Dynamic Analysis of Two-Degree-of-Freedom Oblique Impact System With Non-Fixed Impact Positions
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摘要: 对两个单摆组成的双自由度、非定点、斜碰撞振动系统的动力学行为进行了详细研究．揭示了在双自由度、非定点、斜碰撞过程中恢复系数、摩擦系数、系统参数和碰撞前后系统状态之间的关系．基于Poincaré映射方法和非定点斜碰撞关系推导出该系统单碰周期n次谐运动存在性判据．根据Floquet理论分析了该系统次谐运动周期解的稳定性问题，给出了Floquet特征乘子的计算公式．通过数值仿真证实了该方法的有效性，同时分析了非定点、斜碰撞系统碰撞点位置的概率分布情况．Abstract: The dynamic behavior of a two-degree-of-freedom oblique impact system consisted of two pendulums with non-fixed impact positions is investigeated. The relations between the restitution coefficient, the friction coefficient, as well as other parameters of the system and the states before or after impact, are clarified in this oblique impact process. The existence criterion of single impact periodic-n subharmonic motions was deduced based on the Poincar map method and the oblique impact relations with non-fixed impact positions. The stability of these subharmonic periodic motions was analyzed by the Floquet theory, and the formulas to calculate the Floquet multipliers were given. The validity of this method is shown through numerical simulation. At the same time, the probability distribution of impact positions in this oblique system with non-fixed impact positions is analyzed.
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Key words:
- impact with non-fixed position /
- oblique impact /
- subharmonic motion /
- existence /
- stability /
- probability distribution
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