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simply-supported rhombus plate. Firstly, using coordinate transformation formula, the solution domain for a rhombus plate is converted into a rectangular one, and the governing equations and the corresponding boundary conditions for the plate in the transformed rectangular domain are obtained. Then, combined with the Fourier series expansion and the perturbation theory, the equation is written in a first order ordinary differential matrix form. Next, the transfer matrix method is used to solve the matrix equations, in order to get the natural frequencies of the free vibration plate. Finally, numerical results are compared with the ones obtained by the finite element method. Example results show that when the difference between the rhombus angle and the corresponding rectangular angle is in a small range, the transfer matrix method proposed in this paper can be applied to analyze the dynamic characteristics of a rhombus plate.

Free vibration analysis on a simply-supported rhombus plate by using transfer matrix method