Acoustic Optimization of an Underwater Vehicle

8/4/2019 Acoustic Optimization of an Underwater Vehicle

1/83

ACOUSTIC OPTIMIZATION OF AN UNDERWATER

VEHICLE

A thesis submitted in partial fulfillment

of the requirements for the degree of

Master of Science in Engineering

By

RAHUL KHAMBASWADKAR

B.E., University of Mumbai, India 2001

2005Wright State University

WRIGHT STATE UNIVERSITY


2/83

SCHOOL OF GRADUATE STUDIES

June 6, 2005

I HEREBY RECOMMEND THAT THE THESIS PREPARED UNDER MYSUPERVISION BY Rahul Khambaswadkar ENTITLED Acoustic Optimization of anUnderwater Vehicle BE ACCEPTED IN PARTIAL FULFILLMENT OF THE

REQUIREMENTS FOR THE DEGREE OF Master of Science in Engineering.

Ravi C. Penmetsa, Ph.D.

Thesis Director

Richard J. Bethke, Ph.D.Department Chair

Committee on

Final Examination

Ravi C. Penmetsa, Ph. D.

Ramana V. Grandhi, Ph.D.

Nathan W. Klingbeil, Ph.D.

Joseph F. Thomas, Jr., Ph.D.Dean, School of Graduate Studies


3/83

ABSTRACT

Khambaswadkar, Rahul, M. S. Engineering., Department of Mechanical and Materials

Engineering, Wright State University, 2005. Acoustic Optimization of an UnderwaterVehicle Involving Fluid-Structure Interaction

A torpedo is a guided missile that travels underwater and detonates when it comes

in proximity of the target. Its speed and accuracy make it one of the most lethal weapons

in navy munitions. The torpedo is a complex system comprising various subsystems:

propulsion, weapon, guidance and control, and many other complicated auxiliary

equipment important for proper operation of the torpedo. The structural design and

optimization of a lightweight torpedo involves multiple disciplines, such as structures,

fluids, and controls, of which acoustic analysis is a critical part.

In underwater warfare, sophisticated active and passive SONAR (SOund NAvigation and

Ranging) techniques are used by the enemy submarines to detect approaching torpedoes.

Therefore, it is very important for a torpedo to be acoustically silent in order to increase

its effectiveness. Each torpedo emits a specific acoustic signature depending on its

propulsion, hydrodynamics, and other auxiliary noise-producing sources. In this thesis,

experimental data available for the gear noise is simulated using computational sound

sources that are then used to determine the acoustic signature of a torpedo. Furthermore,

the Finite Element Method (FEM) is used to quantify acoustic behavior for the

computational model of a lightweight torpedo. A framework for computational modeling

of experimental data from various sources, incorporation of this information into the

acoustic analysis, and multidisciplinary optimization of a lightweight torpedo are the

main focal points of this thesis.

iii


4/83

TABLE OF CONTENTS

1. Introduction.... 1

1.1 Literature Review.. 2

1.2 Project Approach... 4

2. Finite Element Modeling of Torpedo, Fluid, and Noise Source... 8

2.1 Modeling of Lightweight Torpedo 8

2.2 Modeling of Fluid. 11

2.3 Fluid-Structure Interaction 19

2.4 Normal Mode Analysis Results 23

3. Torpedo Noise Modeling...... 28

3.1 Sources of Noise Generation. 29

3.2 Experimental Setup and Noise Profile 31

3.3 Optimization Formulation for Noise Source Modeling...... 33

3.4 Results and Discussion.. 37

4. Multidisciplinary Design Optimization (MDO) of Lightweight Torpedo 41

4.1 Optimization Formulation......... 46

4.2 Optimization in NASTRAN. 47

4.3 Optimization Results and Discussion 49

5. Concluding Remarks ... 54

Appendix........ 56

Appendix A: C++ Program to generate torpedo model input file.... 56

Appendix B: MATLAB file to read NASTRAN output and calculate error 63

Appendix C: NASTRAN input deck for Optimization Run. 65

iv


5/83

References 70

v


6/83

LIST OF FIGURES

Figure 1.1 Flowchart of Research Approach 5

Figure 2.1 Dimensions of Radial and Longitudinal Stiffeners 9

Figure 2.2 Finite Element Model of the Lightweight Torpedo 10

Figure 2.3 Fluid and Structural Finite Element Models 15

Figure 2.4 Tolerances for Fluid-Structure Interaction 16

Figure 2.5 First Bending Mode 24

Figure 2.6 Second Bending Mode 25

Figure 2.7 Breathing Mode 25

Figure 3.1 Important Sources of Noise Generation in a Torpedo 29

Figure 3.2 Experimental Setup Used for Gear Noise 31

Figure 3.3 Noise Levels on the Meridian of Hemisphere

about the MK-40 Torpedo 32

Figure 3.4 Finite Element Model of Air Chamber 34

Figure 3.5 Noise Recovery Points in the Air Chamber 34

Figure 3.6 Optimization Algorithm to Determine Source Strength 36

Figure 3.7 Intensity of a Pulsating Point Source 38

Figure 3.8 Results for a Constant Profile Case 39

Figure 3.9 Variation Between Experimental and NASTRAN Results 40

Figure 4.1 Air Mesh Inside Torpedos Transmission Section 43

Figure 4.2 Torpedo and Node Locations 43

Figure 4.3 Design Variables for the Problem 46

Figure 4.4 Method of feasible direction 48

vi


7/83


8/83

LIST OF TABLES

Table 2.1 Dimensions of MK-48 Lightweight Torpedo 9

Table 2.2 Structural Frequencies 24

Table 2.3 Coupled Structural Frequencies 26

Table 2.4 Frequencies of the Fluid Model 26

Table 4.1 Noise Levels with Infinite Boundary Condition 44

Table 4.2 Noise Levels without Infinite Boundary Condition 45

Table 4.3 Torpedo Optimal Configuration 52

viii


9/83

Acknowledgement

I would like to thank my advisor Dr. Ravi Penmetsa for his guidance and support and for

giving me opportunity to work on this project. He was instrumental in directing me

towards successful completion of this thesis.

My sincere thanks go to Dr. Ramana Grandhi for his constructive comments and

encouragement. Also, a special mention has to be made about efforts taken by Dr.

Vipperla Venkayya throughout this research work. His eagerness to guide me in proper

direction is highly appreciated. I would like to express my gratitude to Dr Klingbeil for

being a part of thesis committee.

I was well supported by all the members at Computational Design and Optimization

Center (CDOC), Wright State University. These are wonderful people to work with.

Apart from that, my friends, especially, Mayur, Nikhil, Ajay, Savio, Arun, Justin, Milind

and Prithvi made my stay at Dayton enjoyable and deserve an appreciation. I would like

to thank Brandy Foster for her help in making this document grammatically correct and

readable.

Finally, I would like to take this opportunity to thank my parents and my elder sister

without whose efforts it would have been impossible for me to come to USA for studies.

ix


10/83

-

I would like to dedicate this thesis to,

My parents

Rekha and Bhagwan Khambaswadkar

x


11/83

1. Introduct ion

A torpedo is an underwater missile that can be launched from a submarine, a ship, or an

aircraft. It is a highly sophisticated weapon whose optimal design requires satisfying

multiple conflicting criteria that are equally important. Since every torpedo has numerous

subsystems that produce easily detectable noise, the acoustic signature of a torpedo

becomes one of the critical design criteria. The early detection of a torpedo gives the

target time to take the necessary countermeasures to avoid the assault and reduces the

effectiveness of the torpedo as a weapon. Therefore, when performing design

optimization of a torpedo, it is important to ensure that the torpedos acoustic signatures

are below the detectable range of certain SONAR systems.

The self-generated noise typically increases with the speed of the torpedo and is

extremely undesirable. Noise produced by the torpedo can have other detrimental

implications as well: It may damage or interfere with the smooth operation of different

electronic sensors inside the torpedo itself, which in turn will have an effect on the

guidance and control of the torpedo. Furthermore, the amplification of structural

vibrations due to this sound might result in fatigue of the panels. Finally, noise produced

by torpedoes that is within a specific frequency can be of concern to the sea life. Due to

all of these reasons, structural design of a torpedo subject to acoustic constraints is

required for improved stealth characteristics.

1


12/83

In this research, a computational finite element model of a lightweight torpedo is

developed that has longitudinal and radial stiffeners to provide additional strength to the

shell. Since these components are absent in most of the conventional torpedoes, the

current model needs to be analyzed and optimized to meet various design requirements.

Due to these structural modifications, it is also important to investigate how structure-

born noise is transmitted to the fluid, which involves solving a fluid-structure interaction

problem.

1.1 Literature Review:

The problem involving the interaction of an elastic structure with fluid has been of

primary interest to many researchers due to its wide applicability. The problems that can

be associated with this phenomenon can be categorized into exterior and interior

applications. The exterior problems are those in which the sound propagation is exterior

to the structure, such as the sound produced by a vibrating cylinder placed in fluid, which

involves the determination of radiated and scattered noise. The interior problems are

associated with acoustic cavities, piping systems, and other applications in which the

sound is propagated within the structure. These problems have applications in ship noise

reduction, acoustic analysis of a car interior, vibration response of underwater structures,

blast analysis, etc.

