Fu Shihui, Ma Huizhen
School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan 450001, People's Republic of China.
Chaos. 2020 Feb;30(2):023128. doi: 10.1063/1.5128555.
This paper mainly investigates the nonlinear dynamics of a friction-induced self-excited vibration when the coefficient of static friction is larger than that of kinetic friction. First, this system is rewritten by a new theory proposed by Jeffrey, which is different from the Filippov theory. Then, the sliding region is obtained from the theory, which is also verified by the numerical simulation. Furthermore, multiple attractors, such as period-1 orbit and equilibrium point, period-2 orbit and equilibrium point, can coexist if the coefficient of static friction exceeds that of kinetic friction, but it is not true if they are equal. Finally, some sliding bifurcations, such as crossing-sliding bifurcation, switching-sliding bifurcation, and grazing-sliding bifurcation, are also found.
本文主要研究静摩擦系数大于动摩擦系数时摩擦诱导自激振动的非线性动力学。首先，利用杰弗里提出的不同于菲利波夫理论的新理论对该系统进行改写。然后，从该理论中得到滑动区域，并通过数值模拟进行验证。此外，如果静摩擦系数超过动摩擦系数，周期1轨道与平衡点、周期2轨道与平衡点等多个吸引子可以共存，但如果它们相等则不会出现这种情况。最后，还发现了一些滑动分岔，如穿越滑动分岔(、)切换滑动分岔和擦边滑动分岔。
