
Ulowast
1minus2WF + 2WM
KTACDC( 1113857 middot DA + KTR
ACRC( 1113857 middot DA + KRTACDC( 1113857 middot RA + KR
ACRC( 1113857 middot RA1113890 1113891
minus1
(11)
2 Shock and Vibration
It can be seen from Equation (11) that the Ulowast index canbe expressed in terms of the internal stiness between theloading point and the arbitrary point of the system Ina structure forces are mainly transferred through the stiestparts in series with the loading point erefore the lineswith the highest Ulowast values (ie the ridge line of the Ulowastdistribution) is dened as the main load paths If a vectorg(minus) is dened as
g(minus) minusgradUlowast (12)
the main load path is the line with the smallest g(minus) evector g(minus) is regarded as the ldquostiness decay vectorrdquo [11]Figures 2(a) and 2(b) elaborate Ulowast and von Mises stressdistributions of a plate with a hole respectively e solidblack lines shown in Figure 2(a) are the main load pathspredicted by the Ulowast index which satisfy the expectationform the engineering point of view As can be seen inFigure 2(b) the higher stresses are formed in the vicinity ofthe hole However since the hole is not important intransferring the forces it is unreasonable to conclude themain load paths pass the locations with those higherstresses
Normally the Ulowast index decreases from the maximumvalue of one (1) at the loading point to the minimum value ofzero (0) at the supporting point In Figure (3) the solid lineelaborates the variation of the Ulowast index along a path ofa load-bearing structure and the dashed line depicts the Ulowastvariation of the desirable condition A uniform decay of theUlowast index means the structural stiness distribution isperfect whereas in reality the Ulowast variation is nonuniformbecause of the structural issues An increase or decrease ofthe rate of the Ulowast decay indicates that the stiness in thecorresponding part is higher or lower than other parts euniformity of the Ulowast decay is dened as the criterion toevaluate the rationality of the stiness distribution of thestructure Structural modications are required when theUlowastcurve is not uniform such as the solid line in Figure 3 e
eective structural modications shall reduce the shade areashown in Figure 3
3 Computational Design Method
ere are mainly three steps in the proposed computationaldesign method Firstly a dynamic model is built anda modal analysis is conducted on the vehicle structure isis to obtain the natural frequency of the original designen the vehicle structure is evaluated by using the Ulowast-based design criterion while modication directions aresuggested based on the Ulowast analysis irdly the naturalfrequency is recalculated to see the improvement from thedesign modication If extra improvement is expected theabove procedures would be repeated until the result isdesired
Figure 4 shows the sample structure a submarine vehicle(or robot) designed by our research group which is used todemonstrate the usefulness of the proposed computationaldesign method e duties of the submarine vehicle areinvestigations of seabed ecosystems and explorations ofocean energy Hence minimizing the dynamic problems caneectively improve the accuracy and stability of data col-lection and dynamic control to the submarine vehicle Inthe current study the dynamic analysis and the designmodication focuse on the vehicle suspension system ematerial properties of the major components of the vehicleare given in Table 1
Figure 5 illustrates the dynamic model of the submarinevehicle for modal analysis e model is created in com-mercial FEA code ANSYS (release 18) e dynamic modelincludes the vehicle body and the major parts of the sus-pension system ignoring the crawler belt systems and thepropellers e properties of each component of thedynamic model are elaborated in Table 1 e boundaryconditions can also be seen from Figure 5 where all thewheel holes in the vertical section of the suspension arefully constrained All the components in the FEAmodel aremodeled using Shell 181 Element with full integration eblock Lanczos method is selected as the mode extractionmethod [13]
Figure 6 demonstrates the static computer model for Ulowastcalculation of the vehicle suspension system In this modelthe vehicle body is not included because the Ulowast analysisfocuses on the load transfer behavior of the vehicle sus-pension system e body weight of the vehicle bodycomponent is applied to the vehicle suspension system as theexternal force e boundary conditions are the same as thedynamic model shown in Figure 6 e Ulowast analysis giveshow the force of the vehicle body gravity is transferredthrough the vehicle suspension system Meanwhile theinsight of the suspension structure behind the load transferpattern is revealed through the Ulowast-based design criterionintroduced in Section 2 Finally design modication can beproposed to the suspension structure based on the Ulowastanalysis
In this study an in-house FEA-based program wasdeveloped for Ulowast calculation in Ansys Parametric DesignLanguage [13] Figure 7 shows the logic and the procedure
A
B
C
FADA
MARA
(a)
A
B
C
FAprime DA
MAprime RA
(b)
Figure 1 Calculation of the Ulowast index (a) original system (b)constrained system [8]
Shock and Vibration 3
for the Ulowast algorithm development e rst step is thecalculation of the total strain energy of the original system asshown in Figure 1(a) Secondly by xing an arbitrary nodeof the system and applying the same displacement to theloading point the total strain energy of the modied system(Figure 1(b)) is calculateden theUlowast value of the arbitrarynode can be computed through Equation (8) By repeatingthis step for each node of the system the Ulowast distribution of
the whole system is obtained e total strain energy of theoriginal system is only calculated once
4 Results
Figure 8 presents the rst three modal frequencies and shapesof the submarine vehicle e rst modal frequency of thevehicle which is regarded as the natural frequency is 376Hze rst modal shape of the vehicle is pitching oscillation thesecond modal shape is heaving oscillation and the third modalshape is rolling oscillation e frequencies of the second andthird modes can be also seen from Figure 8
e Ulowast distribution of the suspension structure is shownin Figure 9(a) It shows the gravity force of the vehicle bodyis transferred through the horizontal part to the vertical partof the suspension In Figure 9(b) the dashed white lineillustrates the ideal situation of the Ulowast variation while thesolid blue line represents the actual Ulowast values along themarked load path in Figure 9(a) We can see the real Ulowastvalues along the load path deviate from the ideal situationespecially the circled area Figure 9(b) indicates the Ulowast indexdecays sharply along the horizontal section of the suspen-sion while it drops slowly along the vertical section ereason of this phenomenon is that the stiness of thehorizontal section of the submarine vehicle suspension is farlower than the vertical section erefore increasing thestiness of the horizontal section can eectively improve theoverall stiness of the suspension and thus raising thenatural frequency of the whole vehicle As discussed aboveto increase the stiness of the horizontal section of thesuspension its thickness was raised from 20mm to 30mm
Figure 10(a) presents the Ulowast contour of the modiedsuspension while Figure 10(b) shows the comparison of theUlowastvalues along the load path between the modied and theoriginal designs From Figure 10(b) we can see that in thehorizontal section the Ulowast values of the modied suspensionare larger than the original design It also can be seen that at thejoint between the horizontal and the vertical sections of thesuspension the Ulowast value of the modied structure is muchcloser to the ideal value compared to the original structureie with respect to the ideal condition the deviation of themodied design is smaller than the original design Toquantitatively show the design improvement ratios of the Ulowastvalues of the modied or the original design to the ideal Ulowast
Loading SupportingMain load paths
1
0
Ulowast
(a)
Stress concentrations
Maxvon m
ises stress
0
Loading Supporting
(b)
Figure 2 Load transfer analysis of a plate with a hole (a) Ulowast distribution and main load paths (b) von Mises stress distribution [9]
00
1
1sl
Ulowast
A C
D B
Figure 3 Ulowast-based design criterion to achieve uniform structuralstiness distribution [5]
Vehicle bodySuspension system
Crawler belt
PropellersZ
YX
Figure 4 Computer-aided design model of a submarine vehicle(robot)
4 Shock and Vibration
values (ie UlowastdesignUlowastideal) were obtained using the data points
from Figure 10(b) and themean and the coecurrencient of variation(COV) of the ratios were then computed respectively andillustrated in Table 2 e mean for the modied design is 101comparing with 086 for the original design and the COV forthe modied design is 17 instead of 33 for the originaldesign e improvement in terms of the Ulowast distributionindicates that the design modication narrowed the gap of thestiness between the horizontal and the vertical sections of the
vehicle structure As a result the stiness distribution of thewhole suspension is more uniform and the overall stiness ofthe whole suspension is improved at the same time
To see the eectiveness of the design modication a newmodal analysis was conducted to the submarine vehicle withthe modied thickness in the horizontal section of the sus-pension e modal shapes and the corresponding frequenciesare depicted in Figure 11 where we can see that the rst threemodal frequencies of the modied vehicle were respectivelyimproved by 435 40 and 48 compared to the originaldesign Due to the design modication the total weight of the
Fully constrainedon all wheel holes
ZY
X
Figure 5 FEA model and mesh of the submarine vehicle structurefor dynamic analysis
Equivalent force of the
vehicle body component
Fully constrained
on all wheel holes
Z
Y X
Figure 6 FEA model and mesh of the submarine vehicle structurefor static Ulowast analysis
Fixing node i
No
Yes
U of original system
Uiprime of constrained system
i = i + 1
If i gt MAX node number
Finish
i = 1
UUiprime
Uilowast = 1 ndash
Figure 7 Flowchart to develop computer program for Ulowastcalculation
Table 1 Material properties of the major parts of the submarine vehicle
Component Material Elastic modulus (MPa) Poisonrsquos ratio ickness (mm) Mass (kg)Vehicle body
Aluminum 70000 033
mdash 30Vertical part of suspension (original) 20 523Horizontal part of suspension (original) 20 357Horizontal part of suspension (modied) 30 535
Shock and Vibration 5
f1 = 376Hz f2 = 787Hz f3 = 936Hz
Figure 8 First three modal shapes and frequencies of the original submarine vehicle structure (a) f1 376Hz (b) f2 787Hz (c) f3 936Hz
1
Ulowast
0
(a)
0
02
04
06
08
1
0 50 100 150 200 250
Ulowast
Path length (mm)
Ulowast variation
OriginalIdeal
(b)
Figure 9 Ulowast analysis of the original submarine vehicle structure (a) Ulowast contour of the structure (b) Ulowast variation along a load path (whitearrow)
1Ulowast
0
(a)
0
02
04
06
08
1
0 50 100 150 200 250
Ulowast
Path length (mm)
Ulowast variation
OriginalModifiedIdeal
(b)
Figure 10 Ulowast analysis of the modied submarine vehicle structure (a) Ulowast contour of the structure (b) Ulowast variation along a load path(white arrow)
6 Shock and Vibration
submarine vehicle was only raised by 46 which was calcu-lated based on the dynamic model shown in Figure 5
5 Conclusion
