Large-amplitude vibration of an initially imperfect moderately thick plate

Non-linear equations of motion for a transversely isotropic plate having initial geometric imperfection are derived. The effects of both transverse shear deformation and rotatory inertia are included. Based on the assumed mode shapes that satisfy the geometric boundary conditions, the modal equation of motion for a simply supported imperfect plate is obtained by performing the Galerkin procedure and then solved by the Runge-Kutta method. It is found that the vibration frequencies are very much dependent on the order of initial amplitude and imperfection and the large amplitude vibration behavior may change drastically from the well known hard-spring to soft-spring vibration under the existence of initial imperfection. The effects of various parameters versus the frequencies are also studied in detail.