A Rayleigh-Ritz approach to transverse vibration of isotropic and anisotropic trapezoidal plates using orthogonal plate functions

Abstract To overcome the lack of a more general method for free vibration analysis of trapezoidal plates, a computationally efficient and highly accurate Rayleigh-Ritz approach with the newly-developed orthogonal plate functions is proposed to solve these problems with any combination of clamped, simply-supported and free edge support conditions. The deflection of the plate is approximated by a set of two-dimensional orthogonal plate functions, generated using the Gram-Schmidt procedure, which expresses the entire plate domain into two implicitly related variables. In the present paper, the effects of the fibre orientation on the vibrational behaviour of the plates are considered. The numerical results for isotropic and anisotropic trapezoidal plates are presented. Where possible, the numerical results are verified with other existing values in the literature.

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