Vibration of plates considering shear and rotatory inertia

Abstract

Introduction T HE large-amplitude vibrations of plates and shells have been receiving considerable attention in the literature in recent years. In particular, rectangular plates have received the attention of many investigators. The results reported so far do not, in many cases, seem to incorporate the effects of transverse shear and rotatory inertia, Wu and Vinson investigated the effects of transverse shear and rotatory inertia on the large-amplitude vibration of isotropic, transversely isotropic, and orthotropic rectangular plates, based on assumed expressions not only for the mode shape w but also for the rotation components a. and j3. The purpose here is to suggest an improvement to the solutions given by Wu and Vinson by altogether eliminating a and 6 from the governing equations, thereby avoiding the necessity to proceed on assumed approximations for a. and /?. The equations developed here are based on Berger approximation. Based on Galerkin's method and an assumption of only mode shape w, the effects of geometric nonlinearity, transverse shear deformation, and rotatory inertia are reported for certain cases of isotropic and orthotropic rectangular plates clamped along the boundaries,