非自治屈曲薄板全局分叉与混沌动力学

基于多自由度哈密尔顿系统的Melnikov理论,研究了参数激励下四边简支矩形薄板在屈曲状态下的全局分叉与混沌动力学.直接对非自治常微分方程进行全局分析,比文献中经过多次化简近似所得到的规范形更加接近原系统的性质.薄板的屈曲状态是文献中用多尺度方法所不能研究的.分析结果表明参数激励下四边简支矩形薄板存在Smale马蹄意义下的混沌,数值模拟进一步验证了解析方法的正确性.

Global bifurcation and chaotic dynamics for a non-autonomous buckled thin plate

By using Melnikov method of multi-degree-of-freedom Hamiltonian systems with perturbations, the global bifurcation and chaotic dynamics of a parametrically excited and simply supported rectangular thin plate are studied. Based on the non-autonomous ordinary differential equations, which are much closer to the original system than the normal form given in the literature, global perturbation analysis of the parametrically excited rectangular thin plate is given by high dimensional Melnikov method. In the formulas of the thin plate, the case of buckling is considered which cannot be obtained after using multiple scales method. The results show that the chaotic motion can occur in the parametrically excited and simply supported rectangular thin plate. Numerical simulations verify the analytical predictions.