e paper proposed a means for designing submarine vehiclesor robots with the higher natural frequency in order to decreasethe potential dynamic problems due to the road or seabedexcitations
With the help of the Ulowast index theory the distribution ofrelative stiness of a structure can be obtained which providesdesigners with useful information in addition to the traditionalFEA approache designmodication based on theUlowast-basedapproach considerably raised the natural frequency of thevehicle by adding a small amount of weight
e results indicate that upgrade of overall stiness ofa structure can increase the structural natural frequencywhile the former can be improved by raising the uniformityof the stiness distribution of the structure Subjected toexternal forces or excitations a structure with uniformstiness distribution can realize the maximum overallstructural stiness based on a constant usage of materiale design criterion based on the Ulowast index theory is ef-fective to evaluate and improve the uniformity of stinessdistribution of a structure
Simply adding materials to each part of the vehiclestructure can also improve its natural frequency However theincrease of the structural weight may cause many otherproblems eg fuel ecurrenciency weight limit or control accu-racy is point can further highlight the usefulness of theproposed Ulowast-based approach in designing submarine vehiclestructures with better dynamic performance e work of thispaper also implies that the Ulowast index theory is able to beapplied for stiness matching between dierent componentsof a vehicle system for addressing vibration problems
Data Availability
All the computational data used to support the ndings of thisstudy are included within the article It includes all the data
related to the CADmodel and the FEA model and the date ofthemodal analysis andUlowast analysis All the original data in thisstudy are available upon request
Conflicts of Interest
e authors declare that they have no concopyicts of interest
Acknowledgments
is work was supported by the NSFC (Natural ScienceFoundation of China) ldquoResearch on the Driving Stability ofUndersea Observation Robot Steering on Slopesrdquo (Grant no51605232) Some of the simulation work was also supportedby the Natural Science Foundation of Zhejiang ProvinceldquoStudy on the Stability of Mobile Robot for Seacopyoor Ex-plorationrdquo (Grant no LQ15E050004)
References
[1] H Cheng and W Li ldquoReducing the frame vibration of deltarobot in pick and place application an acceleration proleoptimization approachrdquo Shock and Vibration vol 2018Article ID 2945314 15 pages 2018
[2] H Hoshino T Sakurai and K Takahashi ldquoVibration re-duction in the cabins of heavy-duty trucks using the theory ofload transfer pathsrdquo JSAE Review vol 24 no 2 pp 165ndash1712003
[3] G Verros S Natsiavas and C Papadimitriou ldquoDesign op-timization of quarter-car models with passive and semi-activesuspensions under random road excitationrdquo JVCJournal VibControl vol 11 no 5 pp 581ndash606 2005
[4] K Takahashi and T Sakurai ldquoExpression of load transferpaths in structuresrdquo Transactions of the Japan Society ofMechanical Engineers Series A vol 71 no 708 pp 1097ndash11022005
[5] Q Wang K Pejhan I Telichev and C Q Wu ldquoDemon-stration of the eectiveness of Ulowast based design criteria onvehicle structural designrdquo Proceedings of the Institution ofMechanical Engineers Part D Journal of Automobile Engi-neering vol 232 no 8 pp 995ndash1002 2017
Table 2 Quantitative comparison with the ideal condition
Design category Mean of (UlowastdesignUlowastideal) COV of (UlowastdesignU
lowastideal)
Modied design 101 17Original design 086 33
f1 = 539Hz f2 = 1103Hz f3 = 1385Hz
Figure 11 First three modal shapes and frequencies of the original submarine vehicle structure (a) f1 539Hz (b) f2 1103Hz (c) f3 1385Hz
Shock and Vibration 7
[6] K Takahashi M Omiya T Iso et al ldquoLoad transfer ustar(Ulowast) calculation in structures under dynamic loadingrdquoTransactions of the Japan Society of Mechanical EngineersSeries A vol 79 no 807 pp 1657ndash1668 2013
[7] Q Wang K Pejhan I Telichev and C Q Wu ldquoExtensions ofthe Ulowast theory for applications on orthotropic composites andnonlinear elastic materialsrdquo International Journal of Me-chanics and Materials in Design vol 13 no 3 pp 469ndash4802017
[8] Q Wang I Telichev and C Q Wu ldquoA new load transferindex (UlowastM) with considering six degrees of freedom and itsapplication in structural design and analysisrdquo MechanicsBased Design of Structures and Machines vol 46 no 4pp 410ndash424 2018
[9] Q Wang W Zhou I Telichev and C Q Wu ldquoLoad transferanalysis of a bus bay section under standard rollover test usingUlowastM index lowastrdquo International Journal of Automotive Tech-nology vol 19 no 4 pp 705ndash716 2018
[10] H Koboyashi T Naito and Y Urushiyama ldquoStudy onsimilarity of load path distribution in body structurerdquo HondaR and D Technical Review vol 23 no 1 pp 80ndash89 2011
[11] E Wang Y Yoshikuni Q Guo et al ldquoLoad transfer in truckcab structures under initial phase of frontal collisionrdquo In-ternational Journal of Vehicle Structures and Systems vol 2no 2 pp 60ndash68 2010
[12] F Beer E Johnston J Dewolf and D MazurekMechanics ofMaterials McGraw Hill Higher Education New York CityNY USA 4th edition 2006
[13] ANSYS ANSYSreg Academic Research Release 180 HelpSystem ANSYS Inc Canonsburg PA United States 2017
8 Shock and Vibration
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
RoboticsJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
VLSI Design
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawiwwwhindawicom
Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
SensorsJournal of
Hindawiwwwhindawicom Volume 2018
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
by automotive manufacturers like Honda and Nissan[10 11]
In this paper instead of load paths analysis theUlowast indextheory was applied as a means to increase the natural fre-quency of submarine vehicles or robots to reduce the dy-namic problems caused by excitations with lower frequenciesA submarine vehicle designed by our research group was usedas the sample structure to demonstrate the effectiveness of theproposed method Firstly the internal relative stiffness dis-tribution of the submarine vehicle structure was computed bythe Ulowast index theory en a Ulowast-based design criterion wasemployed to improve the overall stiffness of the submarinevehicle structure by only adding a small amount of massFinally due to the improvement of the stiffness distributionthe natural frequency of the submarine vehicle structure wasraised by 435while the structural weight was only increasedby 46
In the following parts of the paper the Ulowast index theoryand theUlowast-based design criterion are presented in Section 2the computational design method of the submarine vehiclestructure is introduced in Section 3 the computationalresults of both original and modified designs are comparedin Section 4 and the conclusion of the paper is drawn inSection 5
2 Theoretical Preliminary Ulowast Index Theory
Figure 1(a) shows a linear elastic body with the loading pointA supporting point B and an arbitrary point C e beamsrepresent the internal stiffness between any two points of thesystem e internal stiffness is the coupling stiffness be-tween two specific points whose meaning is totally differentfrom the stiffness matrix in FEA e following equationdescribes the force-displacement relationship among pointsA B and C
FAFBFCMA
MB
MC
⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣
⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦
KTAA middot middot middot KT
AC KTRAA middot middot middot KTR
AC
⋮ ⋱ ⋮ ⋮ ⋱ ⋮
KTCA middot middot middot KT
CC KTRCA middot middot middot KTR
CC
KRTAA middot middot middot KRT
AC KRAA middot middot middot KR
AC
⋮ ⋱ ⋮ ⋮ ⋱ ⋮
KRTCA middot middot middot KRT
CC KRCA middot middot middot KR
CC
⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣
⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦
DA
DB
DC
RA
RB
RC
⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣
⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦
(1)
where Fi(iABC) Mi(iABC) Di(iABC) and Ri(iABC) areall three-dimensional vectors representing forces bend-ing moments translations and rotations respectivelyKT
ij(iABCjABC) KRij(iABCjABC) KTR
ij(iABCjABC) andKRT
ij(iABCjABC) are the internal stiffness tensors and theyrespectively characterize the relationships between forcesand translations moments and rotations forces and rota-tions and moments and translations
In Figure 1(a) since point B is fixed (DB RB 0)
FA KTAADA + KT
ACDC + KTRAARA + KTR
ACRC (2)
MA KRTAADA + KRT
ACDC + KRAARA + KR
ACRC (3)
e external work of the system caused by the force FAand the bending moment MA is presented in Equations (4)and (5) respectively
WF 12FA middot DA
12
KTAADA + KT
ACDC + KTRAARA + KTR
ACRC1113872 1113873 middot DA
(4)
WM 12MA middot RA
12
KRTAADA + KRT
ACDC + KRAARA + KR
ACRC1113872 1113873 middot RA
(5)
Figure 1(b) shows the arbitrary point C (DC RC 0) ofthe system is restrained while same displacements DA andRA are applied at point A Equations (6) and (7) indicate theexternal work of the constrained system induced by the forceFAprime and the bending moment MAprime respectively
WFprime 12FAprime middot DA
12
KTAADA + KTR
AARA1113872 1113873 middot DA (6)
WMprime 12MAprime middot RA
12
KRTAADA + KR
AARA1113872 1113873 middot RA (7)
e Ulowast index under six DOFs is defined as
Ulowast
1minusU
Uprime 1minus
WF + WM
WFprime + WMprime (8)
where U is the total strain energy of the original system(Figure 1(a)) and Uprime is the total strain energy of theconstrained system (Figure 1(b)) Here the total strainenergy of the system is transformed from the externalwork [12]
Equation (8) can be rewritten as
1minusWF + WM
WFprime + WMprime minus
WFprime + WMprime
WF + WM( 1113857minus WFprime + WMprime( 11138571113890 1113891
minus1
(9)
By subtracting 1 and then adding 1 Equation (9) equalsto
minusWFprime + WMprime
WF + WM( 1113857minus WFprime + WMprime( 1113857minus
WF + WM( 1113857minus WFprime + WMprime( 1113857
WF + WM( 1113857minus WFprime + WMprime( 1113857+ 11113890 1113891
minus1
1minusWF + WM
WF + WM( 1113857minus WFprime + WMprime( 11138571113890 1113891
minus1
(10)
By substituting Equations (4)ndash(7) into Equation (10) weget
Ulowast
1minus2WF + 2WM
KTACDC( 1113857 middot DA + KTR
ACRC( 1113857 middot DA + KRTACDC( 1113857 middot RA + KR
ACRC( 1113857 middot RA1113890 1113891
minus1
(11)
2 Shock and Vibration
It can be seen from Equation (11) that the Ulowast index canbe expressed in terms of the internal stiness between theloading point and the arbitrary point of the system Ina structure forces are mainly transferred through the stiestparts in series with the loading point erefore the lineswith the highest Ulowast values (ie the ridge line of the Ulowastdistribution) is dened as the main load paths If a vectorg(minus) is dened as
g(minus) minusgradUlowast (12)
the main load path is the line with the smallest g(minus) evector g(minus) is regarded as the ldquostiness decay vectorrdquo [11]Figures 2(a) and 2(b) elaborate Ulowast and von Mises stressdistributions of a plate with a hole respectively e solidblack lines shown in Figure 2(a) are the main load pathspredicted by the Ulowast index which satisfy the expectationform the engineering point of view As can be seen inFigure 2(b) the higher stresses are formed in the vicinity ofthe hole However since the hole is not important intransferring the forces it is unreasonable to conclude themain load paths pass the locations with those higherstresses
