Transverse vibration of trapezoidal plates having some combinations of clamped and simply supported edge conditions

Free lateral vibrations of isotropic and anisotropic trapezoidal plates that have clamped and simply supported mixed boundary conditions has been investigated by using Galerkin's method. The shape function is assumed as a multiplication of two parts: The first part satisfies the essential boundary conditions associated to the plate edges and the second one represent the deflection distribution over the plate surface with respect to that of a certain origin in the plate domain. The convergence of results is ensured by considering some successive different expansions of the deflection function. To demonstrate the accuracy of the present solutions, several numerical examples are analyzed and the results are compared with those available in the literature. A series of tables and graphs that indicate the variation of the natural frequency coefficients with both the geometry and the boundary conditions of the plate are presented. The effect of variation of the composite filament angle on the natural frequency coefficients of clamped plates is also studied.