Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Stochastic free vibration analysis of smart random composite plates

  • Singh, B.N. (Department of Aerospace Engineering, Indian Institute of Technology) ;
  • Vyas, N. (Department of Aerospace Engineering, Indian Institute of Technology) ;
  • Dash, P. (Department of Aerospace Engineering, Indian Institute of Technology)
  • Received : 2008.03.01
  • Accepted : 2008.07.13
  • Published : 2009.03.30
⟨ Previous Next ⟩

Abstract

The present study is concerned with the stochastic linear free vibration study of laminated composite plate embedded with piezoelectric layers with random material properties. The system equations are derived using higher order shear deformation theory. The lamina material properties of the laminate are modeled as basic random variables for accurate prediction of the system behavior. A $C^0$ finite element is used for spatial descretization of the laminate. First order Taylor series based mean centered perturbation technique in conjunction with finite element method is outlined for the problem. The outlined probabilistic approach is used to obtain typical numerical results, i.e., the mean and standard deviation of natural frequency. Different combinations of simply supported, clamped and free boundary conditions are considered. The effect of side to thickness ratio, aspect ratio, lamination scheme on scattering of natural frequency is studied. The results are compared with those available in literature and an independent Monte Carlo simulation.

Keywords

References

  1. Chen, X.L., Hua, H.X. and Liu, Y.J. (2000), 'A higher-order FEM for vibration control of composite plates with distributed piezoelectric sensors and actuators', Proceedings of Advances in Computational Engineering & Sciences, Tech Science Press, 1506-151
  2. Correia Franco, V.M., Mota Soares, C.M. and Mota Soares, C.A. (1997), 'Higher order models on the eigen frequency analysis and optimal design of laminated composite structures', Compos. Struct., 39(3-4), 237-253 https://doi.org/10.1016/S0263-8223(97)00118-9
  3. Correia Franco, V.M., Aguiar Gomes M.A., Suleman, A.S., Suleman, A., Mota Soares, C.M. and Mota Soares, C.A. (2000), 'Modelling and design of adaptive composite structures', Comput. Meth. Appl. Mech. Eng., 185, 325-346 https://doi.org/10.1016/S0045-7825(99)00265-0
  4. Englested, S.P. and Reddy, J.N. (1994), 'Probabilistic methods for the analysis of metal matrix composite', Compos. Sci. Technol., 50, 91-107 https://doi.org/10.1016/0266-3538(94)90129-5
  5. Huang, J.H. and Tseng, L.W. (1996), 'Analysis of hybrid multilayered piezoelectric plates”' Int. J. Eng. Sci., 34(2), 171-181 https://doi.org/10.1016/0020-7225(95)00087-9
  6. Ibrahim, R.A. (1987), 'Structural dynamics with parameter uncertainties', Appl. Mech. Rev., 40, 309-328 https://doi.org/10.1115/1.3149532
  7. Kleiber, M. and Hein, T.D. (1992), The Stochastic Finite Element Method, Wiley, Chichester, U. K
  8. Liessa, A.W. and Martin, A.F. (1990), 'Vibration and buckling of rectangular of composite plates with variable fibre spacing', Compos. Struct., 14, 339-357 https://doi.org/10.1016/0263-8223(90)90014-6
  9. Liu, W.K., Belytschko, T. and Mani, A. (1986), 'Random field finite elements', Int. J. Numer. Meth. Eng., 23, 1831-1845 https://doi.org/10.1002/nme.1620231004
  10. Manohar, C.S. and Ibrahim, R.A. (1999), 'Progress in structural dynamics with stochastic parameter variations: 1987-1998', Appl. Mech. Rev., 52, 177-196 https://doi.org/10.1115/1.3098933
  11. Nakagiri, S., Tatabatake, H. and Tani, S. (1990), 'Uncertain eigen value analysis of composite laminated plate by sfem', Compos. Struct. 14, 9-12
  12. Naveenthraj, B., Iyengar, N.G.R. and Yadav, D. (1998), 'Response of composite plates with random material properties using FEM and Monte Carlo simulation', Adv. Compos. Mater., 7(3), 219-237 https://doi.org/10.1163/156855198X00165
  13. Nigam, N.C. and Narayanan, S. (1994), Application of Random Vibrations, Springer-Verlag, Narosa Publishing House, NewDelhi
  14. Onkar, A.K. and Yadav, D. (2003), 'Non-linear response statistics of composite laminates with random material properties under random loading', Compos. Struct., 60, 375-383 https://doi.org/10.1016/S0263-8223(03)00049-7
  15. Reddy, J.N. (1984), A simple higher-order theory for laminated composite plates', J. Appl. Mech., ASME, 51, 745-752 https://doi.org/10.1115/1.3167719
  16. Sadek, I.S., Bruch Jr., J.C., Sloss, J.M. and Adali, S. (2003), 'Feedback control of vibrating plates with piezoelectric patch sensors and actuators', Compos. Struct., 62, 397-402 https://doi.org/10.1016/j.compstruct.2003.09.011
  17. Salim, S., Yadav, D. and Iyengar, N.G.R. (1993), 'Analysis of composite plates with random material characteristics', Mech. Res. Commun., 20(5), 405-414 https://doi.org/10.1016/0093-6413(93)90031-I
  18. Saravanos, A.D., Heyliger, R.P. and Hopkins, A.D. (1997), 'Layer wise mechanics and finite element for the dynamic analysis of piezoelectric composite plates', Int. J. Solid Struct., 34(3), 359-378 https://doi.org/10.1016/S0020-7683(96)00012-1
  19. Shu, X. (2005), 'Free vibration of laminated piezoelectric composite plates based on an accurate theory', Comput. Struct., 67, 375-382 https://doi.org/10.1016/j.compstruct.2004.01.022
  20. Simoes Moita, J.M., Correia, I.F.P., Mota Soares, C.M. and Mota Soares, C.A. (2004), 'Active control of adaptive laminated structures with bonded piezoelectric sensors and actuators', Comput. Struct., 82, 1349-1358 https://doi.org/10.1016/j.compstruc.2004.03.030
  21. Singh, B.N., Iyengar, N.G.R. and Yadav, D. (2002), ' Stability of curved composite panels with random material properties', J. Aerospace. Eng., ASCE, 15, 46-54 https://doi.org/10.1061/(ASCE)0893-1321(2002)15:2(46)
  22. Singh, B.N., Yadav, D. and Iyengar, N.G.R. (2001), 'Natural frequencies of composite plates with random material properties using higher-order shear deformation theory', Int. J. Mech. Sci., 43, 2193-2214 https://doi.org/10.1016/S0020-7403(01)00046-7
  23. Tiersten, H.F. (1969), Linear Piezoelectric Plate Vibrations, Plenum Press, New York
  24. Tripathi, V., Singh, B.N. and Shukla, K.K. (2007), 'Free vibration of laminated composite conical shells with random material properties', Compos. Struct., 81(1), 96-104 https://doi.org/10.1016/j.compstruct.2006.08.002
  25. Tzou H.S. and Tseng C.I. (1991), 'Distributed modal identification and vibration control of continua: Piezoelectric finite element formulation and analysis', J. Appl. Mech. - T ASME, 113, 500-505 https://doi.org/10.1115/1.2896438
  26. Umrao, A., Singh, B.N., Shukla, K.K. and Vyas, N. (2008), 'Second-order statistics of natural frequencies of smart laminated composite plates with random material properties', J. Smart Struct. Syst., 4(1), 1-11 https://doi.org/10.12989/sss.2008.4.1.001
  27. Zang, Z. and Chen, S. (1991), 'The standard deviations of the eigen solutions for random MDOF systems', Compos. Struct., 39(6), 603-607 https://doi.org/10.1016/0045-7949(91)90201-V
  28. Zhou, X. and Chattopadhyay, H.G. (2000), 'Dynamic responses of smart composites using a coupled thermopiezoelectriccmechanical model', AIAA J., 38(10), 1939-1949 https://doi.org/10.2514/2.848

