Nonlinear Vibrations Of Axisymmetric Circular
Plates With Variable Thickness
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
Related Book
Other papers in this volume
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