Mechanical manifestations of bursting oscillations in slowly rotating systems
Mechanical manifestations of bursting oscillations in slowly rotating systems
复制标题
DOI：
10.1016/j.ymssp.2016.03.006
复制
发表时间：
2016-12
影响因子：
8.4
通讯作者：
Z. Rakaric;I. Kovacic
中科院分区：
文献类型：
--
作者：
Z. Rakaric;I. Kovacic
本研究是关于某些机械系统，包括离散质量移动沿着缓慢旋转的对象。推导出相应的相对运动方程，旋转运动产生缓慢变化的外部激励。根据系统参数的不同，我们区分了两种情况：双势阱和单势阱，即Duffing振子和纯立方振子。结果表明，这两个系统可以表现出突发振荡，由周围的慢流的快速振荡。它们的机制被解释的分叉理论：第一个相对于某些鞍结分叉点的存在，和第二个通过创建一个一定的磁滞回线。慢流的精确表达式推导出来，在第一种情况下作为一个不连续的曲线，在第二个作为一个连续的曲线。数值模拟了激发幅值作为一个潜在的控制参数对爆发振荡特性的影响。
This study is concerned with certain mechanical systems that comprise discrete masses moving along slowly rotating objects. The corresponding equation of relative motion is derived, with the rotating motion creating slowly varying external excitation. Depending on the system parameters, two cases are distinguished: two-well and single-well potential, i.e. the Duffing bistable oscillator and a pure cubic oscillator. It is illustrated that both systems can exhibit bursting oscillations, consisting of fast oscillations around the slow flow. Their mechanisms are explained in terms of bifurcation theory: the first one with respect to the existence of certain saddle-node bifurcation points, and the second one by creation of a certain hysteresis loop. The exact expressions for the slow flow are derived, in the first case as a discontinuous curve, and in the second one as a continuous curve. The influence of the excitation magnitude, which is a potential control parameter, on the characteristics of bursting oscillations is numerically illustrated.