The global bifurcations and multi-pulse chaotic dynamics of a simply supported honeycomb sandwich rectangular plate under combined parametric and transverse excitations are investigated in this paper for the first time. The extended Melnikov method is generalized to investigate the multi-pulse chaotic dynamics of the non-autonomous nonlinear dynamical system. The main theoretical results and the formulas are obtained for the extended Melnikov method of the non-autonomous nonlinear dynamical system. The nonlinear governing equation of the honeycomb sandwich rectangular plate is derived by using the Hamilton's principle and the Galerkin's approach. A two-degree-of-freedom non-autonomous nonlinear equation of motion is obtained. It is known that the less simplification processes on the system will result in a better understanding of the behaviors of the multi-pulse chaotic dynamics for high-dimensional nonlinear systems. Therefore, the extended Melnikov method of the non-autonomous nonlinear dynamical system is directly utilized to analyze the global bifurcations and multi-pulse chaotic dynamics of the two-degree-of-freedom non-autonomous nonlinear system for the honeycomb sandwich rectangular plate. The theoretical results obtained here indicate that multi-pulse chaotic motions can occur in the honeycomb sandwich rectangular plate. Numerical simulation is also employed to find the multi-pulse chaotic motions of the honeycomb sandwich rectangular plate. It also demonstrates the validation of the theoretical prediction.
Chaotic and periodic motions of an FGM cylindrical panel in hypersonic flow are investigated. The cylindrical panel is also subjected to in-plane external loads and a linear temperature variation in the thickness direction. The temperature dependent material properties of panel which are assumed to be changed through the thickness direction only can be determined by a simple power distribution in terms of the volume fractions. With Hamilton’s principle for an elastic body, a nonlinear dynamical model based on Reddy’s first-order shear deformation shell theory and von Karman type geometric nonlinear relationship is derived in the form of partial equations. A third-order piston theory is adopted to evaluate the hypersonic aerodynamic load. Here, Galerkin’s method is employed to discretize this continuous nonlinear dynamic system to ordinary differential governing equations involving two degrees of freedom. The chaotic and periodic response are studied by the direct numerical simulation method for influences of different Mach number and the value of in-plane load. The bifurcations, Poincare section, waveform, and phase plots are presented.
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