应用数学和力学2012，Vol.33Issue(9)：1115-1128,14.DOI:10.1007/s10483-012-1609-9
Global bifurcations and multi-pulse chaotic dynamics of rectangular thin plate with one-to-one internal resonance
Global bifurcations and multi-pulse chaotic dynamics of rectangular thin plate with one-to-one internal resonance
摘要
Abstract
Global bifurcations and multi-pulse chaotic dynamics for a simply supported rectangular thin plate are studied by the extended Melnikov method.The rectangular thin plate is subject to transversal and in-plane excitation. A two-degree-of-freedom nonlinear nonautonomous system governing equations of motion for the rectangular thin plate is derived by the von Karman type equation and the Galerkin approaoh.A one-toone internal resonance is considered.An averaged equation is obtained with a multi-scale method.After transforming the averaged equation into a standard form,the extended Melnikov method is used to show the existence of multi-pulse chaotic dynamics,which can be used to explain the mechanism of modal interactions of thin plates.A method for calculating the Melnikov function is given without an explicit analytical expression of homoclinic orbits.Furthermore,restrictions on the damping,excitation,and detuning parameters are obtained,under which the multi-pulse chaotic dynamics is expected.The results of numerical simulations are also given to indicate the existence of small amplitude multi-pulse chaotic responses for the rectangular thin plate.关键词
rectangular thin plate/global bifurcation/multi-pulse chaotic dynamics/extended Melnikov methodKey words
rectangular thin plate/global bifurcation/multi-pulse chaotic dynamics/extended Melnikov method分类
数理科学引用本文复制引用
Shuang-bao LI,Wei ZHANG..Global bifurcations and multi-pulse chaotic dynamics of rectangular thin plate with one-to-one internal resonance[J].应用数学和力学,2012,33(9):1115-1128,14.基金项目
Project supported the National Natural Science Foundation of China (Nos.10732020,11072008,and 11102226),the Scientific Research Foundation of Civil Aviation University of China (No.2010QD04X),and the Fundamental Research Funds for the Central Universities of China (Nos.ZXH2011D006 and ZXH2012K004) （Nos.10732020,11072008,and 11102226）