Normally the Ulowast index decreases from the maximumvalue of one (1) at the loading point to the minimum value ofzero (0) at the supporting point In Figure (3) the solid lineelaborates the variation of the Ulowast index along a path ofa load-bearing structure and the dashed line depicts the Ulowastvariation of the desirable condition A uniform decay of theUlowast index means the structural stiness distribution isperfect whereas in reality the Ulowast variation is nonuniformbecause of the structural issues An increase or decrease ofthe rate of the Ulowast decay indicates that the stiness in thecorresponding part is higher or lower than other parts euniformity of the Ulowast decay is dened as the criterion toevaluate the rationality of the stiness distribution of thestructure Structural modications are required when theUlowastcurve is not uniform such as the solid line in Figure 3 e
eective structural modications shall reduce the shade areashown in Figure 3
3 Computational Design Method
ere are mainly three steps in the proposed computationaldesign method Firstly a dynamic model is built anda modal analysis is conducted on the vehicle structure isis to obtain the natural frequency of the original designen the vehicle structure is evaluated by using the Ulowast-based design criterion while modication directions aresuggested based on the Ulowast analysis irdly the naturalfrequency is recalculated to see the improvement from thedesign modication If extra improvement is expected theabove procedures would be repeated until the result isdesired
Figure 4 shows the sample structure a submarine vehicle(or robot) designed by our research group which is used todemonstrate the usefulness of the proposed computationaldesign method e duties of the submarine vehicle areinvestigations of seabed ecosystems and explorations ofocean energy Hence minimizing the dynamic problems caneectively improve the accuracy and stability of data col-lection and dynamic control to the submarine vehicle Inthe current study the dynamic analysis and the designmodication focuse on the vehicle suspension system ematerial properties of the major components of the vehicleare given in Table 1
Figure 5 illustrates the dynamic model of the submarinevehicle for modal analysis e model is created in com-mercial FEA code ANSYS (release 18) e dynamic modelincludes the vehicle body and the major parts of the sus-pension system ignoring the crawler belt systems and thepropellers e properties of each component of thedynamic model are elaborated in Table 1 e boundaryconditions can also be seen from Figure 5 where all thewheel holes in the vertical section of the suspension arefully constrained All the components in the FEAmodel aremodeled using Shell 181 Element with full integration eblock Lanczos method is selected as the mode extractionmethod [13]
Figure 6 demonstrates the static computer model for Ulowastcalculation of the vehicle suspension system In this modelthe vehicle body is not included because the Ulowast analysisfocuses on the load transfer behavior of the vehicle sus-pension system e body weight of the vehicle bodycomponent is applied to the vehicle suspension system as theexternal force e boundary conditions are the same as thedynamic model shown in Figure 6 e Ulowast analysis giveshow the force of the vehicle body gravity is transferredthrough the vehicle suspension system Meanwhile theinsight of the suspension structure behind the load transferpattern is revealed through the Ulowast-based design criterionintroduced in Section 2 Finally design modication can beproposed to the suspension structure based on the Ulowastanalysis
In this study an in-house FEA-based program wasdeveloped for Ulowast calculation in Ansys Parametric DesignLanguage [13] Figure 7 shows the logic and the procedure
A
B
C
FADA
MARA
(a)
A
B
C
FAprime DA
MAprime RA
(b)
Figure 1 Calculation of the Ulowast index (a) original system (b)constrained system [8]
Shock and Vibration 3
for the Ulowast algorithm development e rst step is thecalculation of the total strain energy of the original system asshown in Figure 1(a) Secondly by xing an arbitrary nodeof the system and applying the same displacement to theloading point the total strain energy of the modied system(Figure 1(b)) is calculateden theUlowast value of the arbitrarynode can be computed through Equation (8) By repeatingthis step for each node of the system the Ulowast distribution of
the whole system is obtained e total strain energy of theoriginal system is only calculated once
4 Results
Figure 8 presents the rst three modal frequencies and shapesof the submarine vehicle e rst modal frequency of thevehicle which is regarded as the natural frequency is 376Hze rst modal shape of the vehicle is pitching oscillation thesecond modal shape is heaving oscillation and the third modalshape is rolling oscillation e frequencies of the second andthird modes can be also seen from Figure 8
e Ulowast distribution of the suspension structure is shownin Figure 9(a) It shows the gravity force of the vehicle bodyis transferred through the horizontal part to the vertical partof the suspension In Figure 9(b) the dashed white lineillustrates the ideal situation of the Ulowast variation while thesolid blue line represents the actual Ulowast values along themarked load path in Figure 9(a) We can see the real Ulowastvalues along the load path deviate from the ideal situationespecially the circled area Figure 9(b) indicates the Ulowast indexdecays sharply along the horizontal section of the suspen-sion while it drops slowly along the vertical section ereason of this phenomenon is that the stiness of thehorizontal section of the submarine vehicle suspension is farlower than the vertical section erefore increasing thestiness of the horizontal section can eectively improve theoverall stiness of the suspension and thus raising thenatural frequency of the whole vehicle As discussed aboveto increase the stiness of the horizontal section of thesuspension its thickness was raised from 20mm to 30mm
Figure 10(a) presents the Ulowast contour of the modiedsuspension while Figure 10(b) shows the comparison of theUlowastvalues along the load path between the modied and theoriginal designs From Figure 10(b) we can see that in thehorizontal section the Ulowast values of the modied suspensionare larger than the original design It also can be seen that at thejoint between the horizontal and the vertical sections of thesuspension the Ulowast value of the modied structure is muchcloser to the ideal value compared to the original structureie with respect to the ideal condition the deviation of themodied design is smaller than the original design Toquantitatively show the design improvement ratios of the Ulowastvalues of the modied or the original design to the ideal Ulowast
Loading SupportingMain load paths
1
0
Ulowast
(a)
Stress concentrations
Maxvon m
ises stress
0
Loading Supporting
(b)
Figure 2 Load transfer analysis of a plate with a hole (a) Ulowast distribution and main load paths (b) von Mises stress distribution [9]
00
1
1sl
Ulowast
A C
D B
Figure 3 Ulowast-based design criterion to achieve uniform structuralstiness distribution [5]
Vehicle bodySuspension system
Crawler belt
PropellersZ
YX
Figure 4 Computer-aided design model of a submarine vehicle(robot)
4 Shock and Vibration
values (ie UlowastdesignUlowastideal) were obtained using the data points
from Figure 10(b) and themean and the coecurrencient of variation(COV) of the ratios were then computed respectively andillustrated in Table 2 e mean for the modied design is 101comparing with 086 for the original design and the COV forthe modied design is 17 instead of 33 for the originaldesign e improvement in terms of the Ulowast distributionindicates that the design modication narrowed the gap of thestiness between the horizontal and the vertical sections of the
vehicle structure As a result the stiness distribution of thewhole suspension is more uniform and the overall stiness ofthe whole suspension is improved at the same time
To see the eectiveness of the design modication a newmodal analysis was conducted to the submarine vehicle withthe modied thickness in the horizontal section of the sus-pension e modal shapes and the corresponding frequenciesare depicted in Figure 11 where we can see that the rst threemodal frequencies of the modied vehicle were respectivelyimproved by 435 40 and 48 compared to the originaldesign Due to the design modication the total weight of the
Fully constrainedon all wheel holes
ZY
X
Figure 5 FEA model and mesh of the submarine vehicle structurefor dynamic analysis
Equivalent force of the
vehicle body component
Fully constrained
on all wheel holes
Z
Y X
Figure 6 FEA model and mesh of the submarine vehicle structurefor static Ulowast analysis
Fixing node i
No
Yes
U of original system
Uiprime of constrained system
i = i + 1
If i gt MAX node number
Finish
i = 1
UUiprime
Uilowast = 1 ndash
Figure 7 Flowchart to develop computer program for Ulowastcalculation
Table 1 Material properties of the major parts of the submarine vehicle
Component Material Elastic modulus (MPa) Poisonrsquos ratio ickness (mm) Mass (kg)Vehicle body
Aluminum 70000 033
mdash 30Vertical part of suspension (original) 20 523Horizontal part of suspension (original) 20 357Horizontal part of suspension (modied) 30 535
Shock and Vibration 5
f1 = 376Hz f2 = 787Hz f3 = 936Hz
Figure 8 First three modal shapes and frequencies of the original submarine vehicle structure (a) f1 376Hz (b) f2 787Hz (c) f3 936Hz
1
Ulowast
0
(a)
0
02
04
06
08
1
0 50 100 150 200 250
Ulowast
Path length (mm)
Ulowast variation
OriginalIdeal
(b)
Figure 9 Ulowast analysis of the original submarine vehicle structure (a) Ulowast contour of the structure (b) Ulowast variation along a load path (whitearrow)
1Ulowast
0
(a)
0
02
04
06
08
1
0 50 100 150 200 250
Ulowast
Path length (mm)
Ulowast variation
OriginalModifiedIdeal
(b)
Figure 10 Ulowast analysis of the modied submarine vehicle structure (a) Ulowast contour of the structure (b) Ulowast variation along a load path(white arrow)
6 Shock and Vibration
submarine vehicle was only raised by 46 which was calcu-lated based on the dynamic model shown in Figure 5
5 Conclusion
e paper proposed a means for designing submarine vehiclesor robots with the higher natural frequency in order to decreasethe potential dynamic problems due to the road or seabedexcitations
With the help of the Ulowast index theory the distribution ofrelative stiness of a structure can be obtained which providesdesigners with useful information in addition to the traditionalFEA approache designmodication based on theUlowast-basedapproach considerably raised the natural frequency of thevehicle by adding a small amount of weight
e results indicate that upgrade of overall stiness ofa structure can increase the structural natural frequencywhile the former can be improved by raising the uniformityof the stiness distribution of the structure Subjected toexternal forces or excitations a structure with uniformstiness distribution can realize the maximum overallstructural stiness based on a constant usage of materiale design criterion based on the Ulowast index theory is ef-fective to evaluate and improve the uniformity of stinessdistribution of a structure
Simply adding materials to each part of the vehiclestructure can also improve its natural frequency However theincrease of the structural weight may cause many otherproblems eg fuel ecurrenciency weight limit or control accu-racy is point can further highlight the usefulness of theproposed Ulowast-based approach in designing submarine vehiclestructures with better dynamic performance e work of thispaper also implies that the Ulowast index theory is able to beapplied for stiness matching between dierent componentsof a vehicle system for addressing vibration problems
