ICA0141.1

ICAS 2000 CONGRESS

FLEXIBLE COMPOSITE WING WITHINTERNAL ACTUATION FOR ROLL MANEUVER

N. S. Khot, J. V. Zweber and D. E. VeleyAir Force Research Laboratory (AFRL/VASD)

H. ÖzOhio State University, Department of Aerospace Engineering and Aviation

F. E. EastepUniversity of Dayton, Department of Mechanical & Aerospace Engineering

Keywords: composite material, flexible wing, control design, roll maneuver, smart structures

Abstract

This paper is concerned with designing an opti-mum composite flexible wing structure toenhance roll maneuver capability at highdynamic pressures using an embedded actuatingsystem without external control surfaces. A min-imum weight design, with constraints onstrength for three different flight conditions, onthe frequency distribution and lift effectivenesswas used for this study. The elastic twist andcamber is achieved by providing a system ofactuating elements distributed within the inter-nal substructure of the wing to provide controlforces. The modal approach is used to developthe dynamic equilibrium equations which culmi-nates in the steady roll maneuver of a wing sub-jected to aerodynamic loads and the actuatingforces. The distribution of actuating forces toachieve the specified steady roll rate and rollangle of the flexible vehicle within a specifiedtime was determined by using IndependentModal-Space Control (IMSC) design approach.Here, a full-scale realistic wing is considered forthe assessment of the strain energy and distribu-tion of actuator forces required to produce theantisymmetric twist and camber deformation toachieve the specified roll performance.

1 Introduction

Traditionally, a pilot provides a rolling maneu-ver for turning of the aircraft with an aileronsystem by rotation of trailing edge control sur-

faces on the right and left wings in a differentialsense. The aileron system increases the lift onone wing and decreases lift on the opposite wingresulting in a rolling moment producing the roll-ing maneuver. This is an effective technique forgenerating rolling moment for an aircraft operat-ing in a low dynamic pressure environmentwhere the wings are essentially “rigid”. How-ever, if the aircraft is operating at high dynamicpressures where the deformations of the wingsare significant, the roll rate is reduced by a detri-mental aerodynamic twisting moment resultingfrom the trailing edge control surface rotation.At roll reversal dynamic pressure the aileronsare rendered completely ineffective for produc-ing the needed rolling moment. Reference [1]describes a technique for prescribing elasticwing twist and camber distribution for theenhancement of the rolling maneuver of a wingat all dynamic pressures without ailerons. Thecontrol forces were obtained from a techniquereferred to as “Fictitious Control Surfaces”. InReference [2] an optimized structure wasdesigned to achieve a specified roll rate withoutailerons at different Mach numbers by using astatic aeroelastic approach. Rather than using anaileron system to achieve an aerodynamic roll-ing moment, here wing deformation is used asan asset rather than impediment to overcome,which avoids the detrimental twisting momentof the aileron and enhances the roll performanceat all dynamic pressures. The wing is twistedand cambered in a differential sense on the right

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14. ABSTRACT This paper is concerned with designing an optimum composite flexible wing structure to enhance rollmaneuver capability at high dynamic pressures using an embedded actuating system without externalcontrol surfaces. A minimum weight design, with constraints on strength for three different flightconditions, on the frequency distribution and lift effectiveness was used for this study. The elastic twist andcamber is achieved by providing a system of actuating elements distributed within the internalsubstructure of the wing to provide control forces. The modal approach is used to develop the dynamicequilibrium equations which culminates in the steady roll maneuver of a wing subjected to aerodynamicloads and the actuating forces. The distribution of actuating forces to achieve the specified steady roll rateand roll angle of the flexible vehicle within a specified time was determined by using IndependentModal-Space Control (IMSC) design approach. Here, a full-scale realistic wing is considered for theassessment of the strain energy and distribution of actuator forces required to produce the antisymmetrictwist and camber deformation to achieve the specified roll performance.

15. SUBJECT TERMS

16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT

SAR

18. NUMBEROF PAGES

10

19a. NAME OFRESPONSIBLE PERSON

a. REPORT unclassified

b. ABSTRACT unclassified

c. THIS PAGE unclassified

Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18

Khot, etc.

ICA0141.2

and left wings as shown in Figure 1, to achievethe required rolling moment for a specifiedsteady roll rate.

