Structural Engineering and Mechanics

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Natural frequency of laminated composite plate resting on an elastic foundation with uncertain system properties

  • Lal, Achchhe (Department of Applied Mechanics, MNNIT) ;
  • Singh, B.N. (Department of Aerospace Engineering, IIT) ;
  • Kumar, Rakesh (Department of Applied Mechanics, MNNIT)
  • Received : 2006.02.17
  • Accepted : 2007.04.05
  • Published : 2007.09.30
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Abstract

Composite laminated structures supported on elastic foundations are being increasingly used in a great variety of engineering applications. Composites exhibit larger dispersion in their material properties compared to the conventional materials due to large number of parameters associated with their manufacturing and fabrication processes. And also the dispersion in elastic foundation stiffness parameter is inherent due to inaccurate modeling and determination of elastic foundation properties in practice. For a better modeling of the material properties and foundation, these are treated as random variables. This paper deals with effects of randomness in material properties and foundation stiffness parameters on the free vibration response of laminated composite plate resting on an elastic foundation. A $C^0$ finite element method has been used for arriving at an eigen value problem. Higher order shear deformation theory has been used to model the displacement field. A mean centered first order perturbation technique has been employed to handle randomness in system properties for obtaining the stochastic characteristic of frequency response. It is observed that small amount of variations in random material properties and foundation stiffness parameters significantly affect the free vibration response of the laminated composite plate. The results have been compared with those available in the literature and an independent Monte Carlo simulation.

Keywords

References

  1. Aiello, M.A. and Ombres, L. (1999), 'Buckling and vibration of unsymmetric laminates resting on elastic foundations under in-plane and shear forces', Compos. Struct., 44, 31-41 https://doi.org/10.1016/S0263-8223(98)00116-0
  2. Handian, J. and Nayfeh, A.H. (1993), 'Free vibration and buckling of shear deformable cross-ply laminated plates using the state-space concept', Compos. Struct., 48, 667-693
  3. Huang, X.-L. and Zheng, J.-J. (2003), 'Nonlinear vibration and dynamic response of simply supported shear deformable laminated plates on elastic foundations', Eng. Struct., 25, 1107-1119 https://doi.org/10.1016/S0141-0296(03)00064-6
  4. Jones, R.M. (1975), Mechanics of Composite Materials, McGraw-Hill, New York
  5. Kareem, A. and Sun, W.J. (1990), 'Dynamic response of structures with uncertain damping', Eng. Struct., 12, 1-8
  6. Kleiber, M. and Hien, T.D. (1992), The Stochastic Finite Element Method, John Wiley & Sons
  7. Lin, S.C. and Kam, T.Y. (2000), 'Probability failure analysis of transversely loaded composite plates using higher-order second moment method', J. Eng. Mech., ASCE, 126(8), 812-820 https://doi.org/10.1061/(ASCE)0733-9399(2000)126:8(812)
  8. Manohar, C.S. and Ibrahim, R.A. (1999), 'Progress in structural dynamics with stochastic parameter variations', Appl. Mech. Rev., 52, 177-196 https://doi.org/10.1115/1.3098933
  9. Naveenthraj, B., Iyengar, N.G.R. and Yadav, D. (1998), 'Response of composite plates with random material properties using FEM and MCS', Adv. Compos. Mat., 7, 219-237 https://doi.org/10.1163/156855198X00165
  10. Nigam, N.C. and Narayanan, S. (1994), Applications of Random Vibrations, Narosa, New Delhi
  11. 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
  12. Onkar, A.K., Upadhyay, C.S. and Yadav, D. (2006), 'Generalized buckling response of laminated plates with random material properties using stochastic finite elements', Int. J. Mech. Sci., 48(7), 780-798 https://doi.org/10.1016/j.ijmecsci.2006.01.002
  13. Reddy, J.N. (1984), 'A simple higher order theory for laminated composite plates', J. Appl., Mech., Trans. ASME, 51, 745-752 https://doi.org/10.1115/1.3167719
  14. Reddy, J.N. (1996), Mechanics of Laminated Composite Plate Theory and Analysis, CRC Press, Florida
  15. Reddy, J.N. and Phan, N.D. (1985), 'Stability and vibration of isotropic, orthotropic and laminated plates according to higher order shear deformation theory', J. Sound Vib., 21, 201-2219
  16. Salim, S., Iyengar, N.G.R. and Yadav, D. (1998), 'Natural frequency characteristic of composite plates with random properties', Struct. Eng. Mech., 6(6), 659-671 https://doi.org/10.12989/sem.1998.6.6.659
  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. Shankara, C.A. and Iyenger, N.G.R. (1996), 'A $C^{0}$ element for the free vibration analysis of laminated composite plates', J. Sound Vib., 191(5), 721-738 https://doi.org/10.1006/jsvi.1996.0152
  19. Shen, H.S., Zheng, J.J. and Huang, X.L. (2003), 'Dynamic response of shear deformable plates under thermo mechanical loading and resting on elastic foundations', Compos. Struct., 60, 57-66 https://doi.org/10.1016/S0263-8223(02)00295-7
  20. Singh, B.N., Yadav, D. and Iyengar, N.G.R. (2001), 'Natural frequencies of composite plates with random material properties', Int. J Mech. Sci., 43, 2193-2214 https://doi.org/10.1016/S0020-7403(01)00046-7
  21. Singh, B.N., Iyengar, N.G.R. and Yadav, D. (2002), 'A $C^{0}$ finite element investigation for buckling of shear deformable laminated composite plates with random material properties', Struct. Eng. Mech., 13(1), 53-74 https://doi.org/10.12989/sem.2002.13.1.053
  22. Vanmarcke, E.H. and Grigoriu, M. (1983), 'Stochastic finite element analysis of simple beam', J. Eng. Mech., ASCE, 109, 1203-1214 https://doi.org/10.1061/(ASCE)0733-9399(1983)109:5(1203)
  23. Venini, P. and Mariani, J. (2002), 'Free vibration of uncertain composite plates via Raleigh-Ritz approaches', Comput. Struct., 64(1-4), 407-423 https://doi.org/10.1016/S0045-7949(96)00161-7
  24. Yamin, Z., Chen, S. and Lue, Q. (1996), 'Stochastic perturbation finite elements', Comput. Sruct., 59(3), 425-429 https://doi.org/10.1016/0045-7949(95)00267-7
  25. Zhang, J. and Ellingwood, B. (1993), 'Effects of uncertain material properties on structural stability', J. Struct Eng., ASCE., 121, 705-716 https://doi.org/10.1061/(ASCE)0733-9445(1995)121:4(705)
  26. Zhang, Z. and Chen, S. (1990), 'The standard deviation of the eigen solutions for random multi degree freedom systems', Comput. Struct., 39(6), 603-607 https://doi.org/10.1016/0045-7949(91)90201-V

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