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中文摘要：
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。
英文摘要：
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.
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