Dynamic and static nonlinear analysis of generally laminated imperfect plates having nonuniform boundary conditions and resting on elastic foundation

A multimode solution to the dynamic von Kármán-type nonlinear equations is presented for the titled plates. The plate edges subjected to inplane forces are elastically restrained against rotation. The variation of rotational stiffness is assumed identical along parallel edges. Generalized double Fourier series with the time-dependent coefficients and the method of harmonic balance are used in the formulation of the solution. Nonlinear bending and postbuckling of the laminate are treated as special cases. Numerical results are presented for nonlinear free vibration and postbuckling of antisymmetric angle-ply and cross-ply laminates.