PIEZOELECTRIC CONTROL, NONLINEAR VISCOELASTIC DAMPING, PROBABILITY OF FAILURE AND SURVIVAL TIMES OF LIGHT WEIGHT PLATES SUBJECTED TO AERODYNAMIC NOISE

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1 Submitted to Journal of Intelligent Materials Systems and Structures 2002 PIEZOELECTRIC CONTROL, NONLINEAR VISCOELASTIC DAMPING, PROBABILITY OF FAILURE AND SURVIVAL TIMES OF LIGHT WEIGHT PLATES SUBJECTED TO AERODYNAMIC NOISE 1 Harry H. Hilton, 2 Cristina E. Beldica 3 and Dhirendra Kubair 4 Aeronautical and Astronautical Engineering Department National Center for Supercomputing Applications University of Illinois at Urbana-Champaign 104 South Wright Street, MC-236 Urbana, IL USA ABSTRACT Analytical and numerical formulations and simulations are carried out in order to conduct sensitivity studies of physical parameters affecting acoustic and motion control by viscoelastic piezoelectric and material damping. Numerical simulations in terms of critical parameters, such as relaxation functions of the structure and piezoelectric devices, aerodynamic coefficients, Mach number, are carried out to evaluate system responses, sensing and structural control. This can be accomplished by providing suitable piezoelectric input voltages, by prescribed electric displacements or by controlling the output emf through appropriate resistors. A brief summary of results is displayed in Figs. 8 and 9. Fig. 8 depicts the decaying amplitudes with and without control. The higher amplitudes diminish in time due to viscoelastic material dissipation alone and the dashed lines indicate the additional effect due to piezo electric control. In either case, it is only a matter of time before failure is encountered and ultimate survival times are reached. The imposition of piezo controls delays failure, but cannot eliminate it because viscoelastic failure properties independently decay in time according at their own rates. Fig. 9 shows probabilities of failure for two temperatures with and without control. The effect of increasing temperatures is to accelerate failures in time by increasing probabilities of failure at earlier times. 1 This research was supported by NCSA DoD Grant No. DAHC C-0005, High Performance Computing Modernization Program (HPCMP-PET). 2 Professor Emeritus of Aeronautical & Astronautical Engineering and Senior Academic Lead for Computational Structural/Solid Mechanics, NCSA. Voice: or FAX: uiuc.edu 3 Research Scientist, AAE & NCSA. Voice: FAX: ncsa.uiuc.edu 4 Graduate Research Assistant, AAE. Now Postdoctoral Research Fellow, Princeton University. dkubair@princeton.edu 1

2 In a previous paper Beldica et al. (1998) presented a comprehensive literature review of aerodynamic noise phenomena and examined effects of linear viscoelastic material damping and piezo control on aerodynamic noise suppression on a rigid panel with viscoelastic supports. This study of such an idealized configuration demonstrated the potential of viscoelastic damping and structural control on noise suppression. In the current investigation a flexible viscoelastic plate is exposed to aerodynamic noise and structural control is provided through viscoelastic plate damping augmented by piezoviscoelastic energy dissipations. Nonlinear effects arise from material properties, geometric considerations, large deformations, in-plane forces and aerodynamic contributions, such as nonlinear lift curves and/or stall conditions (Beldica & Hilton 2000, Hilton & Yi 1999). Aerodynamic noise, i. e. flow generated acoustical disturbances in skin panels, ducts, combustors, helicopter and turbine blades, etc., is ever present in flight vehicles and may lead to breaches in structural integrity as well as crew and passenger discomfort. While efficient aerodynamic design may lead to some noise reduction, its ultimate disposal can only be achieved through light weight energy dissipation devices, such as material damping or piezoelectric generated potentials used for either active or passive motion and sound control. Although these noise problems are inherently stochastic, the present pilot simulations are deterministic in order to reduce the number of contributing parameters and to gain fundamental insight into the physical phenomena. The present analysis, then, deals with the union and interaction of several areas: aeroacoustics, aeroelasticity, viscoelastic materials, piezoelectric effects and damping to produce motions of small amplitudes and decaying sound transmissions. Aerodynamic noise generated by a variety of flows has been studied extensively since first systematically analyzed by Lighthill (1952, 1954) and subsequently expanded by Cremer et al. (1988), Goldstein (1976) and Hubbard (1991), among others. Additional extensive aerodynamic noise treatises may be found in Atassi (1993), Beranek (1971), Crighton et al. (1992), Hardin & Hussaini (1993) and Junger & Feit (1986). The theory of aeroelasticity is well established and may be found described in detail in such classical texts as Bisplinghoff et al. (1955), Dowell (1975) and Dowell et al. (1988, 1995). Analyses of viscoelastic damping effects (Cao & Mlejnek 1995, Hilton 1957, 1960, 1991a; Hilton & Vail 1993; Unger 1971; Yi et al. 1996) have shown that energy dissipation due to material and/or structural damping may produce either stabilizing or destabilizing contributions to the system s self-excited dynamic motion depending on phase relationships of the state variables. For instance, this phenomenon leads to viscoelastic flutter velocities which are either smaller or larger than corresponding elastic ones for aerodynamically, dynamically and geometrically identical lifting surfaces. Piezoelectric control of elastic and viscoelastic structures has been demonstrated in numerous publications, which have been discussed by Hilton et al. (1997). Recent formulations and analyses of piezo-aero-thermo-viscoelastic effects by Beldica et al. (1998) and Hilton & 2

