Steel and Composite Structures

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Postbuckling and nonlinear vibration of composite laminated trapezoidal plates

  • Jiang, Guoqing (College of Mechanical Engineering, Beijing University of Technology) ;
  • Li, Fengming (College of Mechanical Engineering, Beijing University of Technology) ;
  • Zhang, Chuanzeng (Department of Civil Engineering, University of Siegen)
  • Received : 2017.04.06
  • Accepted : 2017.09.23
  • Published : 2018.01.10
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Abstract

The thermal effects on the buckling, postbuckling and nonlinear vibration behaviors of composite laminated trapezoidal plates are studied. Aiming at the complex plate structure and to simulate the temperature distribution of the plate, a finite element method (FEM) is applied in this paper. In the temperature model, based on the thermal diffusion equation, the Galerkin's method is employed to establish the temperature equation of the composite laminated trapezoidal plate. The geometrical nonlinearity of the plate is considered by using the von Karman large deformation theory, and combining the thermal model and aeroelastic model, Hamilton's principle is employed to establish the thermoelastic equation of motion of the composite laminated trapezoidal plate. The thermal buckling and postbuckling of the composite laminated rectangular plate are analyzed to verify the validity and correctness of the present methodology by comparing with the results reported in the literature. Moreover, the effects of the temperature with the ply-angle on the thermal buckling and postbuckling of the composite laminated trapezoidal plates are studied, the thermal effects on the nonlinear vibration behaviors of the composite laminated trapezoidal plates are discussed, and the frequency-response curves are also presented for the different temperatures and ply angles.

