Bifurcation and chaos of rectangular moderately thick cracked plates on an elastic foundation subjected to periodic load

Based on Reissner plate theory and Hamilton variational principle, the nonlinear equations of motion are derived for the rectangular moderately thick plates with transverse surface penetrating crack on an elastic foundation under the action of periodic load. Suitable expressions of trial functions satisfying all boundary conditions and crack’s continuous conditions are proposed. The nonlinear equations are solved by using the Galerkin and the Runge–Kutta integration methods. Possible bifurcation and chaos behaviors of the system are analyzed. The influence of the different locations and depths of cracks and external loads on the bifurcation and chaos behaviors of the rectangular moderately thick plates with freely supported boundary is investigated numerically.