Analytical Solution of Free Vibration of Thick Transversely Isotropic Rectangular Plates, Based on First Order Shear Deformation Theory

In this paper, a reformulation for equations of motion for transversely isotropic plates has been obtained based on first shear deformation theory. Unlike the three coupled original equations, this new reformulation consists of two decoupled partial differential equations which can be solved much easier. For free vibration analysis of transversely isotropic plates, the mentioned equations have been solved for two cases. In the first case, using double Fourier series, closed-form solution has been achieved for natural frequencies of simply supported plates. In the second case, free vibration of a plate with arbitrary boundary conditions in two parallel edges has been considered. In order to satisfy the arbitray boundary conditions, some relations have been presented for unknown functions of the original system of equations in terms of the unknowns of the decoupled equations. Finally, numerical results for six possible cases of classical boundary conditions have been presented. Besides, some important results of the presented analysis have been presented for transversely isotropic plates. The results show that despite of the small differences between the natural frequencies of the thin isotropic and transversely isotropic plates, the differences are more significant for the natural frequencies of the thick plate. Also, effects of increasing thickness on the value of natural frequencies for transversely isotropic plates are more than the isotropic ones.