Periodic motions and grazing in a harmonically forced, piecewise, linear oscillator with impacts
Periodic motions and grazing in a harmonically forced, piecewise, linear oscillator with impacts
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DOI：
10.1016/j.chaos.2004.09.028
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发表时间：
2005-04
影响因子：
7.8
通讯作者：
A. Luo;Lidi Chen
中科院分区：
文献类型：
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作者：
A. Luo;Lidi Chen
本文提出了一种理想化的分段线性系统来模拟齿轮传动系统的振动。本文用解析方法预测了具有理想塑性碰撞的广义分段线性振子的周期运动。周期运动的解析预测是基于映射结构的，并发展了基于不连续边界的一般映射。这种非光滑动力系统周期运动的解析预报方法，可以根据适当的映射结构给出所有可能的周期运动。得到了系统在特定周期运动下的稳定性和分岔条件。给出了周期性运动和掠动运动。该模型适用于齿轮传动系统非线性动力学中周期运动的预测。
In this paper, an idealized, piecewise linear system is presented to model the vibration of gear transmission systems. Periodic motions in a generalized, piecewise linear oscillator with perfectly plastic impacts are predicted analytically. The analytical predictions of periodic motion are based on the mapping structures, and the generic mappings based on the discontinuous boundaries are developed. This method for the analytical prediction of the periodic motions in non-smooth dynamic systems can give all possible periodic motions based on the adequate mapping structures. The stability and bifurcation conditions for specified periodic motions are obtained. The periodic motions and grazing motion are demonstrated. This model is applicable to prediction of periodic motion in nonlinear dynamics of gear transmission systems.