Free vibration analysis of thin rectangular cracked plate with four free edges on nonlinear elastic foundation

摘要

In this paper, free vibration analysis on nonlinear elastic behavior of thin rectangular plate with four free edges is investigated. Based on Hamilton variation principle, the equations of motion for the thin rectangular plate with transverse surface penetrating crack on nonlinear elastic foundation are established. In the case of four free edges, the suitable expressions of trial functions satisfied all boundary conditions and the crack's conditions for the problem were proposed. Then, the equations are solved by using Galerkin method and harmonic balance method. In the analysis of numerical computations, the effects of the crack location and depth、the structural parameters of plate and the parameters of foundation were discussed in the free vibration behaves for the cracked thin rectangular plate.