Cited by

  1. Uncertainty analysis of a structural–acoustic problem using imprecise probabilities based on p-box representations vol.80, 2016, https://doi.org/10.1016/j.ymssp.2016.04.009
  2. Hybrid probabilistic interval analysis of bar structures with uncertainty using a mixed perturbation Monte-Carlo method vol.47, pp.7, 2011, https://doi.org/10.1016/j.finel.2011.01.007
  3. Hybrid uncertain analysis for the prediction of exterior acoustic field with interval and random parameters vol.141, 2014, https://doi.org/10.1016/j.compstruc.2014.05.004
  4. Geometrically Nonlinear Free Vibration of Laminated Composite Plate Embedded With Piezoelectric Layers Having Uncertain Material Properties vol.134, pp.6, 2012, https://doi.org/10.1115/1.4006757
  5. Evidence-theory-based analysis for the prediction of exterior acoustic field with epistemic uncertainties vol.50, 2015, https://doi.org/10.1016/j.enganabound.2014.09.014
  6. Stochastic Nonlinear Free Vibration Analysis of Piezolaminated Composite Conical Shell Panel Subjected to Thermoelectromechanical Loading With Random Material Properties vol.79, pp.6, 2012, https://doi.org/10.1115/1.4006765
  7. Stochastic nonlinear bending analysis of piezoelectric laminated composite plates with uncertainty in material properties vol.49, pp.2, 2009, https://doi.org/10.1080/15397734.2019.1674663