Author(s)

M. S. Nerantzaki & J. T. Katsikadelis

Abstract

The BEM is developed for nonlinear vibration analysis of axisymmetric circular plates with variable thickness undergoing large deflections. General boundary conditions are considered which may be also nonlinear. The problem is formulated in terms of displacements. The solution is based on the concept of the analog equation, according to which the two coupled nonlinear differential equations with variable coefficients, pertaining to the inplane radial and transverse deformation, are converted to two uncoupled linear ones of a substitute beam with unit axial and unit bending stiffness, respectively, under fictitious quasi-static load distributions. Numerical examples are presented, which illustrate the method and demonstrate its efficiency and accuracy. Keywords: circular plate, nonlinear, vibrations, large deflections, variable thickness, boundary elements, analog equation method. 1 Introduction Although much progress has been made in the plate bending analysis by the BEM, only few articles have been published on the analysis of plates with variable thickness. The reason is that the differential equations, which govern the response of the plate, have variable coefficients and thus no fundamental solution is available to derive the boundary integral equations. The problem becomes much more complicated when large deflections are considered. In this case the governing differential equations are coupled and nonlinear in addition to having variable coefficients. For the nonlinear static problem a BEM solution based on the AEM (Analog Equation Method) for arbitrary shaped plate with variable thickness has been presented by Nerantzaki and Katsikadelis [1]. For

Keywords

circular plate, nonlinear, vibrations, large deflections, variable thickness, boundary elements, analog equation method