两自由度含间隙和预紧弹簧碰撞振动系统动力学分析.pdfVIP

第 28 卷第 3 期 Vol.28 No.3 工 程 力 学 2011 年 3 月 Mar. 2011 ENGINEERING MECHANICS 209 文章编号：1000-4750(2011)03-0209-09 两自由度含间隙和预紧弹簧碰撞振动系统 动力学分析 *张 惠，丁旺才，李 飞 (兰州交通大学机电工程学院，兰州 730070) 摘 要：研究了一类两自由度含间隙和预紧弹簧的碰撞振动系统动力学模型，建立了系统的 Poincaré 映射，推导 出了映射的 Jacobian 矩阵。研究了系统的周期和非周期运动，利用 Lyapunov 指数谱分析了系统的稳定性，用测 试函数预测了系统发生“擦边”现象的参数范围；研究了系统的倍化序列和 Hopf 分岔过程因碰撞质块与约束“擦 边”而中断或不连续的现象；分析了由边界碰撞引起的 Jacobian 矩阵在“擦边”点附近特征值、行列式、迹的变 化情况。 关键词：非光滑系统；弹性碰撞；Poincaré 映射；Lyapunov 指数谱；边界碰撞 中图分类号：O322 文献标识码：A DYNAMICS OF A TWO-DEGREE-OF-FREEDOM IMPACT SYSRTEM WITH CLEARANCE AND PRE-COMPRESSED SPRING * ZHANG Hui , DING Wang-cai , LI Fei (School of Mechanical Engineering Lanzhou Jiaotong University, Lanzhou 730070, China) Abstract: A two-degree-of-freedom impact system with a clearance and pre-compressed spring is studied. The Poincaré map and its Jacobian matrix are constructed for analyzing the stability of the system. The periodic and aperiodic motions of the system are investigated, and verified by Lyapunov exponents. The parameter regions, where a boundary grazing phenomena may happen, are predicted by a test function. The phenomena of period-doubling and Hopf bifurcations intermitted due to boundary grazing motion are investigated. The changes of the eigenvalues, determinants and traces at the grazing points due to border collision are analyzed. Key words: non-smooth system; soft impact; Poincaré map; Lyapunov exponents; border collision 存在间隙的弹性碰撞振动系统广泛存在于机 性碰撞系统的边界碰撞进行了研究，对由擦边引起 械系统之中[1―2] ，这类系统的向量场是连续的，但 的不动点处的 Jacobian 矩阵的变化进行了重点关 由于间隙和弹性约束引起刚度突变，从而使系统向 注。文献[4]推导