支持点を有する長方形板の非線形自由振動

概要

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We present an analysis of nonlinear vibration of simply supported rectangular plates with a point support. Linear free vibrations of a point-supported plate are solved by the Ritz method with Lagrange multipliers prior to the nonlinear analysis. A stress function is introduced to describe governing equations for nonlinear vibration of the plates. Eigenfunctions for the linear free vibration are used to express out-of-plane displacements, approximately, in the nonlinear analysis of the point-supported plate. Applying the Galerkin method to the governing equations, a nonlinear equation for the time function of the out-of-plane displacement is derived. Periods of vibration are calculated using the complete elliptic integral of the first kind. Period-amplitude curves are shown for several positions of the point support and the effects of the position of the point support are studied.
1996-11-25