Nonlinear free vibration of a shear deformable laminated composite annular elliptical plate

The nonlinear free vibration of a laminated composite annular elliptical plate with elliptically orthotropic plies is investigated. The effects of out-of-plane shear deformations, rotatory inertia and geometrical nonlinearity are taken into account. The problem is solved numerically using a new polynomially enriched sector elliptic p-element. The nonlinear equations of free motion are obtained using the harmonic balance method and solved iteratively by the linearized updated mode method. Results for the fundamental linear and nonlinear frequencies are obtained. Comparison is made with published results for a polar orthotropic annular plate and shows very good agreement. The minor semi-axis ratio, thickness ratio, moduli ratio, number of plies, layup sequence, and boundary conditions are shown to influence the hardening behavior.