An extended high-dimensional Melnikov analysis for global and chaotic dynamics of a non-autonomous rectangular buckled thin plate  

作　　者：ZHANG JunHua ZHANG Wei 

机构地区：[1]College of Mechanical Engineering, Beijing University of Technology, Beijing 100124, China

出　　处：《Science China(Physics,Mechanics & Astronomy)》2012年第9期1679-1690,共12页中国科学：物理学、力学、天文学（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant Nos. 11072008,10732020 and 11002005);the Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality(PHRIHLB)

摘　　要：By using an extended Melnikov method on multi-degree-of-freedom Hamiltonian systems with perturbations,the global bifurcations and chaotic dynamics are investigated for a parametrically excited,simply supported rectangular buckled thin plate.The formulas of the rectangular buckled thin plate are derived by using the von Karman type equation.The two cases of the buckling for the rectangular thin plate are considered.With the aid of Galerkin's approach,a two-degree-of-freedom nonautonomous nonlinear system is obtained for the non-autonomous rectangular buckled thin plate.The high-dimensional Melnikov method developed by Yagasaki is directly employed to the non-autonomous ordinary differential equation of motion to analyze the global bifurcations and chaotic dynamics of the rectangular buckled thin plate.Numerical method is used to find the chaotic responses of the non-autonomous rectangular buckled thin plate.The results obtained here indicate that the chaotic motions can occur in the parametrically excited,simply supported rectangular buckled thin plate.By using an extended Melnikov method on multi-degree-of-freedom Hamiltonian systems with perturbations, the global bifur- cations and chaotic dynamics are investigated for a parametrically excited, simply supported rectangular buckled thin plate. The formulas of the rectangular buckled thin plate are derived by using the von Karman type equation. The two cases of the buckling for the rectangular thin plate are considered. With the aid of Galerkin＇s approach, a two-degree-of-freedom non- autonomous nonlinear system is obtained for the non-autonomous rectangular buckled thin plate. The high-dimensional Melnikov method developed by Yagasaki is directly employed to the non-autonomous ordinary differential equation of motion to analyze the global bifurcations and chaotic dynamics of the rectangular buckled thin plate. Numerical method is used to find the chaotic responses of the non-autonomous rectangular buckled thin plate. The results obtained here indicate that the chaotic motions can occur in the parametrically excited, simply supported rectangular buckled thin plate.

关 键 词：extended high-dimensional Melnikov method rectangular buckled thin plate non-autonomous nonlinear system chaotic motions 

分 类 号：O415.5[理学—理论物理] O343.1[理学—物理]