非线性弹性直杆纵振时的混沌行为

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振动与冲击 ›› 2011, Vol. 30 ›› Issue (3) : 135-138.

论文

非线性弹性直杆纵振时的混沌行为

韩志军; 王建军; 崔艳; 路国运; 张善元

作者信息 +

The Chaotic Behavior of Nonlinear Elastic Straight Bar During Lonitudinal Vibration

HAN Zhi-Jun; WANG Jian-Jun; CUI Yan; LU Guo-Yun; ZHANG Shan-Yuan

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文章历史 +

摘要

研究了形本构关系的弹性直杆纵振时的混沌行为。用Galerkin原理将杆纵振时的动力控制方程转化为二阶三次非线性微分动力系统；给出了其产生同宿轨道和异宿轨道的条件，得到了同宿轨道的参数方程;借助Melnikov函数给出了系统发生混沌的临界条件；数值计算给出了混沌运动区域随和的变化规律，用分岔图、位移时程曲线、相平面图和Poincaré映射判断了系统的运动行为即定常还是混沌。进一步的研究还表明本构关系中的二次非线性项对系统的动力响应具有很大的影响。

Abstract

The chaotic motion of nonlinear elastic straight bar that has constitutive relation of the -shape during lonitudinal vibration are investigated.The dynamic equation of bar during lonitudinal vibration is changed into differential dynamic system by Galerkin principle.The conditions that the system has homoclinic orbit or heteroclinic orbit are given ,and the parameter equations of homoclinic orbit are solved. Using the Melnikov function ,the critical conditions that the system enters chaotic states are given. The regularity of chaotic motive region with and are obtained by numerical analysis, and the bifurcation diagrams,Displacement-time history diagram,Phase-plane diagram and Poincaré map show that the system occur steady motion or chaotic motion.The further research show that the quadric nonlinear item in constitutive relation has great effect on the dynamic behavior.

导出引用

韩志军;王建军;崔艳;路国运;张善元. 非线性弹性直杆纵振时的混沌行为 [J]. 振动与冲击, 2011, 30(3): 135-138

HAN Zhi-Jun;WANG Jian-Jun;CUI Yan;LU Guo-Yun;ZHANG Shan-Yuan. The Chaotic Behavior of Nonlinear Elastic Straight Bar During Lonitudinal Vibration[J]. Journal of Vibration and Shock, 2011, 30(3): 135-138