Keywords

Acknowledgement

Supported by : National Natural Science Foundation of China

References

  1. Amabili, M. and Carra, S. (2009), "Thermal effects on geometrically nonlinear vibrations of rectangular plates with fixed edges", J. Sound Vib., 321(3-5), 936-954. https://doi.org/10.1016/j.jsv.2008.10.004
  2. Attia, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2015), "Free vibration analysis of functionally graded plates with temperature-dependent properties using various four variable refined plate theories", Steel Compos. Struct., 18(1), 187-212. https://doi.org/10.12989/scs.2015.18.1.187
  3. Bhimaraddi, A. (1993), "Nonlinear vibrations of heated antisymmetric angle-ply laminated plates", Int. J. Solid. Struct., 30(9), 1255-1268. https://doi.org/10.1016/0020-7683(93)90015-Y
  4. Chen C.S., Tsai T.C., Chen W.R. and Wei C.L. (2013b), "Dynamic stability analysis of laminated composite plates in thermal environments", Steel Compos. Struct., 15(1), 57-79. https://doi.org/10.12989/scs.2013.15.1.57
  5. Chen, C.S., Chen, C.W., Chen, W.R. and Chang, Y.C. (2013a), "Thermally induced vibration and stability of laminated composite plates with temperature-dependent properties", Meccanica, 48(9), 2311-2323. https://doi.org/10.1007/s11012-013-9750-7
  6. Chen, H. and Lawrence, N.V. (2006), "Finite element analysis of post-buckling dynamics in plates. I: An asymptotic approach", Int. J. Solid. Struct., 43(13), 3983-4007. https://doi.org/10.1016/j.ijsolstr.2005.04.036
  7. Chen, L.W. and Chen, L.Y. (1989), "Thermal postbuckling analysis of laminated composite plates by the finite element method", Compos. Struct., 12(4), 257-270. https://doi.org/10.1016/0263-8223(89)90075-5
  8. Geng, Q., Li, H. and Li, Y. (2014), "Dynamic and acoustic response of a clamped rectangular plate in thermal environments: Experiment and numerical simulation", J. Acoust. Soc. Am., 135(5), 2674-2682. https://doi.org/10.1121/1.4870483
  9. Gupta, A.K. and Sharma, S. (2010), "Thermally induced vibration of orthotropic trapezoidal plate of linearly varying thickness", J. Vib. Control, 17(10), 1591-1598. https://doi.org/10.1177/1077546310384641
  10. Gupta, A.K. and Sharma, S. (2014), "Free transverse vibration of orthotropic thin trapezoidal plate of parabolically varying thickness subjected to linear temperature distribution", Shock Vib., 2014, Article ID 392325.
  11. Heuer, R., Irschik, H. and Ziegler, F. (1993), "Nonlinear random vibrations of thermally buckled skew plates", Prob. Eng. Mech., 8(3-4), 265-271. https://doi.org/10.1016/0266-8920(93)90020-V
  12. Huang, X.L. and Shen, H.S. (2004), "Nonlinear vibration and dynamic response of functionally graded plates in thermal environments", Int. J. Solid. Struct., 41(9-10), 2403-2427. https://doi.org/10.1016/j.ijsolstr.2003.11.012
  13. Jaberzadeh, E., Azhari, M. and Boroomand, B. (2013), "Thermal buckling of functionally graded skew and trapezoidal plates with different boundary conditions using the element-free Galerkin method", Eur. J. Mech. A/Solid., 42, 18-26. https://doi.org/10.1016/j.euromechsol.2013.03.006
  14. Jeyaray, P. (2013), "Buckling and free vibration behavior of an isotropic plate under nonuniform thermal load", Int. J. Struct. Stab. Dyn., 13(3), 1250071. https://doi.org/10.1142/S021945541250071X
  15. Jiang, G.Q., Li, F.M. and Li, X.W. (2016), "Nonlinear vibration analysis of composite laminated trapezoidal plates", Steel Compos. Struct., 21(2), 395-409. https://doi.org/10.12989/scs.2016.21.2.395
  16. Kundu, C.K. and Sinha, P.K. (2007), "Post buckling analysis of laminated composite shells", Compos. Struct., 78(3), 316-324. https://doi.org/10.1016/j.compstruct.2005.10.005
  17. Liew, K.M., Yang J. and Kitipornchai S. (2003), "Postbuckling of piezoelectric FGM plates subject to thermo-electro-mechanical loading", Int. J. Solid. Struct., 40(15), 3869-3892. https://doi.org/10.1016/S0020-7683(03)00096-9
  18. Liu, C.F. and Huang, C.H. (1996), "Free vibration of composite laminated plates subjected to temperature changes", Compos. Struct., 60(1), 95-101. https://doi.org/10.1016/0045-7949(95)00358-4
  19. Malekzadeh, P., Shahpari, S.A. and Ziaee, H.R. (2010), "Threedimensional free vibration of thick functionally graded annular plates in thermal environment", J. Sound Vib., 329(4), 425-442. https://doi.org/10.1016/j.jsv.2009.09.025
  20. Matsunaga, H. (2005), "Thermal buckling of cross-ply laminated composite and sandwich plates according to a global higherorder deformation theory", Compos. Struct., 68(4), 439-454. https://doi.org/10.1016/j.compstruct.2004.04.010
  21. Meyers, C.A. and Hyer, M.W. (1991), "Thermal buckling and postbuckling of symmetrically laminated composite plates", J. Therm. Stress., 14(4), 519-540. https://doi.org/10.1080/01495739108927083
  22. Moradi, S. and Mansouri, M.H. (2012), "Thermal buckling analysis of shear deformable laminated orthotropic plates by differential quadrature", Steel Compos. Struct., 12(2), 129-147. https://doi.org/10.12989/scs.2012.12.2.129
  23. Pandey, R., Shukla, K.K. and Jain, A. (2009), "Thermoelastic stability analysis of laminated composite plates: An analytical approach", Commun. Nonlin. Sci. Numer. Simul., 14(4), 1679-1699. https://doi.org/10.1016/j.cnsns.2008.02.010
  24. Pandey, S. and Pradyumna, S. (2015), "Free vibration of functionally graded sandwich plates in thermal environment using a layerwise theory", Eur. J. Mech. A/Solid., 51, 55-66. https://doi.org/10.1016/j.euromechsol.2014.12.001
  25. Shiau, L.C., Kuo, S.Y. and Chen, C.Y. (2010), "Thermal buckling behavior of composite laminated plates", Compos. Struct., 92(2), 508-514. https://doi.org/10.1016/j.compstruct.2009.08.035
  26. Singha, M.K., Ramachandra, L.S. and Bandyopadhyay J.N. (2006), "Vibration behavior of thermally stressed composite skew plate", J. Sound Vib., 296(4-5), 1093-1102. https://doi.org/10.1016/j.jsv.2006.01.070
  27. Sundararajan, N., Prakash, T. and Ganapathi, M. (2005), "Nonlinear free flexural vibrations of functionally graded rectangular and skew plates under thermal environments", Finite Elem. Anal. Des., 42(2), 152-168. https://doi.org/10.1016/j.finel.2005.06.001
  28. Taj, M.G., Chakrabarti, A. and Prakash, V. (2014), "Vibration characteristics of functionally graded material skew plate in thermal environment", Int. J. Mech. Aerosp. Indus. Mech. Eng., 8(1), 142-153.
  29. Vosoughi, A.R., Malekzadeh, P. and Banan, M.R. (2011), "Thermal postbuckling of laminated composite skew plates with temperature-dependent properties", Thin Wall. Struct., 49(7), 913-922. https://doi.org/10.1016/j.tws.2011.02.017
  30. Zhou, F.X., Li, S.R. and Lai, Y.M. (2011), "Three-dimensional analysis for transient coupled thermoelastic response of a functionally graded rectangular plate", J. Sound Vib., 330(16), 3990-4001. https://doi.org/10.1016/j.jsv.2011.03.015

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