非线性弹性梁中的混沌带现象

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基金项目: 国家自然科学基金资助项目(10172063)

Chaotic Belt Phenomena in Nonlinear Elastic Beam

Institute of Applied Mechanics, Taiyuan University of Technology, Taiyuan 030024, P.R.China

摘要: 研究了非线性弹性梁的混沌运动,梁受到轴向载荷的作用。非线性弹性梁的本构方程可用三次多项式表示。计及材料非线性和几何非线性,建立了系统的非线性控制方程。利用非线性Galerkin法,得到微分动力系统。采用Melnikov方法对系统进行分析后发现,当载荷P₀和f满足一定条件时,系统将发生混沌运动,且混沌运动的区域呈现带状。还详尽分析了从次谐分岔到混沌的路径,确定了混沌发生的临界条件。
- 混沌 /
- 次谐分岔 /
- 异宿轨道 /
- 周期轨道
Abstract: The chaotic motions of axial compressed nonlinear elastic beam subjected to transverse load were studied.The damping force in the system is nonlinear.Considering material and geometric nonlinearity,nonlinear governing equation of the system was derived.By use of nonlinear Galerkin method,differential dynamic system was set up.Melnikov method was used to analyze the characters of the system.The results showed that chaos may occur in the system when the load parameters P₀ and f satisfy some conditions.The zone of chaotic motion was belted.The route from subharmonic bifurcation to chaos was analyzed.The critical conditions that chaos occurs were determined.
- chaos /
- subharmonic bifurcation /
- heteroclinic orbit /
- periodic orbit

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