Data Availability
All the computational data used to support the ndings of thisstudy are included within the article It includes all the data
related to the CADmodel and the FEA model and the date ofthemodal analysis andUlowast analysis All the original data in thisstudy are available upon request
Conflicts of Interest
e authors declare that they have no concopyicts of interest
Acknowledgments
is work was supported by the NSFC (Natural ScienceFoundation of China) ldquoResearch on the Driving Stability ofUndersea Observation Robot Steering on Slopesrdquo (Grant no51605232) Some of the simulation work was also supportedby the Natural Science Foundation of Zhejiang ProvinceldquoStudy on the Stability of Mobile Robot for Seacopyoor Ex-plorationrdquo (Grant no LQ15E050004)
References
[1] H Cheng and W Li ldquoReducing the frame vibration of deltarobot in pick and place application an acceleration proleoptimization approachrdquo Shock and Vibration vol 2018Article ID 2945314 15 pages 2018
[2] H Hoshino T Sakurai and K Takahashi ldquoVibration re-duction in the cabins of heavy-duty trucks using the theory ofload transfer pathsrdquo JSAE Review vol 24 no 2 pp 165ndash1712003
[3] G Verros S Natsiavas and C Papadimitriou ldquoDesign op-timization of quarter-car models with passive and semi-activesuspensions under random road excitationrdquo JVCJournal VibControl vol 11 no 5 pp 581ndash606 2005
[4] K Takahashi and T Sakurai ldquoExpression of load transferpaths in structuresrdquo Transactions of the Japan Society ofMechanical Engineers Series A vol 71 no 708 pp 1097ndash11022005
[5] Q Wang K Pejhan I Telichev and C Q Wu ldquoDemon-stration of the eectiveness of Ulowast based design criteria onvehicle structural designrdquo Proceedings of the Institution ofMechanical Engineers Part D Journal of Automobile Engi-neering vol 232 no 8 pp 995ndash1002 2017
Table 2 Quantitative comparison with the ideal condition
Design category Mean of (UlowastdesignUlowastideal) COV of (UlowastdesignU
lowastideal)
Modied design 101 17Original design 086 33
f1 = 539Hz f2 = 1103Hz f3 = 1385Hz
Figure 11 First three modal shapes and frequencies of the original submarine vehicle structure (a) f1 539Hz (b) f2 1103Hz (c) f3 1385Hz
Shock and Vibration 7
[6] K Takahashi M Omiya T Iso et al ldquoLoad transfer ustar(Ulowast) calculation in structures under dynamic loadingrdquoTransactions of the Japan Society of Mechanical EngineersSeries A vol 79 no 807 pp 1657ndash1668 2013
[7] Q Wang K Pejhan I Telichev and C Q Wu ldquoExtensions ofthe Ulowast theory for applications on orthotropic composites andnonlinear elastic materialsrdquo International Journal of Me-chanics and Materials in Design vol 13 no 3 pp 469ndash4802017
[8] Q Wang I Telichev and C Q Wu ldquoA new load transferindex (UlowastM) with considering six degrees of freedom and itsapplication in structural design and analysisrdquo MechanicsBased Design of Structures and Machines vol 46 no 4pp 410ndash424 2018
[9] Q Wang W Zhou I Telichev and C Q Wu ldquoLoad transferanalysis of a bus bay section under standard rollover test usingUlowastM index lowastrdquo International Journal of Automotive Tech-nology vol 19 no 4 pp 705ndash716 2018
[10] H Koboyashi T Naito and Y Urushiyama ldquoStudy onsimilarity of load path distribution in body structurerdquo HondaR and D Technical Review vol 23 no 1 pp 80ndash89 2011
[11] E Wang Y Yoshikuni Q Guo et al ldquoLoad transfer in truckcab structures under initial phase of frontal collisionrdquo In-ternational Journal of Vehicle Structures and Systems vol 2no 2 pp 60ndash68 2010
[12] F Beer E Johnston J Dewolf and D MazurekMechanics ofMaterials McGraw Hill Higher Education New York CityNY USA 4th edition 2006
[13] ANSYS ANSYSreg Academic Research Release 180 HelpSystem ANSYS Inc Canonsburg PA United States 2017
8 Shock and Vibration
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
RoboticsJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
VLSI Design
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawiwwwhindawicom
Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
SensorsJournal of
Hindawiwwwhindawicom Volume 2018
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
It can be seen from Equation (11) that the Ulowast index canbe expressed in terms of the internal stiness between theloading point and the arbitrary point of the system Ina structure forces are mainly transferred through the stiestparts in series with the loading point erefore the lineswith the highest Ulowast values (ie the ridge line of the Ulowastdistribution) is dened as the main load paths If a vectorg(minus) is dened as
g(minus) minusgradUlowast (12)
the main load path is the line with the smallest g(minus) evector g(minus) is regarded as the ldquostiness decay vectorrdquo [11]Figures 2(a) and 2(b) elaborate Ulowast and von Mises stressdistributions of a plate with a hole respectively e solidblack lines shown in Figure 2(a) are the main load pathspredicted by the Ulowast index which satisfy the expectationform the engineering point of view As can be seen inFigure 2(b) the higher stresses are formed in the vicinity ofthe hole However since the hole is not important intransferring the forces it is unreasonable to conclude themain load paths pass the locations with those higherstresses
Normally the Ulowast index decreases from the maximumvalue of one (1) at the loading point to the minimum value ofzero (0) at the supporting point In Figure (3) the solid lineelaborates the variation of the Ulowast index along a path ofa load-bearing structure and the dashed line depicts the Ulowastvariation of the desirable condition A uniform decay of theUlowast index means the structural stiness distribution isperfect whereas in reality the Ulowast variation is nonuniformbecause of the structural issues An increase or decrease ofthe rate of the Ulowast decay indicates that the stiness in thecorresponding part is higher or lower than other parts euniformity of the Ulowast decay is dened as the criterion toevaluate the rationality of the stiness distribution of thestructure Structural modications are required when theUlowastcurve is not uniform such as the solid line in Figure 3 e
eective structural modications shall reduce the shade areashown in Figure 3
3 Computational Design Method
ere are mainly three steps in the proposed computationaldesign method Firstly a dynamic model is built anda modal analysis is conducted on the vehicle structure isis to obtain the natural frequency of the original designen the vehicle structure is evaluated by using the Ulowast-based design criterion while modication directions aresuggested based on the Ulowast analysis irdly the naturalfrequency is recalculated to see the improvement from thedesign modication If extra improvement is expected theabove procedures would be repeated until the result isdesired
Figure 4 shows the sample structure a submarine vehicle(or robot) designed by our research group which is used todemonstrate the usefulness of the proposed computationaldesign method e duties of the submarine vehicle areinvestigations of seabed ecosystems and explorations ofocean energy Hence minimizing the dynamic problems caneectively improve the accuracy and stability of data col-lection and dynamic control to the submarine vehicle Inthe current study the dynamic analysis and the designmodication focuse on the vehicle suspension system ematerial properties of the major components of the vehicleare given in Table 1
Figure 5 illustrates the dynamic model of the submarinevehicle for modal analysis e model is created in com-mercial FEA code ANSYS (release 18) e dynamic modelincludes the vehicle body and the major parts of the sus-pension system ignoring the crawler belt systems and thepropellers e properties of each component of thedynamic model are elaborated in Table 1 e boundaryconditions can also be seen from Figure 5 where all thewheel holes in the vertical section of the suspension arefully constrained All the components in the FEAmodel aremodeled using Shell 181 Element with full integration eblock Lanczos method is selected as the mode extractionmethod [13]
Figure 6 demonstrates the static computer model for Ulowastcalculation of the vehicle suspension system In this modelthe vehicle body is not included because the Ulowast analysisfocuses on the load transfer behavior of the vehicle sus-pension system e body weight of the vehicle bodycomponent is applied to the vehicle suspension system as theexternal force e boundary conditions are the same as thedynamic model shown in Figure 6 e Ulowast analysis giveshow the force of the vehicle body gravity is transferredthrough the vehicle suspension system Meanwhile theinsight of the suspension structure behind the load transferpattern is revealed through the Ulowast-based design criterionintroduced in Section 2 Finally design modication can beproposed to the suspension structure based on the Ulowastanalysis
In this study an in-house FEA-based program wasdeveloped for Ulowast calculation in Ansys Parametric DesignLanguage [13] Figure 7 shows the logic and the procedure
A
B
C
FADA
MARA
(a)
A
B
C
FAprime DA
MAprime RA
(b)
Figure 1 Calculation of the Ulowast index (a) original system (b)constrained system [8]
Shock and Vibration 3
for the Ulowast algorithm development e rst step is thecalculation of the total strain energy of the original system asshown in Figure 1(a) Secondly by xing an arbitrary nodeof the system and applying the same displacement to theloading point the total strain energy of the modied system(Figure 1(b)) is calculateden theUlowast value of the arbitrarynode can be computed through Equation (8) By repeatingthis step for each node of the system the Ulowast distribution of
the whole system is obtained e total strain energy of theoriginal system is only calculated once
4 Results
Figure 8 presents the rst three modal frequencies and shapesof the submarine vehicle e rst modal frequency of thevehicle which is regarded as the natural frequency is 376Hze rst modal shape of the vehicle is pitching oscillation thesecond modal shape is heaving oscillation and the third modalshape is rolling oscillation e frequencies of the second andthird modes can be also seen from Figure 8
e Ulowast distribution of the suspension structure is shownin Figure 9(a) It shows the gravity force of the vehicle bodyis transferred through the horizontal part to the vertical partof the suspension In Figure 9(b) the dashed white lineillustrates the ideal situation of the Ulowast variation while thesolid blue line represents the actual Ulowast values along themarked load path in Figure 9(a) We can see the real Ulowastvalues along the load path deviate from the ideal situationespecially the circled area Figure 9(b) indicates the Ulowast indexdecays sharply along the horizontal section of the suspen-sion while it drops slowly along the vertical section ereason of this phenomenon is that the stiness of thehorizontal section of the submarine vehicle suspension is farlower than the vertical section erefore increasing thestiness of the horizontal section can eectively improve theoverall stiness of the suspension and thus raising thenatural frequency of the whole vehicle As discussed aboveto increase the stiness of the horizontal section of thesuspension its thickness was raised from 20mm to 30mm