Many different formulations were proposed to solve these problems and studies have

been conducted to see the relative trade-offs between these formulations by many

researchers. The methods available in the literature are: boundary element [1-2], finite

element [3-14], coupled boundary-finite elements [2], energy finite elements [15-16], and

2


13/83

various decoupling approximations [17-18], to name a few. The numerical modeling

schemes used to model the fluid differentiate these methods from one another. The

usefulness of each of these formulations is highly problem-dependent, and their

availability or the users experience with a particular kind of tool become significant

factors. Methods involving boundary elements generally use the dynamic response of the

structure as input to a boundary element code, which is used to obtain the far field

acoustic response in the fluid domain [1]. The decoupling approximation methods

decouple the structural response from the fluid response and can reduce computational

complications involved with solving coupled equations [18]. Many researchers, including

Zienkiewicz and Newton [3], were instrumental in initiating efforts towards the

successful use of finite elements to solve structural acoustic problems. Everstine, Marcus

et al, [4, 6], continued on the same research and formulated methods that use the

capabilities of the finite element code NASTRAN to solve the fluid-structure interaction

problems. Everstine summarized different finite element-based formulations to solve

structural acoustics problems [7].

Finite element-based methods have the advantage that they can use the matrix capabilities

of sophisticated commercial codes, which are easily accessible and have sophisticated

visualization capabilities. In the current version of NASTRAN, the pressure analog

method developed by Everstine [4, 9] is implemented in the acoustic module. This

method uses solid finite elements to represent scalar fluid fields by modifying the

material properties so that they represent fluid. This method uses an analogy between

equations of elasticity for structure and acoustic wave equations, which will be discussed

in detail in later chapters. In this thesis, the finite element method is used to solve an

3


14/83

acoustic radiation problem for a lightweight torpedo structural model. This method is also

used to model the noise source that would result in gear noise characteristics similar to

the experimental data.

1.2 Project Approach:

The main objective of this study is to minimize this structure-born noise in a lightweight

torpedo through the modification of structural parameters. In order to study the sound

radiation from the lightweight torpedo structure, a noise source needs to be modeled that

has the same characteristics as the experimental data available for the gear machinery.

4


15/83

Experimental DataFluid

FEA Modeling

Optimization BasedSourceModeling

Structure

Modal Analysis Noise Modeling

Acoustic Analysis

The design methodology is divided into different units that are identified in Figure 1.1.

The first important step in the process is the modeling phase. The proposed

computational model of the torpedo has a shell structure that is supported with ring and

longitudinal stiffeners. These stiffeners provide additional stiffness to the structure with

minimal increase in weight. The fluid surrounding the structure is also modeled using

Minimize: Mass

Subject to: Constraints

Is Design Optimum?

ModifiedStructure

Frequency

Sound

Optimum structure

Figure 1.1 Flowchart of Research Approach

5


16/83

finite elements by using an analogy between equations of elasticity and the acoustic wave

equation. In the fluid-structure interaction, structural displacements cause variations in

fluid pressure and these variations in turn affect the structural behavior. The coupling

effect becomes more significant when modal frequencies for the structure and fluid are

similar. Frequency analysis is performed to ensure that the structure-borne noise is not

amplified due to matching of the fluid and structural frequencies. The results of this

eigenvalue analysis provide information about which structural frequencies to avoid

while redesigning the torpedo.

The next task is the modeling of the source that produces structural vibrations, which

result in pressure variations in the fluid. This pressure distribution around the torpedo is

its acoustic signature subject to the noise that is modeled. There are many sources of

noise that excite the torpedo; however, the current research effort is targeted towards

modeling noise due to speed reduction machinery, such as gears, in the torpedo. Even

though this is not the most critical noise source, it is selected because only its

experimental data is available in the public literature [22]. The goal of this research is to

develop a methodology to obtain computational noise sources that produce similar

characteristics as the experimental data.

An optimization-based problem formulation is used to generate a computational model of

the experimental noise data for gears. The fluid model represents the sea, which is

modeled as an infinite domain. To represent the infinite nature of the water model, the

finite element model of the fluid is truncated at a certain distance from the structure and a

doubly asymptotic approximations-based radiation boundary condition is applied on the

6


17/83

outer surface of the fluid to ensure that there are no reflections back into the fluid from

the boundaries.

Once the modeling of the structure, fluid, and source is completed, the frequency

response analysis, with the modeled source as excitation is performed. Finally, a

multidisciplinary design optimization problem is formulated to reduce structural mass

with the frequency and acoustics response as constraints. A constraint that reduces noise

generated by the torpedo will result in increased weight. And the amount of this

increment depends on the desired reduction of sound. Therefore, a multi-objective

optimization problem is solved to obtain the Pareto frontier that clearly shows the

tradeoff between the weight and sound produced.

The following chapters will discuss these individual tasks in detail. Chapter 2 discusses

the finite element models used to model the fluid and structure that was used in this

research. Chapter 3 discusses the noise sources and the methodology developed to

determine the computational source that would simulate experimental data. Chapter 4

discusses the multidisciplinary design optimization problem formulation and the Pareto

frontier results obtained.

7


18/83

2. Finite Element Modeling of Torpedo, Fluid, and Noise Source

2.1 Modeling of Lightweight Torpedo

A torpedo structure is essentially a cylindrical shell. The dimensions for the torpedo

configuration used in this research are based on the data available in the public literature

about the lightweight torpedo. The diameter of 0.32 m and a length of 2.42 m are selected

for the structure. The nose and tail sections of the torpedo are tapered cones with lengths

of 0.12 m and 0.35 m, respectively. Longitudinal and ring stiffeners are placed along the

torpedo shell to improve structural rigidity. The width and thickness of these stiffeners is

taken as 0.015 m and 0.01 m, respectively. The thickness for the torpedo shell is assumed

to be 0.00635 m. Table 2.1 shows the dimensional parameters of the torpedo structure.

Figure 2.1 shows the solid model of the torpedo with the longitudinal and radial

stiffeners. The stiffeners in this research are modeled without specifying any offset from

the nodes that are used to model the shell elements. The fundamental frequency of the

torpedo structure has a one percent variation from the offset stiffeners model, at the

configuration shown in Table 2.1. This variation is considered to be negligible compared

to the complexities that will be introduced in the optimization problem in which the

offsets need to be adjusted in each iteration, based on the shell thickness.

8


19/83

Overall Length 2.42 m

Body Diameter 0.32 m

Nose Length 0.12 m

Tail Length 0.35 m

Shell Thickness 0.00635 m

Stiffener Width 0.015 m

Stiffener Thickness 0.01 m

Table 2.1: Dimensions of MK-48 Lightweight Torpedo

Longitudinal

Radial

Figure 2.1 Dimensions of Radial and Longitudinal Stiffeners

The shell surface is modeled using quadrilateral and triangular plate elements and the

circular rings and longitudinal stiffeners are modeled with bar/beam elements. The

surface plate elements are called QUAD4 or TRIA3 elements for quadrilateral or

triangular elements. The torpedos auxiliary equipments, warhead, and fuel contribute to

9


20/83

its total mass. These non-structural components are modeled using mass elements

distributed along the torpedo body at nodal locations. The overall mass of the torpedo

structure is assumed to be 254 Kg. The material chosen for the torpedo structure is

aluminum-2024.

Initial analysis suggests that the finite element model of the nose was introducing local

modes that restricted the determination of the actual axial, bending, and breathing modes

of the torpedo structure. These local modes were clearly dominated by the nose model

rather than the torpedo structure. Therefore, in order to capture the behavior of the entire

structure, rigid elements were introduced in the torpedo nose to connect the tip of the

torpedo to the first section of the main body of the torpedo. These rigid elements provide

enough strength to the otherwise flimsy nose structure to capture the global vibration

characteristics of the torpedo.

Longitudinal Stiffeners

Ring Stiffeners

Figure 2.2 Finite Element Model of Lightweight Torpedo

10


21/83

Figure 2.2 shows the finite element model of the torpedo structure used in this research.

The box-like structures distributed all along the model are the mass elements that

represent the non-structural components of the torpedo. This non-structural mass

becomes critical when optimizing the torpedo structure for frequency and frequency-

dependent responses.

2.2 Modeling of Fluid

The three-dimensional fluid is modeled using the conventional solid finite elements

available in NASTRAN. These solid finite elements are used to represent the fluid using

an analogy between the equations of elasticity, which are generally used for solving

structural problems, and the wave equation, which represents fluid acoustics [21, 24, 26].

The pressure analog method [4, 9] developed by Everstine is used in the current version

on NASTRAN. The structural-acoustic analogy is discussed in detail here.