Presently, there are DARPA sponsoredprojects [3] for demonstration of the applicationof smart materials for twist control to improveaircraft performance based solely on test resultsfrom small wind-tunnel models. Here, it is pro-posed that a full scale finite element model of arealistic wing be considered for proper elasticwing twist and camber for roll control in a highdynamic pressure environment. The approachselected here is a two step process. In the firststep, an optimum structural design satisfyingrequirements on strength, frequency distributionand lift effectiveness is obtained. The optimiza-tion problem was solved by using ASTROS [4]version 20 for three flight condition at 9-g sym-metric pull-up maneuver at M=0.85. In the sec-ond step the axial load carrying cross rodelements mounted to the internal structure areused as actuators exerting tensile /compressiveloads to twist and camber the optimum wingstructure via an active control strategy to achievespecified roll rates and roll angles. The controldesign approach is based on using IndependentModal-Space Control (IMSC) [5]. The presentpaper contains a short summary of this approachas applied to the roll maneuver of a flexible air-craft.

2 ANALYTICAL APPROACH

2.1 Modal Dynamic Equilibrium EquationsThe dynamic equilibrium equations for steadyroll maneuver can be written as [2], [6]

(1)

where is the mass matrix, is the damp-ing matrix, is the structural stiffness matrixof the finite element model, is the vector ofnodal displacements, is the dynamic pres-sure, [T] is the transformation matrix from struc-tural degrees of freedom to the aerodynamicdegrees of freedom, is the vector of angles

of attack at the aerodynamic panels, is theapplied actuator load distribution matrix and

is the vector of actuator stimuli which isa function of time t. The product isthe vector of generated control forces generatedat the structural node points due to the actuatorforces or due to the voltages applied tothe solid state actuators. In the latter case the ele-ments of matrix would depend on the num-ber of stacks, number of cycles and theproperties of the solid state actuators in additionto the direction cosines associated with the actu-ators.

The displacement vector can bedefined as a linear combination of rigid bodymodes and elastic vibration modes as

(2)

where is the rigid body mode, is thespecified number of antisymmetric low fre-quency modes, is the generalized rigidbody displacements and in present case it isequal to the roll angle . In Equation (2) represents the elastic displacements. The sub-scripts r and e are used to indicate rigid body andflexible vibration modes.

The angles of attack at the controlpoints of aerodynamic panels can be written as

(3)

where is the free stream velocity. Using Equa-tion (2) the angles of attack can be written as

(4)

where is the roll rate , U is the chord wisecomponent of V in the direction ,

is the matrix of flexible modegradients with respect to the coordinate. Equa-tion (4) can be written as

(5)

M[ ] rs··{ } C[ ] rs

·{ } K[ ] rs{ }qd T[ ]T

A[ ] α{ } F[ ] u t( ){ }+ + +

+ 0=

M[ ] C[ ]K[ ]

rs{ }qd

α{ }

F[ ]

u t( ){ }F[ ] u t( ){ }

u t( ){ }

F[ ]

rs{ }

rs{ } Ψr[ ] qr{ } Ψe[ ] qe{ }+ ψ[ ] q{ }= =

Ψr[ ] ψe[ ]

qr{ }

φ qe{ }

α{ }

α{ } 1V--- T[ ] rs

·{ }=

V

α{ } 1V--- T[ ] Ψr[ ] q·r{ } U

∂ψe

∂x--------- qe{ }+=

q·r Z*

x∂ψe( ) ∂x( )⁄[ ]

x

α[ ] Ψr

V------

∂ψe

∂qe

---------q·r

qe

=

Flexible Composite Wing with Internal Actuation for Roll Maneuver

ICA0141.3

where and are the rigidand vibration modes expressed in aerodynamicdegrees of freedom. Using Equation (5) the equi-librium Equation (1) can be written in terms ofgeneralized coordinates as

(6)

where (7)

, (8)

(9)

(10)

(11)

(12)

in which and are the modal structuralmass and stiffness matrices respectively; and are the modal aerodynamic dampingand aerodynamic stiffness matrices, respec-tively; is the modal aeroelastic stiffnessmatrix. In Equation (11) the aerodynamic damp-ing matrix is obtained from with allelements set to zero except the first column and

is obtained from with first column ele-ments set to zero. Equation (6) represents theaeroelastic roll dynamics equations of motion inthe configuration space represented by the gen-eralized coordinates which are the structuralmodal coordinates and represents the gen-eralized control loads in the same configurationspace.