Figure 10(a) presents the Ulowast contour of the modiedsuspension while Figure 10(b) shows the comparison of theUlowastvalues along the load path between the modied and theoriginal designs From Figure 10(b) we can see that in thehorizontal section the Ulowast values of the modied suspensionare larger than the original design It also can be seen that at thejoint between the horizontal and the vertical sections of thesuspension the Ulowast value of the modied structure is muchcloser to the ideal value compared to the original structureie with respect to the ideal condition the deviation of themodied design is smaller than the original design Toquantitatively show the design improvement ratios of the Ulowastvalues of the modied or the original design to the ideal Ulowast
Loading SupportingMain load paths
1
0
Ulowast
(a)
Stress concentrations
Maxvon m
ises stress
0
Loading Supporting
(b)
Figure 2 Load transfer analysis of a plate with a hole (a) Ulowast distribution and main load paths (b) von Mises stress distribution [9]
00
1
1sl
Ulowast
A C
D B
Figure 3 Ulowast-based design criterion to achieve uniform structuralstiness distribution [5]
Vehicle bodySuspension system
Crawler belt
PropellersZ
YX
Figure 4 Computer-aided design model of a submarine vehicle(robot)
4 Shock and Vibration
values (ie UlowastdesignUlowastideal) were obtained using the data points
from Figure 10(b) and themean and the coecurrencient of variation(COV) of the ratios were then computed respectively andillustrated in Table 2 e mean for the modied design is 101comparing with 086 for the original design and the COV forthe modied design is 17 instead of 33 for the originaldesign e improvement in terms of the Ulowast distributionindicates that the design modication narrowed the gap of thestiness between the horizontal and the vertical sections of the
vehicle structure As a result the stiness distribution of thewhole suspension is more uniform and the overall stiness ofthe whole suspension is improved at the same time
To see the eectiveness of the design modication a newmodal analysis was conducted to the submarine vehicle withthe modied thickness in the horizontal section of the sus-pension e modal shapes and the corresponding frequenciesare depicted in Figure 11 where we can see that the rst threemodal frequencies of the modied vehicle were respectivelyimproved by 435 40 and 48 compared to the originaldesign Due to the design modication the total weight of the
Fully constrainedon all wheel holes
ZY
X
Figure 5 FEA model and mesh of the submarine vehicle structurefor dynamic analysis
Equivalent force of the
vehicle body component
Fully constrained
on all wheel holes
Z
Y X
Figure 6 FEA model and mesh of the submarine vehicle structurefor static Ulowast analysis
Fixing node i
No
Yes
U of original system
Uiprime of constrained system
i = i + 1
If i gt MAX node number
Finish
i = 1
UUiprime
Uilowast = 1 ndash
Figure 7 Flowchart to develop computer program for Ulowastcalculation
Table 1 Material properties of the major parts of the submarine vehicle
Component Material Elastic modulus (MPa) Poisonrsquos ratio ickness (mm) Mass (kg)Vehicle body
Aluminum 70000 033
mdash 30Vertical part of suspension (original) 20 523Horizontal part of suspension (original) 20 357Horizontal part of suspension (modied) 30 535
Shock and Vibration 5
f1 = 376Hz f2 = 787Hz f3 = 936Hz
Figure 8 First three modal shapes and frequencies of the original submarine vehicle structure (a) f1 376Hz (b) f2 787Hz (c) f3 936Hz
1
Ulowast
0
(a)
0
02
04
06
08
1
0 50 100 150 200 250
Ulowast
Path length (mm)
Ulowast variation
OriginalIdeal
(b)
Figure 9 Ulowast analysis of the original submarine vehicle structure (a) Ulowast contour of the structure (b) Ulowast variation along a load path (whitearrow)
1Ulowast
0
(a)
0
02
04
06
08
1
0 50 100 150 200 250
Ulowast
Path length (mm)
Ulowast variation
OriginalModifiedIdeal
(b)
Figure 10 Ulowast analysis of the modied submarine vehicle structure (a) Ulowast contour of the structure (b) Ulowast variation along a load path(white arrow)
6 Shock and Vibration
submarine vehicle was only raised by 46 which was calcu-lated based on the dynamic model shown in Figure 5
5 Conclusion
e paper proposed a means for designing submarine vehiclesor robots with the higher natural frequency in order to decreasethe potential dynamic problems due to the road or seabedexcitations
With the help of the Ulowast index theory the distribution ofrelative stiness of a structure can be obtained which providesdesigners with useful information in addition to the traditionalFEA approache designmodication based on theUlowast-basedapproach considerably raised the natural frequency of thevehicle by adding a small amount of weight
e results indicate that upgrade of overall stiness ofa structure can increase the structural natural frequencywhile the former can be improved by raising the uniformityof the stiness distribution of the structure Subjected toexternal forces or excitations a structure with uniformstiness distribution can realize the maximum overallstructural stiness based on a constant usage of materiale design criterion based on the Ulowast index theory is ef-fective to evaluate and improve the uniformity of stinessdistribution of a structure
Simply adding materials to each part of the vehiclestructure can also improve its natural frequency However theincrease of the structural weight may cause many otherproblems eg fuel ecurrenciency weight limit or control accu-racy is point can further highlight the usefulness of theproposed Ulowast-based approach in designing submarine vehiclestructures with better dynamic performance e work of thispaper also implies that the Ulowast index theory is able to beapplied for stiness matching between dierent componentsof a vehicle system for addressing vibration problems
Data Availability
All the computational data used to support the ndings of thisstudy are included within the article It includes all the data
related to the CADmodel and the FEA model and the date ofthemodal analysis andUlowast analysis All the original data in thisstudy are available upon request
Conflicts of Interest
e authors declare that they have no concopyicts of interest
Acknowledgments
is work was supported by the NSFC (Natural ScienceFoundation of China) ldquoResearch on the Driving Stability ofUndersea Observation Robot Steering on Slopesrdquo (Grant no51605232) Some of the simulation work was also supportedby the Natural Science Foundation of Zhejiang ProvinceldquoStudy on the Stability of Mobile Robot for Seacopyoor Ex-plorationrdquo (Grant no LQ15E050004)
References
[1] H Cheng and W Li ldquoReducing the frame vibration of deltarobot in pick and place application an acceleration proleoptimization approachrdquo Shock and Vibration vol 2018Article ID 2945314 15 pages 2018
[2] H Hoshino T Sakurai and K Takahashi ldquoVibration re-duction in the cabins of heavy-duty trucks using the theory ofload transfer pathsrdquo JSAE Review vol 24 no 2 pp 165ndash1712003
[3] G Verros S Natsiavas and C Papadimitriou ldquoDesign op-timization of quarter-car models with passive and semi-activesuspensions under random road excitationrdquo JVCJournal VibControl vol 11 no 5 pp 581ndash606 2005
[4] K Takahashi and T Sakurai ldquoExpression of load transferpaths in structuresrdquo Transactions of the Japan Society ofMechanical Engineers Series A vol 71 no 708 pp 1097ndash11022005
[5] Q Wang K Pejhan I Telichev and C Q Wu ldquoDemon-stration of the eectiveness of Ulowast based design criteria onvehicle structural designrdquo Proceedings of the Institution ofMechanical Engineers Part D Journal of Automobile Engi-neering vol 232 no 8 pp 995ndash1002 2017
Table 2 Quantitative comparison with the ideal condition
Design category Mean of (UlowastdesignUlowastideal) COV of (UlowastdesignU
lowastideal)
Modied design 101 17Original design 086 33
f1 = 539Hz f2 = 1103Hz f3 = 1385Hz
Figure 11 First three modal shapes and frequencies of the original submarine vehicle structure (a) f1 539Hz (b) f2 1103Hz (c) f3 1385Hz
Shock and Vibration 7
[6] K Takahashi M Omiya T Iso et al ldquoLoad transfer ustar(Ulowast) calculation in structures under dynamic loadingrdquoTransactions of the Japan Society of Mechanical EngineersSeries A vol 79 no 807 pp 1657ndash1668 2013
[7] Q Wang K Pejhan I Telichev and C Q Wu ldquoExtensions ofthe Ulowast theory for applications on orthotropic composites andnonlinear elastic materialsrdquo International Journal of Me-chanics and Materials in Design vol 13 no 3 pp 469ndash4802017
[8] Q Wang I Telichev and C Q Wu ldquoA new load transferindex (UlowastM) with considering six degrees of freedom and itsapplication in structural design and analysisrdquo MechanicsBased Design of Structures and Machines vol 46 no 4pp 410ndash424 2018
[9] Q Wang W Zhou I Telichev and C Q Wu ldquoLoad transferanalysis of a bus bay section under standard rollover test usingUlowastM index lowastrdquo International Journal of Automotive Tech-nology vol 19 no 4 pp 705ndash716 2018
[10] H Koboyashi T Naito and Y Urushiyama ldquoStudy onsimilarity of load path distribution in body structurerdquo HondaR and D Technical Review vol 23 no 1 pp 80ndash89 2011
[11] E Wang Y Yoshikuni Q Guo et al ldquoLoad transfer in truckcab structures under initial phase of frontal collisionrdquo In-ternational Journal of Vehicle Structures and Systems vol 2no 2 pp 60ndash68 2010
[12] F Beer E Johnston J Dewolf and D MazurekMechanics ofMaterials McGraw Hill Higher Education New York CityNY USA 4th edition 2006
[13] ANSYS ANSYSreg Academic Research Release 180 HelpSystem ANSYS Inc Canonsburg PA United States 2017
8 Shock and Vibration
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
RoboticsJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
VLSI Design
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawiwwwhindawicom
Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
SensorsJournal of
Hindawiwwwhindawicom Volume 2018
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
for the Ulowast algorithm development e rst step is thecalculation of the total strain energy of the original system asshown in Figure 1(a) Secondly by xing an arbitrary nodeof the system and applying the same displacement to theloading point the total strain energy of the modied system(Figure 1(b)) is calculateden theUlowast value of the arbitrarynode can be computed through Equation (8) By repeatingthis step for each node of the system the Ulowast distribution of
the whole system is obtained e total strain energy of theoriginal system is only calculated once
4 Results
Figure 8 presents the rst three modal frequencies and shapesof the submarine vehicle e rst modal frequency of thevehicle which is regarded as the natural frequency is 376Hze rst modal shape of the vehicle is pitching oscillation thesecond modal shape is heaving oscillation and the third modalshape is rolling oscillation e frequencies of the second andthird modes can be also seen from Figure 8
e Ulowast distribution of the suspension structure is shownin Figure 9(a) It shows the gravity force of the vehicle bodyis transferred through the horizontal part to the vertical partof the suspension In Figure 9(b) the dashed white lineillustrates the ideal situation of the Ulowast variation while thesolid blue line represents the actual Ulowast values along themarked load path in Figure 9(a) We can see the real Ulowastvalues along the load path deviate from the ideal situationespecially the circled area Figure 9(b) indicates the Ulowast indexdecays sharply along the horizontal section of the suspen-sion while it drops slowly along the vertical section ereason of this phenomenon is that the stiness of thehorizontal section of the submarine vehicle suspension is farlower than the vertical section erefore increasing thestiness of the horizontal section can eectively improve theoverall stiness of the suspension and thus raising thenatural frequency of the whole vehicle As discussed aboveto increase the stiness of the horizontal section of thesuspension its thickness was raised from 20mm to 30mm
