Solution for large amplitude vibrations of circular plates via modified Berger's approximation

摘要

Complex mathematical formulations for the geometrically nonlinear analysis of structural members have been presented by many researchers using the von-Karman strain-displacement relations. Berger proposed a simplifying approximation to take care of the geometric nonlinearity by neglecting the second strain invariant. Although it is a reasonable approximation, it poses problems when applied to circular plates. This is mainly due to the coupling between the radial and circumferential inplane strains, by the radial displacement. In this article, a modification to the Berger's approximation, applicable to the circular plates, is proposed. The main motivation of the present study is to examine how the modified Berger's approximation works in the case of the large amplitude vibrations of circular plates. It is shown that the modified Berger's approximation gives consistently accurate results, for both the simply supported and clamped circular plates, when compared to the classical results.