Nonlinear dynamics of a bistable system impacting a sinusoidally vibrating shaker
Nonlinear dynamics of a bistable system impacting a sinusoidally vibrating shaker
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DOI：
10.1007/s11071-022-07793-w
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发表时间：
2022-09
影响因子：
5.6
通讯作者：
Michael Rouleau;Steven R. Craig;Yiwei Xia;Roy Shieh;Major L. Robinson;Chengzhi Shi;J. Meaud
中科院分区：
文献类型：
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作者：
Michael Rouleau;Steven R. Craig;Yiwei Xia;Roy Shieh;Major L. Robinson;Chengzhi Shi;J. Meaud
近年来，双稳系统在从能量采集、冲击缓解和航空航天到精密传感和超材料等领域的应用引起了极大的兴趣。然而，大多数对双稳系统的研究只考虑了连续的外力。关于振动冲击动力学的文献很多，但大多局限于单稳态系统。在这项工作中，我们通过考虑单自由度双稳系统在正弦振动筛的冲击振动作用下的基本问题来推进知识的状态。利用计算模型，我们发现通过改变激励幅度和频率，可以观察到丰富的非线性动力学行为。一些响应只表现出井内动态，而另一些响应表现出可能收敛到第二个平衡的井间运动。推导出与观测井间运动所需的激励幅度相对应的幅度阈值的解析公式。激励频率对系统非线性动力学的影响包括阈值存在局部极小值，该极小值与系统的非线性共振有关。此外，可以通过包括周期1到6的响应的非周期(包括混沌)和周期响应来区分响应类型。除了计算模拟外，周期轨道的存在和稳定性是用打靶法根据单个周期的响应来确定的。利用磁性双稳摆进行的实验工作定性地验证了理论发现。
Bistable systems have seen significant interest in recent years, in applications ranging from energy harvesting, impact mitigation, and aerospace, to precision sensing and metamaterials. However, most investigations of bistable systems consider only continuous external forcing. The literature on the topic of vibroimpact dynamics is vast, but is mostly limited to monostable systems. In this work, we advance the state of knowledge by considering the fundamental problem of a one degree-of-freedom bistable system subjected to vibroimpact forcing by a sinusoidally vibrating shaker. Using computational models, we find that by varying excitation amplitude and frequency, a rich nonlinear dynamic behavior can be observed. Some responses exhibit only intrawell dynamics, while others display interwell motion that may converge to a second equilibrium. Analytical equations are derived to estimate the amplitude threshold that corresponds to the excitation amplitude required to observe interwell motion. The influence of the excitation frequency on the nonlinear dynamics of the system includes the presence of a local minimum in the threshold which is linked to a nonlinear resonance of the system. Further, response types can be differentiated by aperiodic (including chaotic) and periodic responses that include responses of periods one through six. In addition to computational simulations, the existence and stability of periodic orbits are determined using a shooting method based on the response over a single cycle. Experimental work using a magnetic bistable pendulum qualitatively validates the theoretical findings.