VIBRATION OF CLAMPED MODERATELY THICK GENERAL CROSS-PLY PLATES USING A GENERALIZED NAVIER APPROACH

A hitherto unavailable analytical solution to the free vibration probl em of general cross-ply laminated rigidly clamped rectangular plates, incorporating first-order shear deformation, and rotatory and in-plane inertias into the formulation, is presented. A recently developed bou ndary continuous displacement-based generalized Navier solution techni que is used to solve the five highly coupled linear second-order parti al differential equations with constant coefficients, and the associat ed geometric boundary conditions. The assumed solution functions are i n the form of double Fourier series, which satisfy the rigidly clamped boundary conditions a priori in a manner similar to the conventional Navier method. Convergence characteristics of the natural frequencies of both symmetric and antisymmetric cross-ply plates are numerically e stablished. Other numerical results presented herein include (i) compa rison with the corresponding available first-order shear deformation t heory-based Galerkin and classical lamination theory-based boundary-di scontinuous analytical solutions, and (ii) study of the effects of thi ckness and aspect ratio on the natural frequencies.