FREE-VIBRATION OF CLAMPED, MODERATELY THICK, ARBITRARILY LAMINATED PLATES USING A GENERALIZED NAVIERS APPROACH

A heretofore unavailable analytical solution to the boundary value pro blem of free vibration of arbitrarily laminated moderately thick recta ngular plates is presented. The YNS (Yang, Norris and Stavsky) theory incorporating first order shear deformation, and rotatory and in-plane inertias, is used in the formulation. A recently developed boundary-c ontinuous displacement-based generalized Navier solution technique is extended to solve the five highly coupled linear second order partial differential equations with constant coefficients, and the rigidly cla mped boundary conditions. The assumed solution functions are in the fo rm of double Fourier series, which satisfy the rigidly clamped boundar y conditions a priori in a manner similar to the conventional Navier m ethod. Convergence characteristics (necessary condition) of the natura l frequencies are established by numerical means. Other numerical resu lts presented herein include (i) comparison with the corresponding ava ilable analytical and Galerkin solutions, and (ii) study of the effect s of lamination, thickness, aspect ratio and fiber orientation angle o n the natural frequencies of angle-ply and arbitrarily laminated plate s.