Three-dimensional vibration analysis of rectangular plates based on differential quadrature method

This paper presents the formulation and numerical analysis of the three-dimensional elasticity plate model using the differential quadrature (DQ) method. The governing equations in terms of displacement, stress displacement relations, and boundary conditions for the three-dimensional plate model are first presented. These equations are then normalized and discretized using the DQ procedure. Example problems on the free vibration of rectangular plates with generic boundary conditions are selected. Two types of mesh pattern, the uniform mesh pattern and the cosine mesh pattern, were used and their convergence characteristics were studied. The cosine mesh was then chosen as the better mesh pattern pertaining to the problems solved. The solutions calculated using the cosine mesh pattern were then compared, where possible, with the exact or the numerical or the analytical solutions. It is found that the differential quadrature method yields accurate results for the plate problems under the current investigation. © 1999 Academic Press.