2.2 Independent Modal -Space Control Design of Aeroelastic SystemThe state space equations corresponding toEquation (6) can be written as5

(13)

Equation (13) can be written as

(14)

where , and represent correspondingmatrices in Equation (13) and is the state vec-tor.

Introducing the general solution form into the homogeneous form of Equa-

tion (14) the right (R) and left (L) conjugateaeroelastic eigenvalue problems can be posed as

, (15)

where and are the right and leftaeroelastic eigenvectors, respectively, corre-sponding to the r-th aeroelastic eigenvalue .Once the complex general conjugate eigenvalueproblems are solved, one no longer needs to dealwith complex quantities and the problem can bedealt with in terms of real modal matrices andreal modal-state variables formed from the realand imaginary parts of the right and left eigen-vectors and the complex modal state. The result-ing real aeroelastic modal state transformationand the bi-orthonormality relationships for theaeroelastic real modal matrices are

, (16)

(17)

(18)

(19)

(20)

(21)

where and are the real conjugate left andright aeroelastic modal matrices, respectively. InEquation (20), is the vector ofaeroelastic modal-states, and (r=1,2,.....n)are a conjugate pair of the r-th real modal-states.In the above equations and denote the r-th pair of eigenvalues. The uncoupled aeroelasticmodal-state-space equations for designing the

Ψr TΨr= Ψe TΨe=

Ms[ ] q··{ } Ca[ ] q·{ } Ksa[ ] q{ }+ + Q{ }=

Ms[ ] Ψ[ ]TM[ ] Ψ[ ]=

Ca[ ] qd Ac[ ]= Ka[ ] qd Ak[ ]=

Ksa[ ] Ks[ ] Ka[ ]+=

Ks[ ] 0 0

0 Ψ[ ]TK[ ] Ψ[ ]

=

A[ ] Ψ[ ]TT[ ]T

A[ ] Ac[ ] Ak[ ]+= =

Q{ } Ψ[ ]TF[ ] u t( ){ }–=

Ms[ ] Ks[ ]Ca[ ]

Ka[ ]

Ksa[ ]

Ac[ ] A[ ]

Ak[ ] A[ ]

Q{ }

Ms 0

0 Ms

q··

q·Ca Ksa

Ms– 0

q·

q+ Q

0=

Mx· Gx+ X=

M G Xx

x vrerλt

=

λrM G+[ ]VRr 0= λrMT

GT

+[ ]VLr 0=

VRr VLr

λr

VLTMVR I= VL

TGVR block-diag ∆r[ ]=

∆r[ ]αr1 ωr

ωr– αr2

=

αr1 r2, Reλr1 r2,= ωr Imλr1 r2,=

x t( ) VRw t( )=

w w1 w2 …wr …wn, , ,[ ]T=

wr ξr t( ) ηr t( )T

=

VL VR

w ns 2n=ξr ηr

r1 r2

Khot, etc.

ICA0141.4

control system can be obtained by utilizing thesolution of the eigenvalue problem given inEquations (15-21) and the generalized configu-ration-space input Q.This approach is known asIndependent Modal Space Control (IMSC). Onenow is free to use his favorite control theory todesign the single modal control input for eachuncoupled pair of modal-state equations. In thispaper, LQR control design approach is used todesign the uncoupled set of state equations. Thecoupling terms arising through the constraintequations are in general very weak and thereforehave virtually a null effect on the system.

The objective function for minimizationselected here in order to determine the contribu-tion of different aeroelastic modes to achievethe desired roll rate Z* is the elastic strain energyto achieve the specified roll rate.The work-energy equation is obtained by taking the scalerproduct of the vector form of Equation (6) withthe incremental generalized coordinate displace-ment vector and integrating betweenspecified time interval during the maneuver.Thus denoting by the work terms due to acceler-ation loads (kinetic energy), elastic loads, aero-dynamic damping and aerodynamic stiffnessloads, and actuator loads, respectively, theenergy equilibrium equation can be written as:

(22)