3 Yi (1999) have demonstrated that sufficient power can be generated by viscoelastic piezoelectric light weight material strips to effectively influence and control static and dynamic motion. Viscoelastic material properties may be found for polymers in Nashif et al. (1985) and Jones (2001), for metals in Lazan (1968) and piezo-viscoelastic properties are displayed in Holloway & Vinogradov (1997), Preumont (1997), Vinogradov & Holloway (1997, 1999), Vinogradov & Schumacher (2001) and Vinogradov (2001). Keywords: aeroacoustics, aerodynamic noise, creep, failure probabilities, material damping, piezoelectric structural control, smart materials, survivability, viscoelasticity PARTIAL LIST OF REFERENCES Abramowitz, M. and Stegun, I.A. Eds. (1964) Handbook of Mathematical Functions. National Bureau of Standards, Washington, DC. Atassi, H.M., Ed. (1993) Unsteady Aerodynamics, Aeroacoustics and Aeroelasticity of Turbomachines and Propellers. Springer-Verlag, New York. Beldica, C.E., Hilton, H.H. and Yi, S. (1998) A sensitivity study of viscoelastic, structural and piezoelectric damping for flutter control, Proceedings of the 39 th AIAA/ASME/ ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, AIAA Paper No Beranek, L.L., Ed. (1971) Noise and Vibration Control. McGraw-Hill, New York. Bisplinghoff, R.L., Ashley, H. and Halfman, R.R. (1955) Aeroelasticity. Addison-Wesley, Cambridge, MA. Bondoux, D. (1996) Piezo-damping: a low power consumption technique for semi-active damping of light structures, Proceedings of the Third International Conference on Intelligent Materials (P. F. Gobin & J. Tatibouët, eds.) SPIE 2779: Brennan, M.J. and Day, M.J. (1994) Piezoceramic flexural and longitudinal wave generators for active vibration control, Proceedings Third International Congress on Air- and Structure-Borne Sound and Vibration (M. J. Crocker, ed.) 3: Cao, X.S. and Mlejnek, H.P. (1995) Computational prediction and redesign for viscoelastically damped structures, Computer Methods in Applied Mechanics and Engineering 125:1 16. Cremer, L., Heckl, M. and Ungar, E.E. (1988) Structure-Borne Sound. Springer-Verlag, NY. Crighton, D.G., Dowling, A.P., Ffowcs Williams, J.E., Heckl, M. and Lippington, F.G. (1992) Modern Methods in Analytical Acoustics. Springer, NY. Christensen, R.M. (1981) Theory of Viscoelasticity - An Introduction, 2 nd ed. Academic Press, NY. Dowell, E.H. (1975) Aeroelasticity of Plates and Shells. Noordhoff, Leyden. 3

