【摘要】 基于 Poincaré映射方法对一类两自由度碰撞系统进行研究.经过详细的理论演算得到单碰周期1/n 的亚谐周期运动的存在性判据,并能精确地找到亚谐周期运动的初始位置.表明碰振系统的周期运动研究可以通过解析与数值方法的结合去实现.数值模拟表明了亚谐周期运动的存在性判据的正确性,并通过计算Jacobi 矩阵的特征值可判断周期运动的稳定性及分岔.更多还原

【Abstract】 An undamped two-degree-of-freedom vibro-impact system with a harmonic excitation is studied based on the theoretical analysis by Poincar(?) map.A criterion for the existence of single impact period—1/ n motions is obtained,and the initial position of the subharmonic periodic motion can be determined.The stability and the bifurcation of periodic motions are studied by computing the characteristic values of the Jacobian matrix.A combination of analytical and numerical techniques is proposed in the study of periodic motions of vibro-impact systems.更多还原