Nonlinear Forced Vibration Analysis for Thin Rectangular Plate on Nonlinear Elastic Foundation

Abstract

In this paper, nonlinear forced vibration analysis for thin rectangular plate with four free edges on nonlinear elastic foundation is researched. Based on Hamilton variation principle, the equations of nonlinear vibration motion for the thin rectangular plate under period loads on nonlinear elastic foundation are established. In the case of four free edges, the suitable expressions of trial functions satisfied all boundary conditions for the problem are proposed. Then, we convert the equations to a system of nonlinear algebraic equations by using Galerkin method and they are solved by using harmonic balance method. In the analysis of numerical computations, the effect to the amplitude-frequency characteristic curve which due to change of the structural parameters of plate、the parameters of foundation and the parameters of excitation force are discussed.