DOI QR코드

DOI QR Code

Nonlinear dynamic response and its control of rubber components with piezoelectric patches/layers using finite element method

  • Manna, M.C. (Department of Aerospace Engineering and Applied Mechanics, Bengal Engineering and Science University) ;
  • Bhattacharyya, R. (Department of Mechanical Engineering, Indian Institute of Technology) ;
  • Sheikh, A.H. (Department of Civil, Environmental and Mining Engineering, University of Adelaide)
  • Received : 2009.03.06
  • Accepted : 2009.10.27
  • Published : 2010.11.25

Abstract

Idea of using piezoelectric materials with flexible structures made of rubber-like materials is quite novel. In this study a non-linear finite element model based on updated Lagrangian (UL) approach has been developed for dynamic response and its control of rubber-elastic material with surface-bonded PVDF patches/layers. A compressible stain energy density function has been used for the modeling of the rubber component. The results obtained are compared with available analytical solutions and other published results in some cases. Some results are reported as new results which will be useful for future references since the number of published results is not sufficient.

Keywords

References

  1. Allik, H. and Hughes, T.J. (1970), "Finite element method for piezoelectric vibration", Int. J. Numer. Meth. Eng., 2, 151-157. https://doi.org/10.1002/nme.1620020202
  2. Austin, E.M. and Ananthasayanam, B. (2002), "Modeling of piezoelectric materials on rubber beams", Proc. SPIE, 4697, 131-138.
  3. Bailey, T. and Hubbard, J.E. (1985), "Distributed piezoelectric-polymer active vibration control of a cantilever beam", J. Guid. Control Dynam., 8(5), 605-611. https://doi.org/10.2514/3.20029
  4. Bathe, K.J. (1996), Finite Element Procedures in Engineering Analysis, Prentice Hall, Englewood Cliffs.
  5. Chattopadhyay, A., Kim, H.S. and Ghosal, A. (2004), "Non-linear vibration analysis of smart composite structures with discrete delamination using a refined layerwise theory", J. Sound Vib., 273(1-2), 387-407. https://doi.org/10.1016/S0022-460X(03)00561-3
  6. Chen, S.H., Wang, Z.D. and Liu, X.H. (1997), "Active vibration control and suppression for intelligent structures", J. Sound Vib., 200(2), 167-177. https://doi.org/10.1006/jsvi.1996.0694
  7. Crawley, E.F. and de Luis, J. (1987), "Use of piezoelectric actuators as elements of intelligent structures", AIAA J., 25(10), 1373-1385. https://doi.org/10.2514/3.9792
  8. Fanson, J.L. and Caughey, T.K. (1987), "Positive position feedback control for large space structures", Proceedings of the 28th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Material Conference, Monterey, California, USA.
  9. Forward, R. (1979), "Electronic damping of vibrations in optical structures", Appl. Optics, 18(5), 690-697. https://doi.org/10.1364/AO.18.000690
  10. Gaudenzi, P., Carbonaro, R. and Benzi, E. (2000), "Control of beam vibrations by means of piezoelectric devices: theory and experiments", Compos. Struct., 50(4), 373-379. https://doi.org/10.1016/S0263-8223(00)00114-8
  11. Gent, A.N. (2001), Engineering with Rubber, 2nd Ed., Hanser Publishers.
  12. Lee, S.J., Reddy, J.N. and Rostam-Abadi, F. (2004), "Transient analysis of laminated composite plates with embedded smart-material layers", Finite Elem. Anal. Des., 40(5-6), 463-483. https://doi.org/10.1016/S0168-874X(03)00073-8
  13. Lim, C.W., He, L.H. and Soh, A.K. (2001), "Three-dimensional electromechanical responses of a parallel piezoelectric bimorph", Int. J. Solids Struct., 38, 2833-2849. https://doi.org/10.1016/S0020-7683(00)00186-4
  14. Manna, M.C., Sheikh, A.H. and Bhattacharyya, R. (2009), "Static analysis of rubber components with piezoelectric patches using nonlinear finite element", Smart Struct. Syst., 5(1), 23-42. https://doi.org/10.12989/sss.2009.5.1.023
  15. Mukherjee, A. and Chaudhuri, A.S. (2004), "Exact solutions for instability control of piezolaminated imperfect struts", AIAA J., 42(4), 857-859. https://doi.org/10.2514/1.9564
  16. Mukherjee, A. and Chaudhuri, A.S. (2005a), "Active control of piezolaminated columns - exact solutions and experimental validation", Smart Mater. Struct., 14, 475-482. https://doi.org/10.1088/0964-1726/14/4/003
  17. Mukherjee, A. and Chaudhuri, A.S. (2005b), "Nonlinear dynamic response of piezoelectric smart beams", Comput. Struct., 83, 1298-1304. https://doi.org/10.1016/j.compstruc.2004.06.008
  18. Newmark, N.M. (1959), "A method of computation for structural dynamics", J. Eng. Mech. Div. ASCE, 85, 67-94.
  19. Ogden, R.W. (1984), Non-linear Elastic Deformations, Ellis Horwood, Chichester.
  20. Olson, H.F. (1956), "Electronic control of noise, vibration, and reverberation", J. Acoust. Soc. Am., 28, 966-972. https://doi.org/10.1121/1.1908532
  21. Park, C. and Chopra, I. (1996), "Modeling piezoceramic actuation of beams in torsion", AIAA J., 34(12), 2582-2589. https://doi.org/10.2514/3.13442
  22. Peng, S.H. and Chang, W.V. (1997), "A compressible approach in finite element analysis of rubber-elastic materials", Comput. Struct., 62, 573-593. https://doi.org/10.1016/S0045-7949(96)00195-2
  23. Ray, M.C., Bhattacharyya, R. and Samanta, B. (1993), "Exact solution for static analysis of intelligent structures", AIAA J., 31(9), 1684-1691. https://doi.org/10.2514/3.11831
  24. Ray, M.C., Bhattacharyya, R. and Samanta, B. (1994), "Static analysis of an intelligent structure by the finite element method", Comput. Struct., 52(4), 617-631. https://doi.org/10.1016/0045-7949(94)90344-1
  25. Ray, M.C., Bhattacharyya, R. and Samanta, B. (1998), "Exact solutions for dynamic analysis of composite plates with distributed piezoelectric layers", Comput. Struct., 66(6), 737-743. https://doi.org/10.1016/S0045-7949(97)00126-0
  26. Samanta, B., Ray, M.C. and Bhattacharyya, R. (1996), "Finite element model for active control of intelligent structures", AIAA J., 34(9), 1885-1893. https://doi.org/10.2514/3.13322
  27. Thornburgh, R.P., Chattopadhyay, A. and Ghosal, A. (2004), "Transient vibration of smart structures using a coupled piezoelectric-mechanical theory", J. Sound Vib., 274(1-2), 53-72. https://doi.org/10.1016/S0022-460X(03)00648-5
  28. Tiersten, H.F. (1969), Linear Piezoelectric Plate Vibrations, 1st Ed., Plenum Press, New York.
  29. Ye, S., Ling, S.F. and Ying, M. (2000), "Large deformation finite element analyses of composite structures integrated with piezoelectric sensors and actuators", Finite Elem. Anal. Des., 35, 1-15. https://doi.org/10.1016/S0168-874X(99)00045-1

Cited by

  1. Stochastic free vibration analysis of laminated composite plates using polynomial correlated function expansion vol.135, 2016, https://doi.org/10.1016/j.compstruct.2015.09.044