3 Aeroelastic Analysis

The Unified Subsonic and Supersonic Aerody-namic Analysis (USSAERO) [7] was used forthe computation of aerodynamic loads on theaircraft wing. This approach uses a superpositionof vortex singularities applied to a discrete num-ber of aerodynamic panels to calculate the dis-crete pressure distribution over the wing surface.In this investigation numerical calculations forrigid and flexible vibration modes, aerodynamicstability derivatives, generalized stiffness matrixetc. are calculated from ASTROS [4]. The spe-cial version of ASTROS was run with bulk datacontaining the location and description of theactuators. In the present case the actuators wereassumed to be rod elements capable of exerting

only axial loads. The required data for solutionof the approach discussed in the last sectionwere written on separate files after execution ofthe ASTROS run. Separate program was writtento obtain the generalized matrices defined inEquations (7) through (12) from the matricescalculated by ASTROS and the IMSC controldesign program was written using MATLABlanguage to calculate the distribution of actuatorforces, time response of the roll rate, work-energy quantities etc.

4 Numerical Examples

A low aspect ratio wing was selected for thisstudy. The wing planform is shown in Figure 2along with the location of the underlying struc-ture. The wing planform was divided into 180aerodynamic boxes. Figure 3 shows the underly-ing structure, consisting of 10 intermediate sparsand 6 intermediate ribs, represented with finiteelements. The wing structure was idealizedusing 167 nodes and was modeled using graph-ite-epoxy wing skins and aluminum substruc-ture. The wing skins were modeled as 40quadrilateral and seven triangular elements perside with a (90, 0, -45, 45) symmetric laminateon each element. The 0 degree direction isdefined to be parallel to the y-axis of the aircraftcoordinate system. The wing substructure wasmodeled as 105 quadrilateral “picture frame”elements. Each quadrilateral rib or spar elementwas built as a shear element to represent the webbounded by bar elements on the top and bottomto model caps and rod elements on the sides,“posts”, to model the additional material neededfor spar to rib connections. In addition to theload-bearing wing structure, appropriate singleand multi-point constraints and structure werespecified for simulation of the wing carry-through structure and an 8000 lbs. mass wasused to simulate the weight of the fuselage.Finally, 1600 lbs. of non-structural mass weredistributed amongst different node points on thewing to simulate fuel, plumbing, wiring and fas-tener weights.

The model was initially sized to obtain theminimum weight structure that would satisfy a

zr*

dq t( )

Wkin Wflx Ward Wars+ + + Wact=

Flexible Composite Wing with Internal Actuation for Roll Maneuver

ICA0141.5

number of constraints. During this design, thethicknesses of the 90, 0 and ±45 degree layers ofthe skin were allowed to vary individually aswell as the thicknesses of the shear elements andthe cross sectional areas of the bar and rod ele-ments in the picture frame elements. Thisresulted in a total of 656 design variables: 282skin variables (47 elements x 2 surfaces x 3 lay-ers) and 374 substructure variables (105 shearpanels + 210 bar elements + 59 rod elements).The constraints on the optimization were that thestresses in the elements being resized did notexceed their allowables at three different flightconditions. The stress constraints were formu-lated as Tsai-Wu for the composite elements andVon Mises for the metallic elements. Additionalconstraints were imposed to limit the frequencyof the first flexible mode was 3 Hz and the lifteffectiveness to at least 0.9 at one flight condi-tion. The lift effectiveness constraint, flexible liftcurve slope divided by rigid lift curve slope, wasapplied at Mach 0.85 at sea level on a standardday.

The flight conditions chosen for the stressconstraints were a dynamic 9-g pull-up at Mach0.85 at a dynamic pressure of 30 psi and steady(zero pitch rate) 9-g pull-ups at Mach 0.85 anddynamic pressures of 15 and 7.43 psi. The 7.43psi case represents match point conditions forsea level on a standard day. The other two condi-tions were chosen to provide different loadingconditions. The reason for these different load-ing conditions can be seen by examining thestatic aeroelastic problem formulation:

(23)

where, (24)

and (25)

For a rigid wing, , achange in dynamic pressure merely results in ascaling of the force term, , as can be seenfrom Equation (24). However, for the case of aflexible wing, the dynamic pressure effect inboth the non-zero term, shown inEquation (25), and the force term result in achanging load distribution as the dynamic pres-sure is varied.