Equation of state:

The equation of state for a fluid relates the internal restoring forces to the corresponding

deformations. Therefore, in fluids terminology it relates pressure to condensation as:

sBp = (2.1)

where,

p = acoustic pressure or excess pressure at any point = -ip 0p

ip = instantaneous pressure at any point

0p = constant equilibrium pressure in the field

11


22/83

B = adiabatic bulk modulus =

0

)/(0 iip

0 = constant equilibrium density of the fluid

i = instantaneous density at any point

s = condensation at any point = ( i - 0 )/ 0

Continuity Equation:

This equation gives the functional relationship between particle velocity and the

instantaneous density. The equation is as follows:

0)( =+

u

t

r

(2.2)

Eulers Equation:

This is a simple nonlinear inviscid force equation that is obtained using Newtons second

law:

ipuut

u

=

+

rrr

)( (2.3)

This equation becomes linear if it is assumed that changes in momentum are negligible,

meaning that the second term inside the bracket vanishes.

ipt

u=

r

0 (2.4)

The Homogeneous Linearized Wave Equation:

The above three equations are combined to obtain a single differential equation with one

dependent variable [21, 24]. Using equations (2.1), (2.2), (2.3) we get:

12


23/83

2

2

2

2 1

t

p

cp ii

= (2.5)

Where,

c = phase speed for acoustics waves in the fluid =0

B

Equation 2.5 represents a compressible, inviscid fluid whose pressure satisfies the above

equation. In Cartesian co-ordinates the above equation can be written as:

2

21111

dt

pd

Bz

p

zy

p

yx

p

x=

+

+

(2.6)

Elastic-Acoustic Analogy:

In classical elasticity, the equation for equilibrium of stresses in the x direction is given as

follows [27].

2

2

dt

ud

zyx

x

s

xzxyxx

=

+

+

(2.7)

Where,

xu = structural displacement in x-direction

xzxyxx ,, = stress components

s = structural mass density

Now stress-strain relation by Hooks law is given by:

, (2.8)

=

xz

xy

xx

xz

xy

xx

GGG

GGG

GGG

664616

464414

161411

where is an element of a 6 by 6 anisotrpic elastic material matrix.ijG

13


24/83

Since displacement components in y and z direction are zero the strain-displacement

relationships becomes,

z

u

y

ux

u

x

xz

x

xy

xxx

=

=

=

Since represents scalar pressure the strains are analogues to pressure gradients.xu

Comparing equations (2.6) and (2.7) and taking,

0

1

1

1

1

1

461614

664411

===

===

=

=

=

=

=

GGG

GGG

z

p

y

p

x

p

B

pu

s

xz

xy

xx

s

x

It can be shown that, with the above assumptions, Equation 2.6 and 2.7 are analogous. It

is clear that the equations of elasticity represent the acoustic fluid wave equation with

certain modifications in the properties of the elements. In NASTRAN, fluid properties

entered on a MAT10 card are internally modified to obtain corresponding analogous

structural properties that are used in matrix manipulations.

14


25/83

Fluid is modeled as a cylinder surrounding the torpedo structure. The sphere diameter of

the cylinder is taken as 2 m and the overall length of the fluid domain is taken as 4m.

Solid elements CTETRA are used to model the fluid with an element edge length of

0.004 m. Figure 2.3 shows the fluid domain modeled surrounding the torpedo structure.

Tetrahedral Solid Elements

2.42

4 m

Torpedo Structure

Figure 2.3 Fluid and Structural Finite Element Models

The interface between the fluid and structure may be modeled so that the grid points of

the fluid are coincident with those of the structure. This is called a matching grid. But,

because of the large size of the fluid domain and the irregular shape of the structure, it is

difficult to obtain the matching grid. Therefore, free meshing is used to create the non-

matching fluid mesh around the structure. NASTRAN uses a method called Body in

15


26/83

White (BW) to determine wetted elements for fluid-structure interaction coupling.

According to this method, a fluid node is coupled to a structural node for the load transfer

based on the tolerances specified by the user. The method used for determining wetted

nodes is called boxing technique.

First step in the BW algorithm is to determine related structural and fluid nodes. Figure

shows the fluid face and a box around in based on the tolerances provided on ACMODL

card.

Figure 2.4 Tolerances for Fluid-Structure Interaction

Here,

L - The smallest edge length for the particular fluid element

D - The distance from centre of the fluid face to the fluid node

NORMAL, SKNEPS, INTOL The tolerances specified on ACMODL card.

The structural nodes in the above mentioned box will be coupled to the fluid nodes of that

specific fluid element. Once the fluid and structural faces have been determined, a face

co-ordinate system is established for each fluid face. The resultant pressure force on each

node on the fluid element is determined by the relation:

16


27/83

{ } Grid/Elem,10;1 NippdSNR jis

fi ====

A virtual work expression used to resolve this resultant pressure force for a unit grid

pressure to grids of the fluid element is as follows:

{ } { } { }ifT

s

fipdSNNF =

The centre of pressure for the fluid face can be obtained using relations:

( )0XXR

FX j

Grids

j i

i

pi=

( )0YYR

FY j

Grids

j i

i

pi=

The resulting load distribution at the grids of the each of the structural element is

calculated using rigid relations such that there is unit motion normal to fluid face with

appropriate moment relationships. The area of each of the structural element is projected

normal to fluid element face is used as weighing factor. The expression for load is as

follows:

{ } ( )

=

0

0])][[][]][[1

i

TT

j

R

RWRRWF

Here,

jF - Vector of resulting load distribution

W- Diagonal weighting matrix

R - Rigid transformation matrix

17


28/83

The forces at the structural grids are looped over at each of the fluid element grids. The

same procedure is repeated for all the wetted elements.

It was important to ensure that the fluid modeled is good enough to capture the fluid-

structure interaction effect based on frequency of excitation. NASTRAN provides

guidelines on how far the fluid should be modeled in order to be able to capture all the

required effects. The rule states that six elements per wavelength are required in all

directions from the structure for approximately 10% accuracy. So for 99% accuracy,

approximately 60 elements are required per wavelength. In the current problem the

excitation frequencies for the load is less than 100 Hz. So, the wavelength for this

frequency is given by:

Hz.inexcitationofFrequency

in water,soundofspeed

=

=

=

f

c

where

f

cwavelength

The wavelength is obtained as 14.5 m, which requires that 60 elements should be used in

14.5 m of fluid extent. For 2 m extent, approximately 8 elements are required in all the

directions from the structure. Since the element edge length used is 0.04 m, the used

mesh density is sufficient to capture the effect of the fluid-structure interaction.

18


29/83

2.3 Fluid-Structure Interaction (FSI):

In general engineering problems, the effect of fluid-structure coupling is investigated

under the following assumptions of the fluid state:

1. Compressible

2. Inviscid

3. Irrotational

The compressibility assumption is required because the acoustic wave equation involves

the speed of sound, which directly depends upon the bulk modulus of the fluid. For

incompressible fluids, the bulk modulus is infinite, so the assumption of compressibility

is required in the current analysis. Moreover, when deriving the boundary conditions for

the wave equation, the viscous terms are neglected, so the assumption of inviscous fluid

is justified. Since the small motion theory is assumed for the fluid particles, the rotational

effects have very little chance of playing a role in the analysis, so irrotational assumption

is required.

NASTRAN uses a potential-based formulation to represent fluid finite elements. In these

formulations, displacement remains the primary unknown for structural grid points

whereas pressure is the primary unknown for fluid grid points.

The standard equation of motion for the structure is given by:

sssss FuKuM =+ }]{[}]{[ && (2.9)

19


30/83

where

sM and are the structural mass and stiffness matrices.sK

Since fluid pressure is applied to the structure as load, the force term on the right hand

side can be divided into external forces on the structure and the fluid pressure on the

interface nodes

}]{[ pAPF ss = . (2.10)

Here, the second term represents the load applied on the structure due to fluid pressure.

The matrix [A] is called a coupling matrix, which is defined as follows:

dSNNAS

sfT }{][ = . (2.11)

Where,

fN and are fluid and structural shape functions, respectively,sN

and is a vector of fluid pressure values at the interface grid points.}{p

So the equation of motion for the structure becomes

}]{[}{}]{[}]{[ pAPuKuM sssss =+&& . (2.12)

Also, the equation of motion for the fluid can be written as

fff FpKpM =+ }]{[}]{[ && . (2.13)

20


31/83

Again, the force term on the right hand side can be divided into a fluid force, or acoustic

disturbance in the fluid, and the force applied on the fluid grid points due to structural

displacement.

}]{[}{ sT

ff uAPF &&+= (2.14)

Here, the second term represents the effect of structural displacement on the fluid grids at

the interface. And the vector is the vector of accelerations of the structural grid

points at the interface.

}{ su&&

So, the fluid equation of motion can be written as

}]{[}]{[}]{[ sT

fff uAPpKpM &&&& +=+ . (2.15)

By combining Equations (2.12) and (2.15), the coupled system of equations is obtained as

=

+

f

ss

f

ss

f

T

s

P

P

p

u

K

AK

p

u

MA

M

0

0

&&

&&. (2.16)

The above equations are unsymmetric and difficult to solve. But, Everstine developed a

symmetric version of these equations by using the potential formulation as follows [23].

Let the velocity potential be defined as

qp &= .

