Effects of geometric imperfections and large amplitudes on vibrations of an initially stressed mindlin plate

Abstract

Non-linear equations of motion for a transversely isotropic plate having geometric imperfections and in a general state of non-uniform initial stresses are derived. The effects of both transverse shear deformation and rotatory inertia are included. The modal equations of a simply supported plate subjected to in-plane extensional stress and pure bending stress are obtained by performing the Galerkin procedure and then solved by the Runge-Kutta integration technique. The effects of geometric imperfections on large amplitude vibration behaviour are investigated. It is found that the vibration behaviour of an initially stressed plate is very much dependent on the order of initial amplitudes as well as geometric imperfections. The effects of various parameters on the non-linear vibration frequencies are studied.