The Study of the Vibration Characteristic of Plate Using the Third Order Shear Deformation Theory

In this paper, an analytical method is presented for studying the vibration characteristic of plate using the third order shear deformation theory (TSDT) on different boundary conditions, which are the any combinations of simply supported, free and clamped. Hamilton principle is used to formulate the governing equations. Then, the method of separation of variable is used to get the solutions of the three partial differential equations. Last, we take the obtained modal functions, which are the series of the corresponding fundamental functions, as the admissible function of the Rayleigh-Ritz method. The natural frequencies and mode shapes function are obtained by using the Rayleigh-Ritz method. The method in this paper has a good generality for solving the vibration problems of thick plates under different boundary conditions.