21


32/83

And by substituting this in the structure Equation (2.12),

}]{[}{}]{[}]{[ qAPuKuM sssss &&& =+ . (2.17)

By integrating the fluid equation with time and multiplying it by -1,

}]{[}]{[}]{[ sT

fff uAdtPqKqM &&& = . (2.18)

Now let = dtPG f .

Now by combing Equations (2.17) and (2.18) the symmetric formulation of the fluid-

structure coupled system is obtained as

=

+

G

P

q

u

K

K

q

u

M

M ss

f

ss

f

s

0

0

0

0

&&

&&. (2.19)

NASTRAN uses this equation by default to solve a coupled system. The output from this

equation is expressed in terms of structural displacement and fluid pressure. It is to be

noted that in all the above equations the damping terms are not included and they can be

added to the equations, if there is damping present in the system. Therefore, the current

approach will be a conservative model that can be improved by incorporating the

structural damping.

22


33/83

2.4 Normal Mode Analysis Results:

One of the most significant analyses required in designing a torpedo is the modal analysis

for determining the natural frequency of vibration. This is important not only to maintain

the structural integrity of the torpedo, but also to ensure that the torpedo does not operate

near certain critical frequencies. These frequencies could be those that would interfere

with the onboard electronics, or those that would match with the fluid frequencies and

amplify the noise generated, or others that are undesirable for safe operation of the

torpedo. A modal complex eigenvalue analysis is performed to obtain structural

frequencies, fluid frequencies, and coupled structural frequencies. Table 2.2 shows the

first eight structural frequencies. Some of the frequencies are grouped due to the two axis

of symmetry present in the current model. This table shows the structural frequencies

with no added mass effects from the surrounding fluid. Table 2.3 shows the coupled

structural frequencies where the added mass effect from the surrounding fluid can clearly

be noticed. The frequencies are reduced compared to the structural model that was

analyzed without the surrounding fluid.

23


34/83

Mode number Frequency (Hz)

1 22.114

2 22.114

3 127.24

4 127.97

5 136.64

6 136.64

7 142.47

8 178.38

Table 2.2 Structural Frequencies

Figure 2.5 First Bending Mode

24


35/83

Figure 2.6 Second Bending Mode

Figure 2.7 Breathing Mode

25


36/83


1 21.52

2 21.62

3 126.92

4 127.71

5 133.91

6 134.31

7 142.47

8 177.97

Table 2.3 Coupled Structural Frequencies


1 26.39

2 52.84

3 58.74

4 63.00

5 63.00

6 67.73

7 68.31

8 79.42

Table 2.4 Frequencies of the Fluid Model

26


37/83

Table 2.4 shows the fluid frequencies that represent the vibration characteristics of the

fluid model surrounding the torpedo. Since this model has two symmetric planes XY and

XZ, the modes 4 and 5 are repeating modes. Similar trend was observed in NASTRAN

verification problems [28]. Since the fluid elements have only pressure as degree of

freedom, the mode shape information models the pressure distribution characteristics in

the fluid. It can clearly be seen that the fluid and structural frequencies do not match in

the current configuration. However, the first fluid frequency is close to the structural

frequency and must be avoided during structural re-design.

27


38/83

3. Torpedo Noise Modeling

In order to determine the acoustic signature of a torpedo, a frequency response analysis is

performed. A frequency-dependent force is used to excite the structure, which interacts

with the fluid surrounding it to produce noise. In the literature, one can find numerous

acoustic simulations in which the noise is modeled as a simple pulsating force with a

wide range of frequencies. By using this forcing function, the sound produced by the

torpedo is analyzed and minimized using structural sizing algorithms. The drawback of

all of these techniques is the failure to realize that the response is entirely dependent on

the spatial distribution of the forcing function and the frequency of excitation that is

determined by the noise source used.

Therefore, this chapter is dedicated to the accurate modeling of the noise source based on

actual experimental data available. In the literature, no emphasis is placed on the

modeling of the noise sources in this manner. In this research, an optimization-based

formulation is used to model the noise source that will mimic the experimental data

available through the literature for the lightweight torpedoes. The noise source thus

modeled will be placed inside the torpedo structure for the multidisciplinary optimization

of the torpedo.

28


39/83

3.1 Sources of Noise Generation:

Figure 3.1 lists some of the major noise sources in a torpedo based upon the information

available in literature. These noises induce structural vibrations at different frequencies

that are then transmitted to the fluid to generate noise.

Exhaust-wake interaction Fans, Converters, Pumps etc.

Guidance & Control

Propulsor

Among these noise sources, the propulsor is the most critical source that is of interest to

the U.S. Navy. However, due to a lack of experimental data available in the public

literature, a less significant but important noise source - engine assembly noise is selected

in this research. Experimental data for this noise source is available along with the details

of the experimental setup. This comprehensive information about the data enabled the

modeling of a computational setup that would mimic the experimental setup.

In a torpedo, the transmission gears or the engine assembly is used in the speed reduction

machinery to control the propeller angular velocity. These gears produce significant

noise, despite their high precision manufacturing [22]. Gear noise comes from a variety

of sources, as follows:

Boundary Layer

Engine Assembly Noise

Figure 3.1 Important Sources of Noise Generation in a Torpedo

29


40/83

Roughness of tooth surface

Deflection of gear tooth

Eccentricity of tooth rotor

Misalignment of tooth rotor

Unbalance of tooth rotor

Noise of rotor bearing

Noise of flexible couplings

Seal rub or squeal

Vibrations transmitted by driving or driven equipments

Most of these noise sources can be avoided, but during severe operating conditions some

of these might result in noise generation. Moreover, in some instances the air trapped

between the gear tooth will result in an amplified noise that would then be propagated

through the structure.

A program of experimental research was undertaken at the U. S. Naval Ordnance Test

Station (NOTS) to improve the basic knowledge of gear noise transmission in torpedoes.

The gears were considered as non-uniform point sources radiating into a sphere, and the

total noise output was calculated by integrating data obtained at numerous locations. The

results of these experiments give the noise profile generated by the transmission gears of

a MK-40 lightweight torpedo. This MK-40 torpedo is the precursor to the currently

operating lightweight torpedoes. In this research, an acoustic source that will emit a noise

pattern similar to that of an experimental setup described below will be determined. An

optimization-based problem formulation is used for designing a computational noise

source model that will represent the experimental data.

30


41/83

3.2 Experimental Setup and Noise Profile:

The experimental test setup involves a gear assembly placed in an acoustically quiet

chamber, with sensitive microphones placed at fixed radial distances from the

transmission [22]. Figure 3.2 shows the details of the experimental setup.

Noise sensors Transmission

TurbineDynamometer

Acoustic cavity

Acoustically silent room

Figure 3.2 Experimental Setup Used for Gear Noise

A steam turbine is used to rotate the transmission gears and is connected by long shafts so

that the turbine noise does not influence the experiment results. The dynamometer is used

to absorb the load and to measure the torque and speed. Here, the concept of spherical

measurement is used to measure noise. Sensitive microphones placed at a distances of

0.32 m from the transmission are used as measuring points to collect information about

the sound produced by the gear mechanism. The transmission-noise profile generated by

the MK-40 lightweight torpedo captured by the above mentioned experimental setup is

shown in Figure 3.3 [22].

31


42/83

110 dB

110 dB

110 dB

114 dB

116 dB

113 dB

110 dB

109 dB

106 dB

103 dB

Figure 3.3 Noise Levels on the Meridian of Hemisphere about the MK-40 Torpedo

Figure 3.3 clearly shows the nonlinear nature of the sound generated by the machinery

noise. The spatial nonlinearity exhibited by the experimental data indicates that the

previous attempts by the researchers to model the noise as a pulsating force at varying

frequencies is inaccurate. This data is used to model a source on the axis of the torpedo

model that can result in a pressure distribution similar to the experimental acoustic data.

The pressure distribution obtained from NASTRAN is converted into the appropriate

decibel level by using the analytical equations shown in the following section.

32


43/83

3.3 Optimization Formulation for Noise SourceModeling:

A finite element model of the air representing the hemisphere on which sensors are

placed is modeled using solid finite elements. The use of these solid finite elements to

represent air is possible because of an acoustic-elastic analogy discussed in the previous

chapter. An acoustic load is applied at the center of the cavity to act as a simple noise

generating source. This simple noise source can be imagined to generate a pulsating

sphere in an infinite space. This source will emit noise in a spherical direction, the

magnitude of which will depend on the strength and frequency of the source. This noise

source is used as excitation in a frequency response analysis. The noise emission at

certain key locations (Figure 3.5) in the air model that match the sensor locations in the

experimental setup is monitored. Therefore, this analysis identifies the source strength

that will give the exact same sound profile as the experimental result. The following

figure shows the air model with the source placed at its center. The current air model has

a diameter of 0.64 m whereas the torpedo has a diameter of 0.32 m. This difference

occurs because the sensor locations in the experimental are at 0.64 m. Therefore, once the

source strength and the frequency that would match the sound levels of the experimental

setup is determined, this source would be placed in a similar air model within the torpedo

internal cavity.

