Non-linear vibration of initially stressed plates with initial imperfections

Abstract

Non-linear partial differential equations of vibration for isotropic plates having initial imperfection are derived. The derivation based on the classical plate theory aims to describe non-linear vibration of imperfect plates in a general state of arbitrary initial stresses. Galerkin method is used to reduce the non-linear partial differential equations to ordinary non-linear differential equations. Runge-Kutta method is used to obtain the non-linear and linear frequencies of vibration. A numerical example is presented to discuss the performances of perfect and imperfect plates. The initial stress is taken to be a combination of pure bending stress plus an extension stress in the plane of the plate. It is found that the existence of initial vibration amplitude, initial stress and geometric imperfect may result in a drastic change on the non-linear vibration behavior. The effects of various parameters on the non-linear free vibrations are discussed.