Fundamental competition of smooth and non-smooth bifurcations and their ghosts in vibro-impact pairs
Fundamental competition of smooth and non-smooth bifurcations and their ghosts in vibro-impact pairs
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DOI：
10.1007/s11071-022-08152-5
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发表时间：
2022-12
影响因子：
5.6
通讯作者：
Larissa Serdukova;R. Kuske;D. Yurchenko
中科院分区：
文献类型：
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作者：
Larissa Serdukova;R. Kuske;D. Yurchenko
光滑和非光滑分叉的综合分析捕获的影响对，一个强制胶囊，其中一个球自由移动的胶囊两端的影响之间的规范模型中的不同的定性过渡的相互作用。分析，通用的影响对上下文，也是相关的应用程序。它被应用到一个倾斜的振动冲击能量采集器设备的模型，其中的能量是通过与胶囊端部上的介电聚合物的球的冲击产生的。虽然在单自由度碰撞模型中已经对分叉序列进行了广泛的研究，但是对于两自由度碰撞系统（例如碰撞副），结果有限。使用的分析特征的影响解决方案和它们的稳定性的基础上的映射之间的影响，我们得到的序列的周期加倍和折叠分叉与放牧分叉，这里特别关注。当密封舱两端的一系列撞击被零速度撞击增强时，就会发生掠射，这种过渡与光滑分叉有根本的不同，光滑分叉的特征在于局部行为的特征值。结合分析允许识别分叉也不稳定或非物理的解决方案分支，我们的术语鬼分叉。虽然这些鬼分叉没有观察到实验或通过简单的数值积分的模型，然而，它们可以影响复杂的行为和额外的掠食过渡的诞生或死亡，证实了与数值结果的比较。不同的分叉和他们的鬼之间的竞争影响有利的能量输出的参数范围，因此，分叉序列的分析产生重要的设计信息。
A combined analysis of smooth and non-smooth bifurcations captures the interplay of different qualitative transitions in a canonical model of an impact pair, a forced capsule in which a ball moves freely between impacts on either end of the capsule. The analysis, generic for the impact pair context, is also relevant for applications. It is applied to a model of an inclined vibro-impact energy harvester device, where the energy is generated via impacts of the ball with a dielectric polymer on the capsule ends. While sequences of bifurcations have been studied extensively in single- degree-of-freedom impacting models, there are limited results for two-degree-of-freedom impacting systems such as the impact pair. Using an analytical characterization of impacting solutions and their stability based on the maps between impacts, we obtain sequences of period doubling and fold bifurcations together with grazing bifurcations, a particular focus here. Grazing occurs when a sequence of impacts on either end of the capsule are augmented by a zero-velocity impact, a transition that is fundamentally different from the smooth bifurcations that are instead characterized by eigenvalues of the local behavior. The combined analyses allow identification of bifurcations also on unstable or unphysical solutions branches, which we term ghost bifurcations. While these ghost bifurcations are not observed experimentally or via simple numerical integration of the model, nevertheless they can influence the birth or death of complex behaviors and additional grazing transitions, as confirmed by comparisons with the numerical results. The competition between the different bifurcations and their ghosts influences the parameter ranges for favorable energy output; thus, the analyses of bifurcation sequences yield important design information.