物理非线性和几何非线性梁的混沌运动  

Chaotic Movement of Phisical and Geometrical Nonlinear Beam

作　　者：张年梅[1] 杨桂通[1] 

机构地区：[1]太原理工大学应用力学研究所,山西太原030024

出　　处：《太原理工大学学报》2003年第1期5-7,共3页Journal of Taiyuan University of Technology

基　　金：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)

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了一阶微分方程组 ,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现带状。文中还详尽分析了从次谐分岔到混沌的路径 。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.

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 

分 类 号：O343.5[理学—固体力学] TU323.3[理学—力学]