功能梯度圆柱壳非线性振动中的模态相互作用  

Mode interaction in nonlinear vibration of functionally graded cylindrical shells

作　　者：杜长城[1,2] 李映辉[2] 

机构地区：[1]西南交通大学牵引动力国家重点实验室四川成都610031 [2]西南交通大学力学与工程学院,四川成都610031

出　　处：《振动工程学报》2013年第5期647-653,共7页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(11072204);中央高校基础研究基金资助项目(SWJTU11ZT15)

摘　　要：借助Hamilton动力学研究了功能梯度薄壁圆柱壳非线性自由振动中的模态相互作用和能量交换现象。采用幂律分布规律描述功能梯度材料的等效材料参数,基于Donnell非线性壳体理论给出了功能梯度薄壁圆柱壳的动能和势能表达式;由Hamilton方程得到了无限长功能梯度薄壁圆柱壳双模态自由振动的控制方程。通过数值积分和Poincaré映射讨论了系统的模态相互作用和能量交换现象,揭示了系统的复杂动力学行为;同时也给出了功能梯度材料的梯度指数对系统发生分岔的能量分岔点的影响。Mode interaction and energy exchange in nonlinear free vibration of functionally graded cylindrical thin shells is studied according to Hamiltonian dynamics.Equivalent material properties of functionally graded material are described as powerlaw distribution function.The kinetic and potential energy expressions of functionally graded cylindrical thin shells are derived based on Donnell＇s nonlinear shell theory.The governing equations for two-mode free vibration of infinitely-long functionally graded cylindrical thin shells are obtained through the Hamilton＇s equation.The phenomena of mode interaction and energy exchange of system are discussed by numerical integration and the Poincaré mapping; the complex dynamic behavior of system is revealed.Meanwhile,the influence of power-law exponent on the energy bifurcation value of system is given.

关 键 词：非线性振动 功能梯度材料 圆柱壳 模态相互作用 混沌 

分 类 号：O322[理学—一般力学与力学基础] O343.7[理学—力学]