33


44/83

Figure 3.4 Finite Element Model of Air Chamber

Figure 3.5 Noise Recovery Points in the Air Chamber

Z

Y

X

Recovery pointsNoise Source

56

7

12

34

8

34


45/83

The objective of the optimization problem is to minimize the squared error between the

noise levels at particular locations in the air model and the experimental values. The

design variables in the problem are the source strength of the acoustic load and the

frequency of the source. The upper and lower bounds on the source strength and

frequency are also applied as side bound constraints in the optimization problem. The

optimization problem can be summarized as follows:

Minimize

( )2ii BA , (3.1)

where

iA = Noise value obtained from acoustic analysis at location i and

iB = Noise value from the literature at location i,

subject to:

0.100001.0 S and (3.2)

100010 f , (3.3)

where is the source strength that is the design variable for the problem and is the

frequency of the source. The flowchart in Figure 3.6 explains the flow of the optimization

algorithm. The Design Optimization Tool is used for the optimization [25].

S f

35


46/83

Nastraninput.cpp

Generate the NASTRAN inputM

odifiedSourceStrengthandFre

quency

NASTRAN

Since gradient-based search methods were used in the optimization iterations, the

sensitivity of the objective to the source strength and frequency were required in this

algorithm [25]. These sensitivities are calculated using the finite difference method

executed using a series of function calls between MATLAB and a C++ program that is

used to generate the NASTRAN model.

Is Error

Minimum

?

DOT

MATLAB

Read NASTRAN Output and Calculates

Error

No

Yes

Final Source

Figure 3.6 Optimization Algorithm to Determine Source Strength

36


47/83

3.4 Results and Discussion

Analytical Verification:

Before optimizing the torpedo for the minimum acoustic signature, it was important to

verify the accuracy of the finite element simulation results for the noise levels in the air

model. For the noise emitted at a certain distance by a simple noise source such as a

pulsating sphere, approximate equations are available that give the source strength

needed for a particular decibel level at a specified location [21]. Since this analytical

equation is applicable for a constant sound profile at a distance from the source, the

profile that is considered is constant strength at all the key locations. Once the

NASTRAN and analytical results are verified, the experimental data can be matched

using a similar approach.

The NASTRAN acoustic source is a simple monopole source; therefore, the acoustic

intensity radiated from this simple point source is given by the following equation:

2

4 r

WI

= , (3.4)

where r is the radius of the sphere in which the source radiates energy and W is source

strength in watts. From the available experimental profile, it can be seen that 116 dB is

the maximum sound emitted by the gear assembly. These decibels can be converted into

intensity by using the relation

( )10)10(

dB

oII = . (3.5)

37


48/83

24 r

WI

=

r

Figure 3.7 Intensity of a Pulsating Point Source

And, by substituting this intensity into the above equation, the analytical source strength

needed to produce 116 dB at 0.32 m from the source is obtained as follows

24 rIWatts = (3.6)

W5122.0

W/cm5981.3

dB,116For2

=

=

Watts

EI

This source strength is given as input to NASTRAN and the noise generated by this

source measured at 0.32 m from the center is analyzed. The finite element model results

were compared to these approximate equations, and the deviation was 4% from the

expected values. This validated the finite element setup to within the required accuracy.

In this case, the optimization problem is solved such that the noise levels at all the desired

locations are expected to be 116 dB. Figure 3.8 shows the difference between the

38


49/83

analytical and the NASTRAN results at various key locations. These key locations are the

same as the sensor locations in the experimental setup.

90

95

100

105

110

115

120

125

1 2 3 4 5 6 7 8

NASTRAN Analytical

Deviation4%

SoundindB

Recovery Points

Figure 3.8 Results for a Constant Profile Case

Matching the Exact Sound Profile:

The experimental noise profile that was shown earlier is highly nonlinear. In this case, the

goal is to match the nonlinear profile as close as possible and then to use the obtained

sources to determine the acoustic signature of the torpedo. Initial attempts to match the

experimental data showed that it is not possible to match the nonlinear profile with only

one design variable; i. e., only one acoustic source. Therefore, in order to match the

profile exactly, more sources are distributed in the transmission section, which increases

the number of design variables for the problem. By using many different combinations of

source distributions in the transmission area and varying the frequency of the sources, the

best fit for the data is obtained. From the optimization results it was clear that we needed

two sources with source strengths 0.9 watts and 0.15 watts at 77.85 Hz. Figure 3.9 shows

39


50/83

the deviation between NASTRAN and the experimental results. The maximum deviation

at a given key location is 4%. The current noise source model with a 4% deviation from

the experimental data is more realistic than the traditional approaches that use pulsating

forces to model the noise source.

The optimization formulation that is used in this research is generic, and can be used for

any experimental data that is available in the future. The general idea behind this whole

effort is to use the source obtained from the optimization problem as a load in the

proposed computational model of the lightweight torpedo for acoustic analysis. This will

ensure that realistic data is used to model the source instead of applying random forces to

excite the structure.

90

95

100

105

110

115

120

125

1 2 3 4 5 6 7 8

NASTRAN Experimental Deviation4%

Sound

indB

Recovery Points

Figure 3.9 Variation Between Experimental and NASTRAN Results

40


51/83

4. Multidisciplinary Design Optimization (MDO) of L ightweight

Torpedo

The torpedo body can be broadly divided in three sections: transmission, fuel and

warhead, and guidance and control. The modeled noise source will be placed in the

transmission section of the torpedo body, and will act as an excitation force in

determining the frequency response of the torpedo. Figure 4.1 shows the source placed in

the transmission section. An air chamber is modeled inside the transmission section using

solid models and material properties that reflect air density and bulk modulus. This model

has half the diameter as the air model used in the source modeling section, because of the

available cavity size inside the torpedo. The source determined from the earlier analysis

is placed in the appropriate location. The boundaries of the air model transverse to the

axis of the torpedo are left free. This condition assumes no transmission of noise along

the torpedo length through the rest of the cavity. The only transmission is through the

structure. Therefore, the fluid-structure interaction conditions are very significant in an

air-torpedo interface and a torpedo-water interface.

The source inside the air cavity produces a pressure variation in the transmission section

of the torpedo that will result in the displacement of the torpedo structure. This

displacement will be transmitted into the water model resulting in a pressure distribution,

which is the acoustic response of the torpedo. The fluid-structure model is analyzed to

41


52/83

verify the effect of the fluid-structure interaction on the results obtained. If the fluid-

structure interaction effect is turned off in the analysis, then the sound intensity in the

water is found to be zero, which indicates that the structural displacements are not

transferred to the fluid model.

As discussed in the modeling section of this document, the outer surface of the fluid has a

radiation boundary condition that simulates the infinite nature of the fluid. In order to

verify the validity of this boundary condition, two analyses, one with the radiation

boundary condition and one without, were performed. The results from the two analyses

can be seen in Figure 4.2 and Tables 4.1 and 4.2. It can be seen from the tables that the

sound is reflecting back from the surface in the case in which there is no absorbing

boundary condition. Also, with an increase in the distance from the source, the noise

should reduce. This is clearly seen from the radiation boundary condition case, but this

trend not very evident in the case without a radiation boundary condition. Therefore, the

infinite boundary condition is a critical component of any underwater acoustic analysis.

When one has to simulate reflections from the ocean floor, one side of the fluid can be

modeled without the infinite boundary conditions.

42


53/83

Air Mesh Transmission Fuel warhead and uidance and control

Acoustic Source

Figure 4.1 Air Mesh inside Torpedos Transmission Section.

14

13

12

11321 4

Vibrating Torpedo

5 6

7

8

9Water Medium

10

Figure 4.2 Torpedo and Node Locations

43


54/83

Node Co-ordinates in mNode

Location

Node

N

Sound in dB

umber X Y Z

1 1514 -1.09 38.470 0

2 5158 -0.82 0.09 0 49.39

3 4592 -0.37 0 0 59.38

4 5095 2.23 0 0 74.81

5 4716 2.77 0 0 64.15

6 1501 2.91 0 0 53.02

7 5771 0.32 -0.621 0 66.56

8 5018 0.32 -0.735 0 65.05

9 4642 0.32 -0.86 0 61.44

10 1808 0.32 -0.995 0 50.77

11 5786 0.32 0.621 0 66.94

12 5101 0.32 0.735 0 64.54

13 4741 0.32 0.86 0 60.25

14 1763 0.32 0.995 0 49.36

Table 4.1 Noise Levels with Infinite Boundary Condition

44


55/83

Node Co-ordinatesNode

Location

Node

N X Y Z

Sound in dB

umber

1 1514 -1.09 88.910 0

2 5158 -0.82 0.09 0 88.99

3 4592 -0.37 0 0 89.23

4 5095 2.23 0 0 81.41

5 4716 2.77 0 0 81.37

6 1501 2.91 0 0 81.38

7 5771 0.32 -0.621 0 87.36

8 5018 0.32 -0.735 0 87.22

9 4642 0.32 -0.86 0 87.13

10 1808 0.32 -0.995 0 87.09

11 5786 0.32 0.621 0 88.941

12 5101 0.32 0.735 0 88.944

13 4741 0.32 0.86 0 88.945

14 1763 0.32 0.995 0 88.945

Table 4.2 Noise Levels without Infinite Boundary Condition

45


56/83

4.1 Optimization Formulation:

t is to determine the optimum configuration of the

inimize:

s of the structure

Subjec

d level at certain location < 70 dB

Hz

The str f different sections of the shell, the

The optimum design is one t mean that the

sound signatures from the structure are increased to meet the requirements. This is

The final objective of this projec

torpedo that would have minimum noise propagated into the surrounding water. To

achieve this, an optimization problem is formulated as follows:

M

Mas

t to:

Soun

Natural frequency of the torpedo >= 23

uctural parameters, such as the thickness o

cross-sectional width, and the height of the ring and longitudinal stiffeners, were used as

design variables for the optimization problem. Figure 4.3 shows these design variables.

