Discontinuity-induced bifurcations in a piecewise-smooth capsule system with bidirectional drifts
Discontinuity-induced bifurcations in a piecewise-smooth capsule system with bidirectional drifts
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DOI：
10.1016/j.cnsns.2021.105909
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发表时间：
2021-06
期刊：
影响因子：
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通讯作者：
Bingyong Guo;J. P. Chávez;Yang Liu;Caishan Liu
中科院分区：
文献类型：
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作者：
Bingyong Guo;J. P. Chávez;Yang Liu;Caishan Liu
不连续摩擦和冲击存在于各种分段光滑的动力系统中，呈现出丰富而复杂的非线性现象。本文研究了分段光滑胶囊系统在双向漂移作用下的不连续引起的掠过和相加-滑动分叉。为此，通过显式求解基本的分段线性模型，研究了碰撞引起的擦伤和摩擦引起的相加-滑动分叉的解析和半解析的启动条件。通过这种方法，得到了揭示系统从定态向正向级数转变的发生机制的参数关系。利用分段光滑动力系统的路径跟踪技术对该分析方法进行了数值验证。数值研究包括对观察到的太空舱的平均速度和功率消耗的参数研究，提出了系统运行的最佳参数。
Discontinuous friction and impact exist in a variety of piecewise-smooth dynamical systems that exhibit rich and complex nonlinear phenomena. This paper aims to study the discontinuity-induced grazing and adding-sliding bifurcations in a piecewise-smooth capsule system subjected to bidirectional drifts. For this purpose, analytical and semi-analytical onset conditions of the impact-induced grazing and the friction-induced adding-sliding bifurcations are investigated by solving explicitly the underlying piecewise-linear model. In this way, parametric relations revealing the occurrence mechanisms of transitions of the system from stationary to forward progression are derived. This analytical approach is verified numerically using path-following techniques for piecewise-smooth dynamical systems. The numerical investigation includes a parametric study of the observed capsule's average velocity and power consumption suggesting optimum parameters for system operation.