Free vibration of composite plates using the finite difference method

The finite difference method was used to solve differential equations of motion of free vibration of composite plates with different boundary conditions. The effects of shear deformation and rotary inertia on the natural frequencies of laminated composite plates are investigated in this paper. Four cases are studied: neglecting both shear deformation and rotary inertia, considering only rotary inertia, considering only shear deformation, and considering both. Solutions were obtained for symmetric and angle-ply laminated plates. The factors that affect natural frequencies of different composite plates, such as span-to-depth ratio, aspect ratio, angle-ply, and lamination sequence were also investigated. Results were found to agree well with exact and approximate solutions reported in literature. Shear deformation showed a considerable effect on the natural frequencies for composite plates, whereas the rotary inertia effect was found to be negligible.