Figure 10(a) presents the Ulowast contour of the modiedsuspension while Figure 10(b) shows the comparison of theUlowastvalues along the load path between the modied and theoriginal designs From Figure 10(b) we can see that in thehorizontal section the Ulowast values of the modied suspensionare larger than the original design It also can be seen that at thejoint between the horizontal and the vertical sections of thesuspension the Ulowast value of the modied structure is muchcloser to the ideal value compared to the original structureie with respect to the ideal condition the deviation of themodied design is smaller than the original design Toquantitatively show the design improvement ratios of the Ulowastvalues of the modied or the original design to the ideal Ulowast
Loading SupportingMain load paths
1
0
Ulowast
(a)
Stress concentrations
Maxvon m
ises stress
0
Loading Supporting
(b)
Figure 2 Load transfer analysis of a plate with a hole (a) Ulowast distribution and main load paths (b) von Mises stress distribution [9]
00
1
1sl
Ulowast
A C
D B
Figure 3 Ulowast-based design criterion to achieve uniform structuralstiness distribution [5]
Vehicle bodySuspension system
Crawler belt
PropellersZ
YX
Figure 4 Computer-aided design model of a submarine vehicle(robot)
4 Shock and Vibration
values (ie UlowastdesignUlowastideal) were obtained using the data points
from Figure 10(b) and themean and the coecurrencient of variation(COV) of the ratios were then computed respectively andillustrated in Table 2 e mean for the modied design is 101comparing with 086 for the original design and the COV forthe modied design is 17 instead of 33 for the originaldesign e improvement in terms of the Ulowast distributionindicates that the design modication narrowed the gap of thestiness between the horizontal and the vertical sections of the
vehicle structure As a result the stiness distribution of thewhole suspension is more uniform and the overall stiness ofthe whole suspension is improved at the same time
To see the eectiveness of the design modication a newmodal analysis was conducted to the submarine vehicle withthe modied thickness in the horizontal section of the sus-pension e modal shapes and the corresponding frequenciesare depicted in Figure 11 where we can see that the rst threemodal frequencies of the modied vehicle were respectivelyimproved by 435 40 and 48 compared to the originaldesign Due to the design modication the total weight of the
Fully constrainedon all wheel holes
ZY
X
Figure 5 FEA model and mesh of the submarine vehicle structurefor dynamic analysis
Equivalent force of the
vehicle body component
Fully constrained
on all wheel holes
Z
Y X
Figure 6 FEA model and mesh of the submarine vehicle structurefor static Ulowast analysis
Fixing node i
No
Yes
U of original system
Uiprime of constrained system
i = i + 1
If i gt MAX node number
Finish
i = 1
UUiprime
Uilowast = 1 ndash
Figure 7 Flowchart to develop computer program for Ulowastcalculation
Table 1 Material properties of the major parts of the submarine vehicle
Component Material Elastic modulus (MPa) Poisonrsquos ratio ickness (mm) Mass (kg)Vehicle body
Aluminum 70000 033
mdash 30Vertical part of suspension (original) 20 523Horizontal part of suspension (original) 20 357Horizontal part of suspension (modied) 30 535
Shock and Vibration 5
f1 = 376Hz f2 = 787Hz f3 = 936Hz
Figure 8 First three modal shapes and frequencies of the original submarine vehicle structure (a) f1 376Hz (b) f2 787Hz (c) f3 936Hz
1
Ulowast
0
(a)
0
02
04
06
08
1
0 50 100 150 200 250
Ulowast
Path length (mm)
Ulowast variation
OriginalIdeal
(b)
Figure 9 Ulowast analysis of the original submarine vehicle structure (a) Ulowast contour of the structure (b) Ulowast variation along a load path (whitearrow)
1Ulowast
0
(a)
0
02
04
06
08
1
0 50 100 150 200 250
Ulowast
Path length (mm)
Ulowast variation
OriginalModifiedIdeal
(b)
Figure 10 Ulowast analysis of the modied submarine vehicle structure (a) Ulowast contour of the structure (b) Ulowast variation along a load path(white arrow)
6 Shock and Vibration
submarine vehicle was only raised by 46 which was calcu-lated based on the dynamic model shown in Figure 5
5 Conclusion
e paper proposed a means for designing submarine vehiclesor robots with the higher natural frequency in order to decreasethe potential dynamic problems due to the road or seabedexcitations
With the help of the Ulowast index theory the distribution ofrelative stiness of a structure can be obtained which providesdesigners with useful information in addition to the traditionalFEA approache designmodication based on theUlowast-basedapproach considerably raised the natural frequency of thevehicle by adding a small amount of weight
e results indicate that upgrade of overall stiness ofa structure can increase the structural natural frequencywhile the former can be improved by raising the uniformityof the stiness distribution of the structure Subjected toexternal forces or excitations a structure with uniformstiness distribution can realize the maximum overallstructural stiness based on a constant usage of materiale design criterion based on the Ulowast index theory is ef-fective to evaluate and improve the uniformity of stinessdistribution of a structure
Simply adding materials to each part of the vehiclestructure can also improve its natural frequency However theincrease of the structural weight may cause many otherproblems eg fuel ecurrenciency weight limit or control accu-racy is point can further highlight the usefulness of theproposed Ulowast-based approach in designing submarine vehiclestructures with better dynamic performance e work of thispaper also implies that the Ulowast index theory is able to beapplied for stiness matching between dierent componentsof a vehicle system for addressing vibration problems
Data Availability
All the computational data used to support the ndings of thisstudy are included within the article It includes all the data
related to the CADmodel and the FEA model and the date ofthemodal analysis andUlowast analysis All the original data in thisstudy are available upon request
Conflicts of Interest
e authors declare that they have no concopyicts of interest
Acknowledgments
is work was supported by the NSFC (Natural ScienceFoundation of China) ldquoResearch on the Driving Stability ofUndersea Observation Robot Steering on Slopesrdquo (Grant no51605232) Some of the simulation work was also supportedby the Natural Science Foundation of Zhejiang ProvinceldquoStudy on the Stability of Mobile Robot for Seacopyoor Ex-plorationrdquo (Grant no LQ15E050004)
References
[1] H Cheng and W Li ldquoReducing the frame vibration of deltarobot in pick and place application an acceleration proleoptimization approachrdquo Shock and Vibration vol 2018Article ID 2945314 15 pages 2018
[2] H Hoshino T Sakurai and K Takahashi ldquoVibration re-duction in the cabins of heavy-duty trucks using the theory ofload transfer pathsrdquo JSAE Review vol 24 no 2 pp 165ndash1712003
[3] G Verros S Natsiavas and C Papadimitriou ldquoDesign op-timization of quarter-car models with passive and semi-activesuspensions under random road excitationrdquo JVCJournal VibControl vol 11 no 5 pp 581ndash606 2005
[4] K Takahashi and T Sakurai ldquoExpression of load transferpaths in structuresrdquo Transactions of the Japan Society ofMechanical Engineers Series A vol 71 no 708 pp 1097ndash11022005
[5] Q Wang K Pejhan I Telichev and C Q Wu ldquoDemon-stration of the eectiveness of Ulowast based design criteria onvehicle structural designrdquo Proceedings of the Institution ofMechanical Engineers Part D Journal of Automobile Engi-neering vol 232 no 8 pp 995ndash1002 2017
Table 2 Quantitative comparison with the ideal condition
Design category Mean of (UlowastdesignUlowastideal) COV of (UlowastdesignU
lowastideal)
Modied design 101 17Original design 086 33
f1 = 539Hz f2 = 1103Hz f3 = 1385Hz
Figure 11 First three modal shapes and frequencies of the original submarine vehicle structure (a) f1 539Hz (b) f2 1103Hz (c) f3 1385Hz
Shock and Vibration 7
[6] K Takahashi M Omiya T Iso et al ldquoLoad transfer ustar(Ulowast) calculation in structures under dynamic loadingrdquoTransactions of the Japan Society of Mechanical EngineersSeries A vol 79 no 807 pp 1657ndash1668 2013
[7] Q Wang K Pejhan I Telichev and C Q Wu ldquoExtensions ofthe Ulowast theory for applications on orthotropic composites andnonlinear elastic materialsrdquo International Journal of Me-chanics and Materials in Design vol 13 no 3 pp 469ndash4802017
[8] Q Wang I Telichev and C Q Wu ldquoA new load transferindex (UlowastM) with considering six degrees of freedom and itsapplication in structural design and analysisrdquo MechanicsBased Design of Structures and Machines vol 46 no 4pp 410ndash424 2018
[9] Q Wang W Zhou I Telichev and C Q Wu ldquoLoad transferanalysis of a bus bay section under standard rollover test usingUlowastM index lowastrdquo International Journal of Automotive Tech-nology vol 19 no 4 pp 705ndash716 2018
[10] H Koboyashi T Naito and Y Urushiyama ldquoStudy onsimilarity of load path distribution in body structurerdquo HondaR and D Technical Review vol 23 no 1 pp 80ndash89 2011
[11] E Wang Y Yoshikuni Q Guo et al ldquoLoad transfer in truckcab structures under initial phase of frontal collisionrdquo In-ternational Journal of Vehicle Structures and Systems vol 2no 2 pp 60ndash68 2010
[12] F Beer E Johnston J Dewolf and D MazurekMechanics ofMaterials McGraw Hill Higher Education New York CityNY USA 4th edition 2006
[13] ANSYS ANSYSreg Academic Research Release 180 HelpSystem ANSYS Inc Canonsburg PA United States 2017
8 Shock and Vibration
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
RoboticsJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
VLSI Design
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawiwwwhindawicom
Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
SensorsJournal of
Hindawiwwwhindawicom Volume 2018
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
values (ie UlowastdesignUlowastideal) were obtained using the data points
from Figure 10(b) and themean and the coecurrencient of variation(COV) of the ratios were then computed respectively andillustrated in Table 2 e mean for the modied design is 101comparing with 086 for the original design and the COV forthe modied design is 17 instead of 33 for the originaldesign e improvement in terms of the Ulowast distributionindicates that the design modication narrowed the gap of thestiness between the horizontal and the vertical sections of the
vehicle structure As a result the stiness distribution of thewhole suspension is more uniform and the overall stiness ofthe whole suspension is improved at the same time
To see the eectiveness of the design modication a newmodal analysis was conducted to the submarine vehicle withthe modied thickness in the horizontal section of the sus-pension e modal shapes and the corresponding frequenciesare depicted in Figure 11 where we can see that the rst threemodal frequencies of the modied vehicle were respectivelyimproved by 435 40 and 48 compared to the originaldesign Due to the design modication the total weight of the