Figure 4.3 Design

Radial Stiffeners

Longitudinal Stiffeners

RW

RH

LW

LT

Torpedo Shell

Variables for the Problem

hat has minimum mass; however, this would

46


57/83

obvious because as the mass is reduced, the shell thickness and dimensions of the

stiffeners decreases, which results in increased noise. Therefore, a realistic solution for

this problem will provide a trade-off analysis between the weight and sound levels

produced by the source.

4.2Optimization in NASTRAN:

ASTRAN has in built design optimization capabilities and most of it comes from

) which is customized to run with NASTRAN. The

directions which is very

strained optimization problems. The basic idea of the

N

Design Optimization Tools (DOT

optimization algorithms that NASTRAN uses are gradient-based methods. The finite

difference method is used for gradient calculation here. In this thesis, for the acoustic

optimization problem method of feasible directions, which is a default method for

NASTRAN, is used. Next section briefly explains this method.

Feasible Directions Method:

Design Optimization Tools (DOT) uses method of feasible

popular method used for con

method is to move from one feasible design to another improved feasible design by

taking small steps. The method tries to keep the design away from boundaries as much as

possible.

0gs jT > gj critical constraints

0gsfsTT


58/83

The first condition is the feasible direction condition. According to this condition, the

arch direction S sh all step in along it

- Push-off factors

feasible usable search direction is obtained from above optimization problem, a

line search is performed to determine how far to proceed along the obtained search

se own in figure 4.6 should be such a way that a sm

should not make the design infeasible. The second condition is called usability condition.

According to this condition the search direction should be such way that the objective

should be reduced if it a minimization problem.

Based on the above two conditions a compromise is defined by following maximization

problem:

g2

g1

s

g1=0g2=0

x

-f

1s

s

00gs-Subject to

i

T

jjj

+

+

Figure 4.4 Method of feasible direction

Maximize

T

0f

Where,

j

Once the

48


59/83

direction. This leads to another feasible design and the process is repeated till

convergence.

4.3 Optimization Results and Discussion:

240

260

280

300

320

62 64 66 68 70 72 74 76

360

340

Sound in dB

O

ptimizedMassinKg

Figure 4.5 Pareto Optimization Curve

This trade-off analysis can be seen in the Pareto frontier shown in Figure 4.4. This figure

shows how the reduction the structure. Based onin sound level increases the weight of

the weight requirements of the torpedo, an appropriate sound level can be determined

from this plot along with the corresponding configuration for the thickness and cross-

section of the stiffeners, which are available from previous optimization solutions.

49


60/83

68.50

69.00

69.50

70.00

70.50

71.00

71.50

72.00

72.50

73.00

73.50

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

SoundindB

Iteration Number

Figure 4.6 Iteration History for Sound

21.00

22.00

23.00

24.00

25.00

26.00

27.00

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

FreuencinHz

Figure 4.7 Iteration History for Frequency

Iteration Number

50


61/83

250.00

255.00

260.00

265.00

270.00

275.00

280.00

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

MassinK

g

Figure 4.8 Iteration History for Mass

Iteration Number

0

5

10

15

20

25

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Ring Width Ring Height

Shell Thickness Long. width

Long. Height

DesignVariablesinmm

Iteration Number

Figure 4.9 Changes in Design Variables with Iterations

51


62/83

Shell

Thickness (m)

Ring

Width (m)

Ring Height

(m)

Longitudinal

Stiffener

Width (m)

Longitudinal

Stiffener

Height (m)

0.0091 0.005 0.005 0.022 0.013

Mass (Kg) Sound (dB) Frequency (Hz)

274.47 70.00 25.76

Table 4.3 Torpedo Optimal Configuration

Figures 4.5, 4.6, and 4.7 show the histories of the objective and constraints as the

optimization iteration progresses. The initial values for ring and longitudinal stiffener

widths are given as 0.015 m, and their thicknesses are taken as 0.01 m, respectively. The

initial shell thickness is taken as 0.0635 m. An inverse relation between the sound and

mass of the structure is evident from these plots. Figure 4.8 shows the variation in all the

design variations with optimization iterations. From this figure, it is clear that the

optimizer is pushing the ring stiffener dimensions to the lower limits and the shell

thickness and longitudinal stiffener dimensions are increased to reduce noise. From

Figure 4.8, it can be observed that shell thickness is the most important design variable

here. Table 4.3 shows the optimal configuration of the torpedo structure from one of the

several optimization runs required to get the Pareto frontier. The table also shows the

weight of the structure and the corresponding sound level at a critical location. This

critical location was determined for one particular configuration, and kept constant in

order to have a continuous function definition for all of the iterations in the optimization

52


63/83

problem. In reality, as the structural model is changed, the location of maximum sound

intensity changes. However, it is assumed in this research that if the intensity at the fixed

critical location is reduced, then the intensity at other locations is also reduced which was

verified to be true.

53


64/83

5. Concluding Remarks

In this research, an acoustic optimization methodology is presented for a computational

model of a lightweight torpedo using the finite element method to model both the fluid

and the structure. Fluid and structural models are coupled to incorporate the effect of the

fluid-structure interaction. As it can be seen from the numerical results, the fluid-structure

interaction and the infinite boundary conditions are critical for the acoustic analysis of

underwater structures. This research has shown that the noise profile generated by the

gear machinery demonstrates spatial nonlinearity, which cannot be represented by the

pulsating force models used by many researchers. Therefore, experimental results and the

corresponding computational noise source models are very important for determining the

acoustic signature of torpedo structures. The optimization problem solved in this work

gives the relative trade-off between the mass of the structure and the sound emitted by it

due to gear noise.

Future work in this area can be directed towards acoustic analysis and optimization of

composite structures based on the source model developed in this research. With the

introduction of composite models, active and passive damping techniques can be

explored through embedded systems in the torpedo shell. However, before the

development of damping technologies is possible, all other sources need to be modeled

and incorporated into the torpedo model. This can only be done through experimental

54


65/83

data collection for noise from the various sources, as discussed earlier. Finally, this thesis

outlines the steps involved in the acoustic design of an underwater vehicle with a

realistically modeled noise source.

55


66/83

APPENDIX

Appendix A

This appendix has C++ code to generate structural model of lightweight torpedo in the

NASTRAN format.

#include

#include

#include

#include

void main()

{

charoutfile[]="Torpedowithoffset.dat";int j=0,k=0;

FILE *stream2;

stream2=fopen(outfile,"w");//Executive Control

fprintf(stream2,"%s\n","ID");

fprintf(stream2,"%s\n","SOL 103");fprintf(stream2,"%s\n","CEND");

fprintf(stream2,"%s\n","SPC=20");

fprintf(stream2,"%s\n","METHOD = 15");

fprintf(stream2,"%s\n","BEGIN BULK");fprintf(stream2,"%s%11d%24d\n","EIGRL",15,20);

int n_x, n_y,n_t, n_r, x,y,r, N1;

double Dia, Len, Nose, th, xc,ti,h,ofs;

Dia=0.32; //Diameter of body

Len=2.0; //Length of bodyNose=0.16; //Length of nose

n_x=40; //Number of rings(node rings) on body

n_y=3; //Number of rings(node rings) on nose

n_t=7; //Number of rings(node rings) on tailn_r=24; //Number of nodes on each ring

ti=0.00635; //Thickness of shell

h=0.010; //Height of ring stiffeners

ofs=(ti/2)+(h/2); //offset for ring stiffnersdouble GridCoordX[10000],GridCoordY[10000],GridCoordZ[10000], theta, X_coord;

theta=360.0/24.0;N1=0;

X_coord=2.00/40.0;

double p = 3.1416;

charGrid[]="GRID";int GridNum=1;

xc=1.0;

// rear tip node

GridCoordX[N1]=-0.30;

GridCoordY[N1]=0.0;GridCoordZ[N1]=0.0;

fprintf(stream2,"%s%12d%16.2f%8.2f%8.2f\n",Grid,GridNum,GridCoordX[N1],GridCoordY[N1],GridCoordZ[N1]);

GridNum=GridNum+1;

N1=N1+1;// Tail section

//-30

th=1.0;

for(r=1;r


67/83

GridCoordZ[N1]=0.5*0.18*sin(th*theta*p/180.0);


GridNum=GridNum+1;

N1=N1+1;

th=th+1.0;}

//-25th=1.0;

for(r=1;r


68/83

GridCoordZ[N1]=0.5*0.28*sin(th*theta*p/180.0);


GridNum=GridNum+1;

N1=N1+1;

th=th+1.0;}

//0th=1.0;

for(r=1;r


69/83

// Nodes for the orientation of the rings(GO entry in the nastran card)

int nor;double R;

R=0.1;

for(nor=1;nor


70/83

fprintf(stream2,"%s%10d%8d%8d%8d%8d%8d\n",ELEM,ElmNum,3,j,j+1,j+n_r+1,j+n_r);ElmNum=ElmNum+1;

j=j+1;}

fprintf(stream2,"%s%10d%8d%8d%8d%8d%8d\n",ELEM,ElmNum,3,j,j-n_r+1,j+1,j+n_r);

ElmNum=ElmNum+1;

j=j+1;}

//Nose tip elements

for(r=1;r


71/83

x=x+3.0;//3X=X+0.15;//15

a1=a1+1;}

//longitudinal bars

double J[30];int i;

J[0]=196.0;J[1]=199.0;

J[2]=202.0;

J[3]=205.0;J[4]=208.0;

J[5]=211.0;

J[6]=214.0;

J[7]=217.0;Y=0;

Z=0;

for(i=0;i


72/83

int el,mp;

int intergrid[200];el=0;

j=196;

for(x=1;x


73/83

Appendix B:

This appendix gives the MATLAB file to read the NASTRAN output file and to calculate

error.

