| 物理非线性和几何非线性梁的混沌运动 |
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| 引用本文： | 张年梅,杨桂通. 物理非线性和几何非线性梁的混沌运动[J]. 太原理工大学学报, 2003, 34(1): 5-7 |
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| 作者姓名： | 张年梅 杨桂通 |
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| 作者单位： | 太原理工大学,应用力学研究所,山西,太原,030024 |
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| 基金项目： | 国家自然科学基金资助项目 (10 172 0 63 )，山西省青年科学基金资助项目 (2 0 0 110 0 4) |
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| 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，计及材料非线性和几何非线性，建立了该动力系统的非线性偏微分方程，并在理想的位移模态条件下得出一阶分方程组，求解该动力系统后发现，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带状。文中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。
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| 关 键 词： | 物理非线性 几何非线性 梁 混沌运动 次谐分岔 异宿轨道 周期轨道 |
| 文章编号： | 1007-9432(2003)01-0005-03 |
| 修稿时间： | 2002-06-11 |
Chaotic Movement of Phisical and Geometrical Nonlinear Beam |
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| ZHANG Nian mei,YANG Gui tong. Chaotic Movement of Phisical and Geometrical Nonlinear Beam[J]. Journal of Taiyuan University of Technology, 2003, 34(1): 5-7 |
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| Authors: | ZHANG Nian mei YANG Gui tong |
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| Abstract: | The chaotic motions of axial compressed nonlinear elastic beam subjected to transverse load were studied. Considering material and geometric nonlinearity, nonlinear partial differential equation of the system was derived. Under ideal displacement conditions,one order differential equations were devived and solved. The results showed that chaos may occur in the system when the load parameters P 0 and f satisfy some conditions. The zone of chaotic motion was belted. The route from subharmonic bifurcation to chaos was analyzed in the paper. The critical conditions that chaos occurs were determined. |
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| Keywords: | chaos subharmonic bifurcation heteroclinic orbit periodic orbit |
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