Fully constrainedon all wheel holes
ZY
X
Figure 5 FEA model and mesh of the submarine vehicle structurefor dynamic analysis
Equivalent force of the
vehicle body component
Fully constrained
on all wheel holes
Z
Y X
Figure 6 FEA model and mesh of the submarine vehicle structurefor static Ulowast analysis
Fixing node i
No
Yes
U of original system
Uiprime of constrained system
i = i + 1
If i gt MAX node number
Finish
i = 1
UUiprime
Uilowast = 1 ndash
Figure 7 Flowchart to develop computer program for Ulowastcalculation
Table 1 Material properties of the major parts of the submarine vehicle
Component Material Elastic modulus (MPa) Poisonrsquos ratio ickness (mm) Mass (kg)Vehicle body
Aluminum 70000 033
mdash 30Vertical part of suspension (original) 20 523Horizontal part of suspension (original) 20 357Horizontal part of suspension (modied) 30 535
Shock and Vibration 5
f1 = 376Hz f2 = 787Hz f3 = 936Hz
Figure 8 First three modal shapes and frequencies of the original submarine vehicle structure (a) f1 376Hz (b) f2 787Hz (c) f3 936Hz
1
Ulowast
0
(a)
0
02
04
06
08
1
0 50 100 150 200 250
Ulowast
Path length (mm)
Ulowast variation
OriginalIdeal
(b)
Figure 9 Ulowast analysis of the original submarine vehicle structure (a) Ulowast contour of the structure (b) Ulowast variation along a load path (whitearrow)
1Ulowast
0
(a)
0
02
04
06
08
1
0 50 100 150 200 250
Ulowast
Path length (mm)
Ulowast variation
OriginalModifiedIdeal
(b)
Figure 10 Ulowast analysis of the modied submarine vehicle structure (a) Ulowast contour of the structure (b) Ulowast variation along a load path(white arrow)
6 Shock and Vibration
submarine vehicle was only raised by 46 which was calcu-lated based on the dynamic model shown in Figure 5
5 Conclusion
e paper proposed a means for designing submarine vehiclesor robots with the higher natural frequency in order to decreasethe potential dynamic problems due to the road or seabedexcitations
With the help of the Ulowast index theory the distribution ofrelative stiness of a structure can be obtained which providesdesigners with useful information in addition to the traditionalFEA approache designmodication based on theUlowast-basedapproach considerably raised the natural frequency of thevehicle by adding a small amount of weight
e results indicate that upgrade of overall stiness ofa structure can increase the structural natural frequencywhile the former can be improved by raising the uniformityof the stiness distribution of the structure Subjected toexternal forces or excitations a structure with uniformstiness distribution can realize the maximum overallstructural stiness based on a constant usage of materiale design criterion based on the Ulowast index theory is ef-fective to evaluate and improve the uniformity of stinessdistribution of a structure
Simply adding materials to each part of the vehiclestructure can also improve its natural frequency However theincrease of the structural weight may cause many otherproblems eg fuel ecurrenciency weight limit or control accu-racy is point can further highlight the usefulness of theproposed Ulowast-based approach in designing submarine vehiclestructures with better dynamic performance e work of thispaper also implies that the Ulowast index theory is able to beapplied for stiness matching between dierent componentsof a vehicle system for addressing vibration problems
Data Availability
All the computational data used to support the ndings of thisstudy are included within the article It includes all the data
related to the CADmodel and the FEA model and the date ofthemodal analysis andUlowast analysis All the original data in thisstudy are available upon request
Conflicts of Interest
e authors declare that they have no concopyicts of interest
Acknowledgments
is work was supported by the NSFC (Natural ScienceFoundation of China) ldquoResearch on the Driving Stability ofUndersea Observation Robot Steering on Slopesrdquo (Grant no51605232) Some of the simulation work was also supportedby the Natural Science Foundation of Zhejiang ProvinceldquoStudy on the Stability of Mobile Robot for Seacopyoor Ex-plorationrdquo (Grant no LQ15E050004)
References
[1] H Cheng and W Li ldquoReducing the frame vibration of deltarobot in pick and place application an acceleration proleoptimization approachrdquo Shock and Vibration vol 2018Article ID 2945314 15 pages 2018
[2] H Hoshino T Sakurai and K Takahashi ldquoVibration re-duction in the cabins of heavy-duty trucks using the theory ofload transfer pathsrdquo JSAE Review vol 24 no 2 pp 165ndash1712003
[3] G Verros S Natsiavas and C Papadimitriou ldquoDesign op-timization of quarter-car models with passive and semi-activesuspensions under random road excitationrdquo JVCJournal VibControl vol 11 no 5 pp 581ndash606 2005
[4] K Takahashi and T Sakurai ldquoExpression of load transferpaths in structuresrdquo Transactions of the Japan Society ofMechanical Engineers Series A vol 71 no 708 pp 1097ndash11022005
[5] Q Wang K Pejhan I Telichev and C Q Wu ldquoDemon-stration of the eectiveness of Ulowast based design criteria onvehicle structural designrdquo Proceedings of the Institution ofMechanical Engineers Part D Journal of Automobile Engi-neering vol 232 no 8 pp 995ndash1002 2017
Table 2 Quantitative comparison with the ideal condition
Design category Mean of (UlowastdesignUlowastideal) COV of (UlowastdesignU
lowastideal)
Modied design 101 17Original design 086 33
f1 = 539Hz f2 = 1103Hz f3 = 1385Hz
Figure 11 First three modal shapes and frequencies of the original submarine vehicle structure (a) f1 539Hz (b) f2 1103Hz (c) f3 1385Hz
Shock and Vibration 7
[6] K Takahashi M Omiya T Iso et al ldquoLoad transfer ustar(Ulowast) calculation in structures under dynamic loadingrdquoTransactions of the Japan Society of Mechanical EngineersSeries A vol 79 no 807 pp 1657ndash1668 2013
[7] Q Wang K Pejhan I Telichev and C Q Wu ldquoExtensions ofthe Ulowast theory for applications on orthotropic composites andnonlinear elastic materialsrdquo International Journal of Me-chanics and Materials in Design vol 13 no 3 pp 469ndash4802017
[8] Q Wang I Telichev and C Q Wu ldquoA new load transferindex (UlowastM) with considering six degrees of freedom and itsapplication in structural design and analysisrdquo MechanicsBased Design of Structures and Machines vol 46 no 4pp 410ndash424 2018
[9] Q Wang W Zhou I Telichev and C Q Wu ldquoLoad transferanalysis of a bus bay section under standard rollover test usingUlowastM index lowastrdquo International Journal of Automotive Tech-nology vol 19 no 4 pp 705ndash716 2018
[10] H Koboyashi T Naito and Y Urushiyama ldquoStudy onsimilarity of load path distribution in body structurerdquo HondaR and D Technical Review vol 23 no 1 pp 80ndash89 2011
[11] E Wang Y Yoshikuni Q Guo et al ldquoLoad transfer in truckcab structures under initial phase of frontal collisionrdquo In-ternational Journal of Vehicle Structures and Systems vol 2no 2 pp 60ndash68 2010
[12] F Beer E Johnston J Dewolf and D MazurekMechanics ofMaterials McGraw Hill Higher Education New York CityNY USA 4th edition 2006
[13] ANSYS ANSYSreg Academic Research Release 180 HelpSystem ANSYS Inc Canonsburg PA United States 2017
8 Shock and Vibration
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
RoboticsJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
VLSI Design
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawiwwwhindawicom
Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
SensorsJournal of
Hindawiwwwhindawicom Volume 2018
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
f1 = 376Hz f2 = 787Hz f3 = 936Hz
Figure 8 First three modal shapes and frequencies of the original submarine vehicle structure (a) f1 376Hz (b) f2 787Hz (c) f3 936Hz
1
Ulowast
0
(a)
0
02
04
06
08
1
0 50 100 150 200 250
Ulowast
Path length (mm)
Ulowast variation
OriginalIdeal
(b)
Figure 9 Ulowast analysis of the original submarine vehicle structure (a) Ulowast contour of the structure (b) Ulowast variation along a load path (whitearrow)
1Ulowast
0
(a)
0
02
04
06
08
1
0 50 100 150 200 250
Ulowast
Path length (mm)
Ulowast variation
OriginalModifiedIdeal
(b)
Figure 10 Ulowast analysis of the modied submarine vehicle structure (a) Ulowast contour of the structure (b) Ulowast variation along a load path(white arrow)
6 Shock and Vibration
submarine vehicle was only raised by 46 which was calcu-lated based on the dynamic model shown in Figure 5
5 Conclusion
e paper proposed a means for designing submarine vehiclesor robots with the higher natural frequency in order to decreasethe potential dynamic problems due to the road or seabedexcitations
With the help of the Ulowast index theory the distribution ofrelative stiness of a structure can be obtained which providesdesigners with useful information in addition to the traditionalFEA approache designmodication based on theUlowast-basedapproach considerably raised the natural frequency of thevehicle by adding a small amount of weight
e results indicate that upgrade of overall stiness ofa structure can increase the structural natural frequencywhile the former can be improved by raising the uniformityof the stiness distribution of the structure Subjected toexternal forces or excitations a structure with uniformstiness distribution can realize the maximum overallstructural stiness based on a constant usage of materiale design criterion based on the Ulowast index theory is ef-fective to evaluate and improve the uniformity of stinessdistribution of a structure
Simply adding materials to each part of the vehiclestructure can also improve its natural frequency However theincrease of the structural weight may cause many otherproblems eg fuel ecurrenciency weight limit or control accu-racy is point can further highlight the usefulness of theproposed Ulowast-based approach in designing submarine vehiclestructures with better dynamic performance e work of thispaper also implies that the Ulowast index theory is able to beapplied for stiness matching between dierent componentsof a vehicle system for addressing vibration problems
Data Availability
All the computational data used to support the ndings of thisstudy are included within the article It includes all the data
related to the CADmodel and the FEA model and the date ofthemodal analysis andUlowast analysis All the original data in thisstudy are available upon request
Conflicts of Interest
e authors declare that they have no concopyicts of interest
Acknowledgments
is work was supported by the NSFC (Natural ScienceFoundation of China) ldquoResearch on the Driving Stability ofUndersea Observation Robot Steering on Slopesrdquo (Grant no51605232) Some of the simulation work was also supportedby the Natural Science Foundation of Zhejiang ProvinceldquoStudy on the Stability of Mobile Robot for Seacopyoor Ex-plorationrdquo (Grant no LQ15E050004)
References
[1] H Cheng and W Li ldquoReducing the frame vibration of deltarobot in pick and place application an acceleration proleoptimization approachrdquo Shock and Vibration vol 2018Article ID 2945314 15 pages 2018
[2] H Hoshino T Sakurai and K Takahashi ldquoVibration re-duction in the cabins of heavy-duty trucks using the theory ofload transfer pathsrdquo JSAE Review vol 24 no 2 pp 165ndash1712003
[3] G Verros S Natsiavas and C Papadimitriou ldquoDesign op-timization of quarter-car models with passive and semi-activesuspensions under random road excitationrdquo JVCJournal VibControl vol 11 no 5 pp 581ndash606 2005