The results of the optimization where thatthe structural mass of the wing was reducedfrom 2353 lbs. to 345 lbs. This optimized weightis reasonable for a 20,000 lbs. fighter. It resultsin a wing weight fraction of about 3.5%. Plots ofthe thickness distribution of the wing skins areshown in Figures 4, 5 and 6 for the 0, 90 and ±45degree layers respectively. As expected, most ofthe thickness was retained in the 0 degree layernear the root. This location is where the materialand fiber orientation can most effectively carrythe bending load of the wing. In addition, it canbe seen that moderate thickness is retained in alllayers near the wing tip. This is likely due to thelift effectiveness constraint. By stiffening thewing tip, the wing is able to withstand the aero-dynamic twisting moment that will otherwisedegrade the lift performance of the wing.

The stiffening of the wing tip can also beseen in Figure 7. This figure shows the thick-nesses of the shear elements of the spar and ribpicture frame elements. In this figure, the thick-est elements are in the two outer most rib. Theseelements are the most effective shear elements incountering a local torsion of the wing.

The final set of structural design variableswere the spar and rib cap and post cross-sec-tional areas. The results for these elements areFigure 8. It can be seen that three spar cap ele-ments at the trailing edge root of the wing aresignificantly larger than any of the other cap orpost elements. This is most likely the result of apath dependency in the optimization. One possi-ble change that could be investigated is model-ing the spar and rib caps as rod elements insteadof bar elements. The areas of the three largestcap elements were omitted from Figure 9 inorder to show the relative sizes of the remainingelements. Figure 9 reinforces the conclusionsthat were presented above. Again, significantstiffness was added to the tip of the wing.

The actuating system to twist and camberthe wing consisted of 40 cross rods along thefive ribs as shown in Figure 3. Actuators were ofa generic nature capable of providing tensile orcompressive forces as required to deform thewing to achieve the specified flexible roll rate.The required total strain energy and the magni-

K AICS qd M,( )–[ ]u Mu··+ P qd M,( )δ=

P qd M,( ) qd G[ ]T AIRFRC M( )[ ]=

AICS qd M,( ) qd G[ ]T AIC M( )[ ] G[ ]=

AICS[ ] AIC[ ] 0= =

P[ ]

AICS[ ]

Khot, etc.

ICA0141.6

tude of forces necessary to twist the wing toachieve specified flexible roll rate at Mach num-bers 0.85 and 1.2 were calculated. The targetflexible roll rate was specified as 90o /sec at analtitude of 20,000 ft.

The controller was designed by using sixaeroelastic modes of the servoelastic modal stateequation.The LQR control design approach wasused to design the single modal control input foreach uncoupled pair of modal-state dynamics. Inthe definition of the LQR performance index foreach aeroelastic mode the state weighting matrixwas assumed to be diagonal and the controlweighting matrix was a scalar. The elements ofthe state weighting matrix were set equal tounity. However, each modal control weightingmatrix was assumed to be the same for all themodes. Different values were used to investi-gate its effect on the time response and the mag-nitude of the actuator forces. As the evaluationmodel, first twenty flexible structural modeswere used in addition to the rigid body roll modeas defined by Equations (2) and (13). The resultsand the work done by the actuators given in thepaper are for the evaluation model even thoughthe control design is based on the reduced-orderaeroelastic modal model. The time response forthe reduced order controller (6 aeroelasticmodes) and the evaluation model (21 structuralmodes) was not much different indicating negli-gible spillover effect. The individual contribu-tion of different modes to achieve 90 deg/sec rollrate was determined by using the modal perfor-mance allocation optimization approach in orderto minimize the total flexible strain energy dueto the work done by the actuators and aerody-namic loads. For Mach number 0.85 the percent-age allocation amongst six aeroelastic modes 1through 6 was 0.0, 42.0, 30.0, 29.0, -0.3, -0.7,respectively. For Mach number 1.2 the percent-age allocation amongst the six modes was 0.0,87.1, 205.1, -197.0, 19.5, -14.7 respectively. Thetime response and the energy quantities werecalculated for a period of four seconds.

Table 1 gives the actuator work associatedwith the flexible modal coordinates of the evalu-ation model for the two Mach numbers 0.85 and1.2 for the control weighting parameter