%This code reads a .pch file and stores the decibel values at ten

%different locations and calcualtes error in the sound

%levels relative to actual value.

clc

clear all

%opens air_shell_nastran.pch in read format

fid=fopen('noisefile1.pch','r');

i=1;

for i=1:90

tline=fgets(fid);

end

aa=sscanf(tline,'%*60c %12c %*8c');

tline=fgets(fid);

tline=fgets(fid);tline=fgets(fid);

tline=fgets(fid);

bb=sscanf(tline,'%*60c %12c %*8c');

tline=fgets(fid);

tline=fgets(fid);

tline=fgets(fid);

tline=fgets(fid);

cc=sscanf(tline,'%*60c %12c %*8c');

tline=fgets(fid);

tline=fgets(fid);

tline=fgets(fid);

tline=fgets(fid);

dd=sscanf(tline,'%*60c %12c %*8c');tline=fgets(fid);

tline=fgets(fid);

tline=fgets(fid);

tline=fgets(fid);

ee=sscanf(tline,'%*60c %12c %*8c');

tline=fgets(fid);

tline=fgets(fid);

tline=fgets(fid);

tline=fgets(fid);

ff=sscanf(tline,'%*60c %12c %*8c');

tline=fgets(fid);

tline=fgets(fid);

tline=fgets(fid);

tline=fgets(fid);gg=sscanf(tline,'%*60c %12c %*8c');

tline=fgets(fid);

tline=fgets(fid);

tline=fgets(fid);

tline=fgets(fid);

hh=sscanf(tline,'%*60c %12c %*8c');

a=str2num(aa)

b=str2num(bb)

63


74/83

c=str2num(cc)

d=str2num(dd)

e=str2num(ee)

f=str2num(ff)

g=str2num(gg)

h=str2num(hh)

S1=[a b c d e f g h]

fclose(fid);

no_exp=116;

% % This line calculates the error value.

Errorsquare=sqrt((a-103)^2+(b-106)^2+(c-109)^2+(d-110)^2+(e-110)^2+(f-

110)^2+(g-114)^2+(h-116)^2);

fid1=fopen('ErrorSquare.dat','w');

fprintf(fid1,'%10.6f\n',Errorsquare);

fclose(fid1);

64


75/83

Appendix C:

This appendix gives the input file for the NASTRAN Optimization Run.

NASTRAN REAL = 63000000

NASTRAN SYSTEM(151)=1

INIT MASTER(NORAM)INIT DBALL LOGICAL=(DBALL(500000))

INIT SCRATCH(NOMEM) LOGICAL=(SCRATCH(1800000)),SCR300=(SCR300(1800000))

ASSIGN OUTPUT2='final_optimization.op2',UNIT=12

ID NoiseModelling

SOL 200

DIAG 8,12

ECHOOFF

CEND

$$$$$$$$$$$$$$$$$$$ CASE CONTROL BEGINS HERE

ECHO=NONE

set 44 = 5951

TITLE=NOISE MODELLING ANALYSIS

SPC=10$DESGLB = 5

DESOBJ(MIN) = 33

subcase 1

ANALYSIS = MODES

METHOD(STRUCTURE)=10

DESSUB = 55

subcase 2

ANALYSIS = MFREQ

METHOD(STRUCTURE)=20

METHOD(FLUID)=20

DLOAD=70

FREQUENCY=15

DISPLACEMENT(SORT1,PRINT,PUNCH)=44

FORCE(SORT1,PRINT,PUNCH)=44DESSUB=117

$ DESOBJ(MIN) = 100

$$$$$$$$$$$$$$$$$$$ BULK DATA BEGINS HERE

BEGIN BULK

ECHO=NONE

EIGRL,10,,,50

EIGRL,20,,,50

$ Define the design variables

DESVAR,1,ringwid,0.015,0.005,0.03

DESVAR,2,ringthic,0.01,0.005,0.03

DESVAR,3,shelthic,0.00635,0.002,0.02

DESVAR,4,longwid,0.015,0.005,0.03

DESVAR,5,longthic,0.01,0.005,0.03$ Relate the Design Varibles to change in stiffener and shell

thicknesses

DVPREL1,1,PSHELL,1,4,0.002,,,,+

+,3,1.0

DVPREL1,2,PSHELL,4,4,0.002,,,,+

+,3,1.0

DVPREL1,3,PSHELL,3,4,0.002,,,,+

+,3,1.0

DVPREL1,4,PBARL,1,12,0.005,,,,+

65


76/83

+,1,1.0

DVPREL1,5,PBARL,2,12,0.005,,,,+

+,4,1.0

DVPREL1,6,PBARL,1,13,0.005,,,,+

+,2,1.0

DVPREL1,7,PBARL,2,13,0.005,,,,+

+,5,1.0

$Define Objective

DRESP1,1,DRUCK,FRDISP,,,1,77.8586,5951

DRESP1,2,DRU,FRDISP,,,7,77.8586,5951

DRESP2,100,BETA,100,

,DRESP1,1,2

$1234567$1234567$1234567$1234567$1234567$1234567$1234567$1234567$123456

7

DEQATN 100 OBJ(R,I) = 20.0 * LOG10(SQRT((R * * 2) + (I * * 2))

/(2.0E-5) )

DCONSTR,117,100,,70.0

$ Define Constraint on weight

DRESP1,33,WEIGHT,WEIGHT,

$DCONSTR,5,22,100.0,2500.0

$ Define Constraint on frequencyDRESP1,3,frequ,FREQ,,,1,

DCONSTR,55,3,23.0

$ Override default optimization parameters

DOPTPRM,DESMAX,20,p1,1,p2,15,CONV1,1E-6

,IPRINT,3

$ Grid points of the Torpedo

GRID 1 -0.30 0.00 0.00

GRID 2 -0.3000 0.0869 0.0233

GRID 3 -0.3000 0.0779 0.0450

GRID 4 -0.3000 0.0636 0.0636

GRID 5 -0.3000 0.0450 0.0779

. . . . .

. . . . .

. . . . .

GRID 1213 1.6000 0.0000 0.0000

GRID 1214 1.7500 0.0000 0.0000

GRID 1215 1.9000 0.0000 0.0000

$

$Grid Points of the surrounding water

$

GRID* 1501 2.9100000000

0.0000000000

* 0.0000000000 -1

GRID* 1502 1.9996380000

0.9959744000

* 0.0000000000 -1

GRID* 1503 1.9996380000 -0.9959744000

* 0.0000000000 -1

. . . . .

. . . . .

. . . . .

GRID* 24964 -0.2567208000 -

0.3616001000

* -0.1620268000 -1

66


77/83

GRID* 24965 1.7692490000 -

0.7309163000

* -0.2201162000 -1

$

$ Grid points of the Air

$

GRID 25001 0.05000 0.11314 0.11314-1

GRID 25002 0.05000-0.11314 0.11314-1

GRID 25003 0.05000 0.09868 0.12595-1

. . . . .

. . . . .

. . . . .

GRID 31663 0.66061-0.10952-0.10952-1

GRID 31664 0.68030-0.10952-0.10952-1

$ This Completes Grid Data

$Now Elements for the Torpedo

CTRIA3 1 1 2 3 1

CTRIA3 2 1 3 4 1

. . . . . .

. . . . . .

. . . . . .

CTRIA3 23 1 24 25 1

CTRIA3 24 1 25 2 1

CQUAD4 25 1 2 3 27 26

CQUAD4 26 1 3 4 28 27

. . . . . . .

. . . . . . .

. . . . . . .

CQUAD4 1199 3 1176 1177 1201 1200

CQUAD4 1200 3 1177 1154 1178 1201

CTRIA3 1201 3 1178 1179 1202

CTRIA3 1202 3 1179 1180 1202

. . . . . .

. . . . . .

. . . . . .