4 Dowell, E.H. and Ilganov, M. (1988) Studies in Nonlinear Aeroelasticity. Springer-Verlag, New York. Dowell, E.H., Crawley, E.F., Curtiss Jr., H.C., Peters, D.A., Scanlan, R.H. and Sisto, F. (1995) AModern Course in Aeroelasticity, 3 rd Ed. Kluwer Academic Publishers, Dordecht. Goldstein, M.E. (1976) Aeroacoustics. McGraw-Hill, NY. Hardin, J.C. and Hussaini, M.Y. (1993) Computational Aeroacoustics. Springer-Verlag, New York. Hilton, H.H. (1957) Pitching instability of rigid lifting surfaces on viscoelastic supports in subsonic or supersonic potential flow, Proceedings of the Third Midwestern Conference on Solid Mechanics Hilton, H.H. (1960) The divergence of supersonic, linear viscoelastic lifting surfaces, including chordwise bending, Journal of the Aero/Space Sciences 27: Hilton, H.H. (1964) An introduction to viscoelastic analysis, Engineering Design for Plastics (E. Baer, ed.) Reinhold Publishing Corp., NY. Hilton, H.H. (1991a) Viscoelastic and structural damping analysis, Proceedings on Damping 91, Air Force Technical Report WL-TR III: ICB 1 15, WPAFB, OH. In press AIAA Journal. Hilton, H.H., Hsu, J. and Kirby, J.S. (1991b) Linear viscoelastic analysis with random material properties, Probabilistic Engineering Mechanics 6: Hilton, H.H. and Yi, S. (1992) Analytical formulation of optimum material properties for viscoelastic damping, Journal of Smart Materials and Structures 1: Hilton, H.H. and Vail, C.F. (1993) Bending-torsion flutter of linear viscoelastic wings including structural damping, Proceedings AIAA/ASME/ASCE/ AHS/ASC 34th Structures, Structural Dynamics and Materials Conference 3: Hilton, H.H. and Ariaratnam, S.T. (1994) Invariant anisotropic large deformation deterministic and stochastic combined load failure criteria, Journal of Solids and Structures 31: Hilton, H.H., Vinson, J.R. and Yi, S. (1997) Anisotropic piezo-electro-thermo-viscoelastic theory with applications to composites, Proceedings of the 11th International Conference on Composite Materials VI: , Gold Coast, Australia. Hilton, H.H. and Yi, S. (1999) Creep divergence of nonlinear viscoelastic lifting surfaces with piezoelectric control, Proceedings Second International Conference on Nonlinear Problems in Aviation and Aerospace 1: , European Conference Publications, Cambridge, UK. Hoff, N.J. (1956) The Analysis of Structures. John Wiley & Sons, New York. Holloway, F. and Vinogradov, A. (1997) Material characterization of thin film piezoelectric polymers, Proc. 11th International Conference on Composite Materials VI: , Gold Coast, Australia. 4

5 Hubbard, H.H. (1991) Aeroacoustics of flight vehicles. 1: Noise sources & II: Noise control, NASA Reference Publication 1258, Washington, DC. Jones, David I. G. (2001) Handbook of Viscoelastic Vibration Damping. John Wiley & Sons, New York. Junger, M.C. and Feit, D. (1986) Sound, Structures, and Their Interaction MIT Press, Cambridge. Lazan, B.J. (1968) Damping of Materials and Members in Structural Mechanics. Pergamon Press, Oxford. Lighthill, M.J. (1952) On sound generated aerodynamically. I. General theory, Proceedings Royal Society (London) 222A: Lighthill, M.J. (1954) On sound generated aerodynamically. II. Turbulence as a source of sound, Proceedings Royal Society (London) 231A:1 32. Nashif, A.D., Jones, D.I.G. and Henderson, J.P. (1985) Vibration Damping. John Wiley & Sons, NY. Preumont, A. (1997) Vibration Control of Active Structures An Introduction. Kluwer Academic Publ. Sears, W.R. (1941) Some aspects of non-stationary airfoil theory and its practical applications, Journal of the Aeronautical Sciences 8: Ungar, E.E. (1971) Damping of panels, Noise and Vibration Control (L.L. Beranek, ed.) , McGraw-Hill, New York. Vinogradov, Aleksandra M. and Frank Holloway (1997) Mechanical testing and characterization of PVDF, a thin film piezoelectric polymer, Journal of Advanced Materials 29: Vinogradov, Aleksandra M. and Frank Holloway (1999) Cyclic creep of piezoelectric polymer polyvinylidene fluoride, AIAA Journal 39: Vinogradov, Aleksandra M. and S. C. Schumacher (2001) Electro-mechanical properties of of the piezoelectric polymer PVDF, Ferroelectrics 226: Vinogradov, Aleksandra M. (2001) Nonlinear characteristics of piezoelectric polymers, Proceedings of 2001 ASME International Mechanical Congress and Exposition, IMECE 2001/AD Yi, S. and Hilton, H.H. (1994) Dynamic finite element analysis of viscoelastic composite plates in the time domain, International Journal for Numerical Methods in Engineering 37: Yi, S., Ahmad, M.F. and Hilton, H.H. (1996) Dynamic responses of plates with viscoelastic damping treatment, ASME Journal of Vibration and Acoustics 118: Yi, S., Ling, S.F., Ying, M., Hilton, H.H. and Vinson, J.R. (1999) Finite element formulation for anisotropic coupled piezo-hygro-thermo-viscoelasto-dynamic problems, International Journal of Numerical Methods in Engineering 45:

6 Fig. 8 STRESS INVARIANTS 1 APPLIEAD STRESS INVARIANTS NO CONTROL MAXIMUM AMPLITUDE APPLIED STRESS INVARIANTS WITH CONTROL FAILURE STRESS INVARIANTS * FAILURE * SURVIVAL TIME (t /τ 0 ) * 6

7 Fig. 9 PROBABILITY OF DELAMINATION ONSET 0 LOG (DELAMINATION PROBABILITY) NO 80 0 C NO 20 0 C PIEZO 80 0 C -20 PIEZO 20 0 C SURVIVAL TIME (t / τ 0 ) 7