, respectively. The actua-tor work was equal to the total energy satisfyingequilibrium Equation 22. The decrease in thetotal energy requirement at high Mach number isdue to the increase in the lift-pressure helping tocreate the required rolling moment. Comparingthe actuator work it is observed that it increaseswith increase in the value of the control weight-ing parameter . For example at MACH=1.2,the flexible wing needed 2673 in-lbs and 3413in-lbs to achieve the roll rate of 90o /sec for thecontrol weighting parameter respectively. Table 2 shows the distribution ofopen-loop and closed-loop eigenvalues for thetwo Mach numbers. For both cases first fourflexible modes are unstable having positive realparts of the open-loop eigenvalues.The closedloop systems are stable. Figure 10 shows theaeroelastic deformation of the wing for Machnumber 0.85. The wing twist and bending pro-vides positive angle of attack at most of the loca-tions.The maximum displacements at the trailingedge of the tip of the wing were different for thetwo Mach numbers. However, the general defor-mation patterns were similar. The maximumdeflection for Mach 0.85 and 1.2 was 1.51 in and1.14 in, respectively. High dynamic pressurerequired smaller deformation than the lowerdynamic pressure.The time history for the rollrate and the actuator forces for Mach 0.85 and1.2 for are shown in Figures11 through 18. In these figures in addition to theroll rate, roll angle is also shown as a function oftime.

The response plots for roll rate and theactuator forces for different values of the controlparameter are shown side by side in order toindicate the relationship between the timerequired to stabilize the roll rate at the desiredvalue and the magnitude of the actuator forces.For smaller values of the roll rate tendto stabilize faster but the magnitude of the actua-tor forces increases. For the roll ratedoes not yet stabilize closer to 90 deg/sec evenafter 4 sec, but the magnitude of maximumforces is very close to 2000 lbs. This is a sub-stantial reduction in the required magnitude ofthe forces, but at the expense of roll rate settling

rwrw

rw 0.1 1.0 and 10.0,=

rw

rw 0.1 and 10.0=

rw 0.1 and 10.0=

rw 0.1=

rw 10.0=

Flexible Composite Wing with Internal Actuation for Roll Maneuver

ICA0141.7

time. It is interesting to note that even though theroll rate tend to stabilize at different times theroll angle is increased nearly at the rate of 90deg/sec throughout the maneuver. This is due tothe average roll rate being nearly equal to 90deg/sec during most of the period. For all thecases presented the roll angle increased from 0deg. at time t =0.0 sec to 360 deg. at sec. If achieving required roll angle is moreimportant than stabilizing the roll rate, theseresults show that it can be achieved with lessermagnitude of the control forces within therequired time with higher magnitude of actuatorwork.(see Table 1)

5 Conclusions

In this investigation, the flexibility of a wing isused as a departure away from the traditionalaileron system, which results in a detrimentalaerodynamic twisting moment and possibly inunacceptable roll performance at high dynamicpressures. A realistic composite wing was opti-mized with constraints on the strength, fre-quency distribution and lift effectiveness toobtain a feasible flexible wing structure. Ratherthan using the traditional aileron, we have inves-tigated the use of elastic twist and camber of thewhole wing to achieve acceptable roll perfor-mance at all dynamic pressures via an activecontrol approach.

A modal-based analytical approach wasused to write the dynamic equilibrium equationsto achieve a steady roll maneuver and the Inde-pendent Modal-Space Control Technique wasutilized to determine the distribution of actuatorforces. The work done by the actuators was cal-culated at different Mach numbers and controlweighting parameters to assess the energyrequirements and the magnitude of actuatorforces. The actuating system consisted of rodsalong the ribs, which were assumed to be ofgeneric nature, capable of exerting tensile orcompressive forces as required. The strainenergy requirement decreased with increase in

dynamic pressure or Mach number. The increasein the control weighting parameter increased thetime required to stabilize the roll rate, howeverthe maximum magnitude of the actuator forcesdecreased. Even though the roll rate stabilized tothe specified magnitude at different times theroll angle increased gradually with time. Ifachieving a desired roll angle within specifiedtime is important and not the roll rate than it canbe attained with less magnitude of controlforces. In the near future, it is anticipated thatelastic twist, adding camber and providing nec-essary stiffness to prevent flutter and local buck-ling can be achieved through the use of future“smart” materials and actuating system.

6 REFERENCES

[1] Khot, N. S., Eastep, F. E. and Kolonay, R. M. “Wingtwist and Camber for the Rolling Maneuver of aFlexible Wing without Ailerons”, AIAA-97-1268Presented at 38th AIAA/ASME/ASCE/AHS/Adaptive Structures Forum, Kissimmee, Fl. April.1997.

[2] Khot, N. S., Appa, K. and Eastep, F. E., “Optimizationof a Flexible Wing without Ailerons for the RollingManeuver”, To be Published in the Journal OfAircraft, 2000.

