非线性热弹耦合椭圆板的混沌运动

基金项目: 国家自然科学基金资助项目(19672038);山西省自然科学基金资助项目(1880342)

Chaotic Motion of a Nonlinear Thermoelastic Elliptic Plate

1.
Department of Mechanics, College of Traffic and Communications, South China University of Technology, Guangzhou 510641, P. R. China;
2.
Institute of Applied Mechanics, Taiyuan University of Technology, Taiyuan 030024, P. R. China

摘要: 计及几何非线性大挠度效应和温度效应的影响,导出了椭圆板周期激励作用下热弹耦合的非线性动力方程,利用Melnikov函数法给出了系统发生混沌运动的临界条件,结合Poincaré映射、相平面轨迹和时程曲线进行数值分析,并对系统通向混沌的道路进行了讨论,从中得到了一些有益的结论.
- 热弹耦合 /
- 混沌 /
- Melnikov函数法 /
- Poincaré映射
Abstract: In the paper the nonlinear dynamic equation of a harmonically forced elliptic plate is derived,with the effects of large deflection of plate and thermoelasticity taken into account.The Melnikov function method is used to give the critical condition for chaotic motion.A demonstrative example is discussed through the Poincaré mapping,phase portrait and time history.Finally the path to chaotic motion is also discussed.Through the theoretical analysis and numerical computation some beneficial conclusions are obtained.
- thermoelasticity /
- chaos /
- Melnikov function /
- Poincaré mapping

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