Multi-pulse Chaotic Dynamics of a Functionally Graded Material Rectangular Plate with One-to-One Internal Resonance

摘要

Global bifurcations and Shilnikov type multi-pulse chaotic dynamics for a simply supported functionally graded material (FGM) rectangular plate are studied by using an extended Melnikov method for the first time. The FGM rectangular plate is subjected to the transversal and in-plane excitations in the uniform thermal environment. Material properties are assumed to be temperature-dependent. A two-degree-of-freedom nonlinear system governing the equation of motion for the FGM rectangular plate, which includes the quadratic and cubic nonlinear terms is derived by using Hamilton's principle and Galerkin's method. The resonant case considered here is 1:1 internal resonance, principal parametric resonance and 1/2-subharmonic resonance. The averaged equation governing the amplitudes and phases of the second-order approximate solution is obtained by using the method of multiple scales. After transforming the averaged equation into a standard form, the extended Melnikov method is employed to indicate the existence of the Shilnikov type multi-pulse chaotic motions. We are able to obtain the explicit restrictive conditions on the damping, excitations and the detuning parameters, under which the multi-pulse chaotic dynamics is expected. The results of numerical simulation also illustrate that there exist the multi-pulse chaotic responses of the FGM rectangular plate.