Maps unlock the full dynamics of targeted energy transfer via a vibro-impact nonlinear energy sink
Maps unlock the full dynamics of targeted energy transfer via a vibro-impact nonlinear energy sink
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DOI：
10.1016/j.ymssp.2023.110158
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发表时间：
2023-05
影响因子：
8.4
通讯作者：
Ruofeng Liu;R. Kuske;D. Yurchenko
中科院分区：
文献类型：
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作者：
Ruofeng Liu;R. Kuske;D. Yurchenko
我们考虑一个模型的振动-冲击非线性能量汇（VI-NES），其中一个球移动的空腔内的外部强制质量，影响任何一端的腔。这些碰撞导致能量从质量传递到球，从而限制了更大系统的振荡。我们开发了一个半分析的地图为基础的方法，最近用于倾斜的影响对模型，在设置中有质量和球之间的能量转移。通过这种方法，我们解析推导出精确的表达式的完整动态的VI-NES系统，而不限制参数的范围内，在最近的其他工作中，一个近似的简化模型是有效的，只有小质量的球，小振幅，和有限的频率范围。我们开发了完整的VI-NES系统的分岔分析，在连续的影响状态之间的精确映射的基础上。这种分析产生了复杂的周期性响应和稳定性分析的O（1）质量的球，强迫频率是不相同的自然频率，和大振幅强迫的参数范围。该方法提供了灵活性，分析研究不同的周期性的解决方案和他们的稳定性，包括各种影响序列的全两个自由度模型的VI-NES的动态。表征能量转移的量的比较指向不同类型的周期性行为的意义，这可能发生在不同的参数组合下。我们的半解析结果还提供了影响阶段，这在能量转移的效率中起着重要的作用。
We consider a model of a vibro-impact nonlinear energy sink (VI-NES), where a ball moves within a cavity of an externally forced mass, impacting either end of the cavity. These impacts result in energy transfer from the mass to the ball, thus limiting the oscillations of the larger system. We develop a semi-analytical map-based approach, recently used for an inclined impact pair model, in the setting where there is energy transfer between the mass and the ball. With this approach we analytically derive exact expressions for the full dynamics of the VI-NES system without restricting the range of parameters, in contrast to other recent work in which an approximate reduced model is valid only for small mass of the ball, small amplitude, and a limited frequency range. We develop the bifurcation analysis for the full VI-NES system, based on exact maps between the states at successive impacts. This analysis yields parameter ranges for complex periodic responses and stability analyses for O (1) mass of the ball, forcing frequencies that are not the same as the natural frequency, and large amplitude forcing. The approach affords the flexibility to analytically study the dynamics of different periodic solutions and their stability, including a variety of impact sequences in the full two degree-of-freedom model of VI-NES. Comparisons of quantities that characterize the energy transfer point to the significance of different types of periodic behavior, which may occur for different parameter combinations. Our semi-analytical results also provide the impact phase, which plays an important role in the efficiency of the energy transfer.