[4] K Takahashi and T Sakurai ldquoExpression of load transferpaths in structuresrdquo Transactions of the Japan Society ofMechanical Engineers Series A vol 71 no 708 pp 1097ndash11022005
[5] Q Wang K Pejhan I Telichev and C Q Wu ldquoDemon-stration of the eectiveness of Ulowast based design criteria onvehicle structural designrdquo Proceedings of the Institution ofMechanical Engineers Part D Journal of Automobile Engi-neering vol 232 no 8 pp 995ndash1002 2017
Table 2 Quantitative comparison with the ideal condition
Design category Mean of (UlowastdesignUlowastideal) COV of (UlowastdesignU
lowastideal)
Modied design 101 17Original design 086 33
f1 = 539Hz f2 = 1103Hz f3 = 1385Hz
Figure 11 First three modal shapes and frequencies of the original submarine vehicle structure (a) f1 539Hz (b) f2 1103Hz (c) f3 1385Hz
Shock and Vibration 7
[6] K Takahashi M Omiya T Iso et al ldquoLoad transfer ustar(Ulowast) calculation in structures under dynamic loadingrdquoTransactions of the Japan Society of Mechanical EngineersSeries A vol 79 no 807 pp 1657ndash1668 2013
[7] Q Wang K Pejhan I Telichev and C Q Wu ldquoExtensions ofthe Ulowast theory for applications on orthotropic composites andnonlinear elastic materialsrdquo International Journal of Me-chanics and Materials in Design vol 13 no 3 pp 469ndash4802017
[8] Q Wang I Telichev and C Q Wu ldquoA new load transferindex (UlowastM) with considering six degrees of freedom and itsapplication in structural design and analysisrdquo MechanicsBased Design of Structures and Machines vol 46 no 4pp 410ndash424 2018
[9] Q Wang W Zhou I Telichev and C Q Wu ldquoLoad transferanalysis of a bus bay section under standard rollover test usingUlowastM index lowastrdquo International Journal of Automotive Tech-nology vol 19 no 4 pp 705ndash716 2018
[10] H Koboyashi T Naito and Y Urushiyama ldquoStudy onsimilarity of load path distribution in body structurerdquo HondaR and D Technical Review vol 23 no 1 pp 80ndash89 2011
[11] E Wang Y Yoshikuni Q Guo et al ldquoLoad transfer in truckcab structures under initial phase of frontal collisionrdquo In-ternational Journal of Vehicle Structures and Systems vol 2no 2 pp 60ndash68 2010
[12] F Beer E Johnston J Dewolf and D MazurekMechanics ofMaterials McGraw Hill Higher Education New York CityNY USA 4th edition 2006
[13] ANSYS ANSYSreg Academic Research Release 180 HelpSystem ANSYS Inc Canonsburg PA United States 2017
8 Shock and Vibration
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
RoboticsJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
VLSI Design
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawiwwwhindawicom
Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
SensorsJournal of
Hindawiwwwhindawicom Volume 2018
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
submarine vehicle was only raised by 46 which was calcu-lated based on the dynamic model shown in Figure 5
5 Conclusion
e paper proposed a means for designing submarine vehiclesor robots with the higher natural frequency in order to decreasethe potential dynamic problems due to the road or seabedexcitations
With the help of the Ulowast index theory the distribution ofrelative stiness of a structure can be obtained which providesdesigners with useful information in addition to the traditionalFEA approache designmodication based on theUlowast-basedapproach considerably raised the natural frequency of thevehicle by adding a small amount of weight
e results indicate that upgrade of overall stiness ofa structure can increase the structural natural frequencywhile the former can be improved by raising the uniformityof the stiness distribution of the structure Subjected toexternal forces or excitations a structure with uniformstiness distribution can realize the maximum overallstructural stiness based on a constant usage of materiale design criterion based on the Ulowast index theory is ef-fective to evaluate and improve the uniformity of stinessdistribution of a structure
Simply adding materials to each part of the vehiclestructure can also improve its natural frequency However theincrease of the structural weight may cause many otherproblems eg fuel ecurrenciency weight limit or control accu-racy is point can further highlight the usefulness of theproposed Ulowast-based approach in designing submarine vehiclestructures with better dynamic performance e work of thispaper also implies that the Ulowast index theory is able to beapplied for stiness matching between dierent componentsof a vehicle system for addressing vibration problems
Data Availability
All the computational data used to support the ndings of thisstudy are included within the article It includes all the data
related to the CADmodel and the FEA model and the date ofthemodal analysis andUlowast analysis All the original data in thisstudy are available upon request
Conflicts of Interest
e authors declare that they have no concopyicts of interest
Acknowledgments
is work was supported by the NSFC (Natural ScienceFoundation of China) ldquoResearch on the Driving Stability ofUndersea Observation Robot Steering on Slopesrdquo (Grant no51605232) Some of the simulation work was also supportedby the Natural Science Foundation of Zhejiang ProvinceldquoStudy on the Stability of Mobile Robot for Seacopyoor Ex-plorationrdquo (Grant no LQ15E050004)
References
[1] H Cheng and W Li ldquoReducing the frame vibration of deltarobot in pick and place application an acceleration proleoptimization approachrdquo Shock and Vibration vol 2018Article ID 2945314 15 pages 2018
[2] H Hoshino T Sakurai and K Takahashi ldquoVibration re-duction in the cabins of heavy-duty trucks using the theory ofload transfer pathsrdquo JSAE Review vol 24 no 2 pp 165ndash1712003
[3] G Verros S Natsiavas and C Papadimitriou ldquoDesign op-timization of quarter-car models with passive and semi-activesuspensions under random road excitationrdquo JVCJournal VibControl vol 11 no 5 pp 581ndash606 2005
[4] K Takahashi and T Sakurai ldquoExpression of load transferpaths in structuresrdquo Transactions of the Japan Society ofMechanical Engineers Series A vol 71 no 708 pp 1097ndash11022005
[5] Q Wang K Pejhan I Telichev and C Q Wu ldquoDemon-stration of the eectiveness of Ulowast based design criteria onvehicle structural designrdquo Proceedings of the Institution ofMechanical Engineers Part D Journal of Automobile Engi-neering vol 232 no 8 pp 995ndash1002 2017
Table 2 Quantitative comparison with the ideal condition
Design category Mean of (UlowastdesignUlowastideal) COV of (UlowastdesignU
lowastideal)
Modied design 101 17Original design 086 33
f1 = 539Hz f2 = 1103Hz f3 = 1385Hz
Figure 11 First three modal shapes and frequencies of the original submarine vehicle structure (a) f1 539Hz (b) f2 1103Hz (c) f3 1385Hz
Shock and Vibration 7
[6] K Takahashi M Omiya T Iso et al ldquoLoad transfer ustar(Ulowast) calculation in structures under dynamic loadingrdquoTransactions of the Japan Society of Mechanical EngineersSeries A vol 79 no 807 pp 1657ndash1668 2013
[7] Q Wang K Pejhan I Telichev and C Q Wu ldquoExtensions ofthe Ulowast theory for applications on orthotropic composites andnonlinear elastic materialsrdquo International Journal of Me-chanics and Materials in Design vol 13 no 3 pp 469ndash4802017
[8] Q Wang I Telichev and C Q Wu ldquoA new load transferindex (UlowastM) with considering six degrees of freedom and itsapplication in structural design and analysisrdquo MechanicsBased Design of Structures and Machines vol 46 no 4pp 410ndash424 2018
[9] Q Wang W Zhou I Telichev and C Q Wu ldquoLoad transferanalysis of a bus bay section under standard rollover test usingUlowastM index lowastrdquo International Journal of Automotive Tech-nology vol 19 no 4 pp 705ndash716 2018
[10] H Koboyashi T Naito and Y Urushiyama ldquoStudy onsimilarity of load path distribution in body structurerdquo HondaR and D Technical Review vol 23 no 1 pp 80ndash89 2011
[11] E Wang Y Yoshikuni Q Guo et al ldquoLoad transfer in truckcab structures under initial phase of frontal collisionrdquo In-ternational Journal of Vehicle Structures and Systems vol 2no 2 pp 60ndash68 2010
[12] F Beer E Johnston J Dewolf and D MazurekMechanics ofMaterials McGraw Hill Higher Education New York CityNY USA 4th edition 2006
[13] ANSYS ANSYSreg Academic Research Release 180 HelpSystem ANSYS Inc Canonsburg PA United States 2017
8 Shock and Vibration
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
RoboticsJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
VLSI Design
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawiwwwhindawicom
Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
SensorsJournal of
Hindawiwwwhindawicom Volume 2018
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
[6] K Takahashi M Omiya T Iso et al ldquoLoad transfer ustar(Ulowast) calculation in structures under dynamic loadingrdquoTransactions of the Japan Society of Mechanical EngineersSeries A vol 79 no 807 pp 1657ndash1668 2013
[7] Q Wang K Pejhan I Telichev and C Q Wu ldquoExtensions ofthe Ulowast theory for applications on orthotropic composites andnonlinear elastic materialsrdquo International Journal of Me-chanics and Materials in Design vol 13 no 3 pp 469ndash4802017
[8] Q Wang I Telichev and C Q Wu ldquoA new load transferindex (UlowastM) with considering six degrees of freedom and itsapplication in structural design and analysisrdquo MechanicsBased Design of Structures and Machines vol 46 no 4pp 410ndash424 2018
[9] Q Wang W Zhou I Telichev and C Q Wu ldquoLoad transferanalysis of a bus bay section under standard rollover test usingUlowastM index lowastrdquo International Journal of Automotive Tech-nology vol 19 no 4 pp 705ndash716 2018
[10] H Koboyashi T Naito and Y Urushiyama ldquoStudy onsimilarity of load path distribution in body structurerdquo HondaR and D Technical Review vol 23 no 1 pp 80ndash89 2011
[11] E Wang Y Yoshikuni Q Guo et al ldquoLoad transfer in truckcab structures under initial phase of frontal collisionrdquo In-ternational Journal of Vehicle Structures and Systems vol 2no 2 pp 60ndash68 2010
[12] F Beer E Johnston J Dewolf and D MazurekMechanics ofMaterials McGraw Hill Higher Education New York CityNY USA 4th edition 2006
[13] ANSYS ANSYSreg Academic Research Release 180 HelpSystem ANSYS Inc Canonsburg PA United States 2017
8 Shock and Vibration
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
RoboticsJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
VLSI Design
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawiwwwhindawicom
Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
SensorsJournal of
Hindawiwwwhindawicom Volume 2018
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
RoboticsJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
VLSI Design
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawiwwwhindawicom
Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
SensorsJournal of
Hindawiwwwhindawicom Volume 2018
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
![[sv] Validity date from LAND Vietnam 00269 [SV] SECTION ... · 2 / 33 [sv] List in force Godkännandenum mer Namn Ort [sv] Regions [sv] Activities [sv] Remark [sv] Date of request](https://static.fdocuments.us/doc/165x107/5d66deeb88c99332038b89d9/sv-validity-date-from-land-vietnam-00269-sv-section-2-33-sv-list.jpg)
![[sv] Validity date from LAND Marocko 00258 [SV] SECTION … · 2020. 5. 22. · 1 / 35 LAND [SV] SECTION Marocko Fiskeriprodukter [sv] Validity date from 10/08/2007 [sv] Date of publication](https://static.fdocuments.us/doc/165x107/5fbce723db71870cc10035f6/sv-validity-date-from-land-marocko-00258-sv-section-2020-5-22-1-35-land.jpg)
