Large-amplitude vibration of an initially stressed plate on elastic foundations

Abstract

Non-linear partial differential equations of motion for a Mindlin plate subjected to non-uniform initial stress were derived, in this study, from Hamilton's principle in order to investigate the large-amplitude vibration of an initially stressed plate on various elastic foundations. Three foundations, Winkler linear, Winkler non-linear and Pasternak foundations, were used in this study to describe plate–foundation interactions. The initial stress was taken to be a combination of a pure bending stress and an extensional stress in the plane of the plate. The effects of initial stress, amplitude of vibration and stiffness of foundation on the large-amplitude vibration of a Mindlin plate on various elastic foundations are discussed in this paper.