CTRIA3 1223 3 1200 1201 1202

CTRIA3 1224 3 1201 1178 1202

CBAR 1225 1 194 195 1203

0.00000-0.00790-0.00212 0.00000-0.00708-

0.00409

CBAR 1226 1 195 196 1203

0.00000-0.00708-0.00409 0.00000-0.00578-

0.00578

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

CBAR 1839 2 1081 1105 1209-0.00000-0.00817-0.00000-0.00000-0.00817-

0.00000

CBAR 1840 2 1105 1129 1209

-0.00000-0.00817-0.00000-0.00000-0.00817-

0.00000

CONM2 1841 196 1.9321

CONM2 1842 199 1.9321

. . . . .

. . . . .

67


78/83

. . . . .

CONM2 1943 1078 1.9321

CONM2 1944 1081 1.9321

RBE2 2000 1202 1 1106 1107 1108 1109

1110

1111 1112 1113 1114 1115 1116 1117

1118

1119 1120 1121 1122 1123 1124 1125

1126

1127 1128 1129

RBE2 3000 1 1 170 171 172 173

174

175 176 177 178 179 180 181

182

183 184 185 186 187 188 189

190

191 192 193

$Now Elements for water

CTETRA 5001 400 1728 4392 3106 4391

CTETRA 5002 400 1728 3106 1729 4391. . . . . . .

. . . . . . .

. . . . . . .

CTETRA 127228 400 20508 22572 21832 21161

CTETRA 127229 400 20508 22572 24965 21832

$ Elements for Air

CHEXA 130001700 25001 25003 25053 25052 25425

25457

27057 27025

CHEXA 130002700 25003 25004 25065 25053 25457

25489

27441 27057

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

CHEXA 135576700 31280 31664 26320 26352 25380

25392

25225 25226

CHEXA 135577700 31664 26256 25872 26320 25392

25223

25211 25225

$Infinite Boundary Condition

CAABSF 150001 4000 1501

CELAS1 140001 5000 1501 1

CAABSF 150002 4000 1502CELAS1 140002 5000 1502 1

. . . . .

. . . . .

. . . . .

CAABSF 154372 4000 9637

CELAS1 144372 5000 9637 1

CAABSF 154373 4000 9638

CELAS1 144373 5000 9638 1

$End of infinite boundary condition data

68


79/83

PAABSF,4000,,,,,2.2572e12

PELAS,5000,9.7169e-5

PSHELL 1 101 0.00635 101

PSHELL 4 102 0.00635 102

PSHELL 3 103 0.00635 103

PBARL,1,300,,BAR

,1.5e-2,1.0e-2

PBARL,2,300,,BAR

,1.5e-2,1.0e-2

MAT1 1017.0E+010 0.33 2780.00

MAT1 1027.0E+010 0.33 2780.00

MAT1 1037.0E+010 0.33 2780.00

MAT1 3007.0E+010 0.33 2780.00

SPC1 10 123 1

SPC1 10 1 2 THRU 25

SPC1 10 2 175 187

SPC1 10 3 181 193

MAT10,800,2.2+9,1026.0

PSOLID,400,800,,,,,PFLUID

$Acoustic Source Dafinition for source one

ACSRCE,70,500,,,2000,1.21,142355.3TABLED1,2000,,,,,,,,+T1

+T1,0.0,0.0,77.76,0.0,77.86,1.0,77.96,0.0,+T2

+T2,1000.0,0.0,ENDT

DAREA,500,25151,1,0.904778,29150,1,0.140919

FREQ,15,77.858604

$Material properties for the fluid

MAT10,900,,1.21,343.0

PARAM,GRDPNT,0

PSOLID,700,900,,,,,PFLUID

PARAM,POST,-2

PARAM,PREFDB,2.-5

PARAM RMS,YES

ACMODL,diff,,,,0.04

PARAM,AUTOSPC,NO

Param,Prgpst,No

ENDDATA

69


80/83

References

1. Allen, M. J., Vlahopoulos, N., Integration of Finite Element and Boundary

Element Methods for Calculating the Radiated Sound from a Randomly Excited

Structure, Computers and Structures, Vol. 77, No. 2, pp. 155-169, 2000.

2. Everstine, G. C., Henderson, F. M., Coupled Finite Element/Boundary Element

Approach for Fluid-Structure Interaction, Journal of Acoustical Society of

America, Vol. 87, 1990.

3. Zienkiewicz, O. C., Newton, R. E., Coupled Vibrations of a Structure

Submerged in a Compressible Fluid, Proceedings of International Symposium on

Finite Element Techniques, Stuttgart, pp. 359-379, 1969.

4. Everstine, G. C., Schroeder, E. A., Marcus, M. S., The Dynamic Analysis of

Submerged Structures, Nastran Users Experience, NASA TM X-3278,

Washington, 1975.

5. Pinsky, P. M., Abboud, N. N., Transient Finite Element Analysis of the Exterior

Structural Acoustics Problem, In: Numerical Techniques in Acoustic Radiation,

American Society of Mechanical Engineers, New York, pp. 35-47, 1989.

6. Marcus, M. S., A Finite Element Method Applied to the Vibration of Submerged

Plates,Journal of Ship Research, Vol. 22, pp. 94-99, 1978.

7. Everstine, G. C., Finite Element Formulations of Structural Acoustic Problems,

Computers and Structures, Vol. 65, pp. 307-321, 1997.

8. Ruzzene, M., Baz, A. Finite Element Modeling of Vibration and Sound

Radiation from Fluid-Loaded Shells,Journal of Thin-Walled Structures, Vol. 36,

pp. 21-46, 2002.

70


81/83

9. Everstine, G. C., A Symmetric Potential Formulation for Fluid-Structure

Interaction,Journal of Sound and Vibration, Vol. 79, pp. 157-160, 1981.

10.Everstine, G. C., Finite Element Solution of Transient Fluid-Structure Interaction

Problems, 19th

NASTRAN Users Colloquium, NASA CP-3111, Washington,

DC, pp. 162-173, 1991.

11.Everstine, G. C., Structural Analogies for a Scalar Field Problem, International

Journal of Numerical Methods in Engineering, Vol. 17, pp. 419-429, 1981.

12.Hunt, J. T., Knittel, M. R., Barach, D., Finite Element Approach to Acoustic

Radiation from Elastic Structures,Journal of Acoustical Society of America ,Vol.

55, pp. 269-280, 1974.

13.Hunt, J. T., Knittel, M. R., Nichols, C. S., Barach, D., Finite Element Approach

to Acoustic Scattering from Elastic Structures, Journal of Acoustical Society of

America, Vol. 57, pp. 287-299, 1975.

14.Everstine, G. C., Henderson, F. M., Lipman, R. R., Finite Element Prediction of

Acoustic Scattering and Radiation from Submerged Elastic Structures,

Proceeding of 12thNASTRAN Users Colloquium,pp. 194-209, 1984.

15.Zienkiwicz, O. C., Taylor, R. L., The Finite Element Method, McGraw-Hill, Vol.

2, 1989.

16.Choi, K. K., Dong, J., Design Sensitivity Analysis and Optimization of High

Frequency Radiation Problems Using Energy Finite Method and Energy

Boundary Element Method, 10th AIAA/ISSMO Multidisciplinary Analysis and

Optimization Conference, AIAA 2004-4615, 30th

August-1st

September, Albany,

New York, 2004.

71


82/83

17.Zhang, W., Wang, A., Vlahopoulos, N., An Alternative Energy Finite Element

Formulation Based on Incoherent Orthogonal Waves and its Validation for

Marine Structures, Finite Elements in Analysis and Design, Vol. 38, pp. 1095-

1113, 2002.

18.Geers, T. L., Felippa, C. A., Doubly Asymptotic Approximations for Vibration

Analysis of Submerged Structures, Journal of Acoustical Society of America,

Vol. 57, Issue. 4, pp. 1152-1159, 1975.

19.Everstine, G. C., Taylor, D. W., A NASTRAN Implementation of the Doubly

Asymptotic Approximation for Underwater Shock Response, NASTRAN Users

Experiences, pp. 207-228, 1976.

20.Rosen, M. W., Acoustic Studies on Power Transmission in Underwater Missile

Propulsion, 1st

ed., Arlington: Compass Publications, pp. 357379, 1967.

21.Kinsler, L. E., Frey, A. R., Coppens, A. B., Sanders, J. V., Fundamentals of

Acoustics, Wiley, NY, 1982.

22.Dudley, D. W., Introduction to Acoustical Engineering of Gear Transmission,

in Underwater Missile Propulsion, 1st

ed., Arlington: Compass Publications, pp.

349357, 1967.

23.NASTRAN Users Manual, Mac-Neal Schwendler Corporation, Los Angeles, CA,

2001.

24.Pierce, A. D., Acoustics: An Introduction to its Principles and Applications,

1st

ed., Acoustical Society of America, 1989.

25. DOT Users Manual, Vanderplaats Research & Development, Inc., Colorado

Springs, CO, 2001.

72

8/4/2019 Acoustic Optimi

Acoustic Optimization of an Underwater Vehicle

Documents

Transcript of Acoustic Optimization of an Underwater Vehicle