[3] Kudva, J., Appa, K., Martin, C., Sendeckyj, G., andHarris, T., “Design, Fabrication and Testing of theDARPA/WL ‘Smart Wing’ Wind Tunnel Model”AIAA-97-1198, Presented at 38th AIAA/ASME/ASCE/AHS/ Adaptive Structures Forum, Kissimmee,Fl. April. 1997 SPIE

[4] ASTROS User’s Reference Manual for Version 20,Universal Analytics, Inc. torrance Ca.

[5] Öz, H., “Aeroservoelastic Design with DistributedActuation for High Performance Aircraft”, 5th SPIESmart Structures Conference, Mathematics andControl in Smart Structures, Vol. 3323, 1998.

[6] Appa, K., Ausman, J. and Khot, N. S., “FeasibilityAssessment and Optimization Study of SmartActuation Systems for Enhanced Aircraft ManeuverPerformance” WL-TR-97-3083, July,1997.

[7] Woodward, F. A., “An Improved Method for theAerodynamic Analysis of Wing - Body- TailConfigurations in Subsonic and Supersonic Flow”,Part I -theory and Application NASA CR-2228, May1973.

tf 4.0=

Khot, etc.

ICA0141.8

Table 1: Actuator work (in lab) from the flexible modal coordinates to achieve 90 deg/sec roll rate

(altitude 20,000 ft)

Control Weighting

Parameter rwMach 0.85 Mach 1.20

0.1 2712 2673

1.0 3211 3093

10.0 3805 3413

Table 2: Aeroelastic eigenvalues

Mode No. real imaginary

Mac

h 0.

85

open

loop

2 4.1604x10-4 ±3.8776x101

3 1.7776x10-3 ±9.6986x101

4 2.8561x10-3 ±1.3232x102

5 2.5933x10-5 ±1.5679x102

6 -1.0297x10-4 ±1.9582x102

clos

ed lo

op

2 -1.6907x10-1 ±3.8776x101

3 -7.1996x10-1 ±9.686x101

4 -9.3953x10-1 ±1.3232x102

5 -1.2060x101 ±1.5679x102

6 -4.3888x10-1 ±1.9582x102

Mac

h 1.

20

open

loop

2 2.7882x10-4 ±4.1934x101

3 4.8244x10-4 ±1.0166x102

4 2.4886x10-3 ±1.3946x102

5 3.5249x10-5 ±1.5687x102

6 -1.7083x10-4 ±1.9621x102

clos

ed lo

op

2 -7.7800x10-1 ±4.1942x101

3 -9.3464x10-1 ±1.0166x102

4 -17028x100 ±1.3946x102

5 -2.5423x10-1 ±1.5687x102

6 -2.3584x10-1 ±1.9621x102

Figure 1.Flexible wing

Figure 2.Aerodynamic grid

Structural wing box

Aerodynamic grid

Fus

elag

e ce

nter

line

Figure 3.Finite Element Model

Flexible Composite Wing with Internal Actuation for Roll Maneuver

ICA0141.9

Figure 4.Bottom Skin 0 degree Ply Thicknesses

Figure 5.Bottom Skin 90 degree Ply Thicknesses

Figure 6.Bottom Skin ±45 degree Ply Thicknesses

Figure 7.Spar and Rib Shear Element Thicknesses

Figure 8.All Spar and Rib Cap and Post Element Cross-Sectional Areas

Figure 9.Selected Spar and Rib Cap and Post Element Cross-Sectional Areas

Figure 10.Mach 0.85 deformation1.51

Khot, etc.

ICA0141.10

Figure 11.Time history of the roll rate and roll angle, M=0.85, control weighting parameter = 0.1

Figure 12.Time history of the roll rate and roll angle, M=0.85, control weighting parameter = 10.0

Figure 13.Time history of the roll rate and roll angle, M=1.20, control weighting parameter = 0.1

Figure 14.Time history of the roll rate and roll angle, M=1.20, control weighting parameter = 10.0

Figure 15.Time history of the actuator forces at M=0.85, control weighting parameter = 0.1

Figure 16.Time history of the actuator forces at M=0.85, control weighting parameter = 10.0

Figure 17.Time history of the actuator forces at M=1.20, control weighting parameter = 0.1

Figure 18.Time history of the actuator forces at M=1.20, control weighting parameter = 10.0