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Nonlinear dynamics of a bistable system impacting a sinusoidally vibrating shaker

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Abstract

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.

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Data availability

The data and source codes used in this work can be made available upon request to the corresponding author Julien Meaud (julien.meaud@me.gatech.edu).

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Funding

This study was supported by NSF Grant CMMI 2037565, the Georgia Institute of Technology Quantum Alliance, and the Woodruff Launch Seed Grant at Georgia Tech.

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Authors and Affiliations

  1. G.W.W. School of Mechanical Engineering, Georgia Institute of Technology, 771 Ferst Drive, Atlanta, GA, 30332, USA

    Michael Rouleau, Steven Craig, Yiwei Xia, Roy Shieh, Major L. Robinson, Chengzhi Shi & Julien Meaud

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  1. Michael Rouleau
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  2. Steven Craig
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  3. Yiwei Xia
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  4. Roy Shieh
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  5. Major L. Robinson
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  6. Chengzhi Shi
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  7. Julien Meaud
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Correspondence to Julien Meaud.

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Rouleau, M., Craig, S., Xia, Y. et al. Nonlinear dynamics of a bistable system impacting a sinusoidally vibrating shaker. Nonlinear Dyn 110, 3015–3030 (2022). https://doi.org/10.1007/s11071-022-07793-w

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  • DOI: https://doi.org/10.1007/s11071-022-07793-w

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