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Qualitative analysis of the response regimes and triggering mechanism of bistable NES

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Abstract

The main focus of this study is the development of an adapted complex variable method with respect to the equilibrium point in bistable nonlinear energy sink (NES), which is mainly investigated in the vicinity of 1:1 resonance. A simplified chaos trigger model is established to describe the distance between the stable phase cycle and the pseudo-separatrix. An analytical expression can predict the excitation threshold for chaos occurrence. The relative positions between the chaos trigger threshold line and the slow invariant manifold structure can interpret the distribution of response regimes under growing harmonic excitation. The degeneration of the response regimes can be demonstrated by the qualitative analysis method, which helps to classify the bistable NES. The experiment confirms the analytical result of intra-well oscillation in the frequency domain. The characteristic response regimes of weak, modest, and strong bistable NES are identified by the experimental results.

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The authors declare that the data supporting the findings of this study are available within the article.

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Acknowledgements

The authors acknowledge the Chinese Scholarship Council under Grant No. 201801810128 for their financial support. The authors declare that they have no conflicts of interest to declare that are relevant to the content of this article.

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The authors acknowledge the Chinese Scholarship Council under Grant No. 201801810128 for their financial support.

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Authors and Affiliations

  1. Institut Clément Ader (ICA), CNRS, INSA-ISAE-Mines Albi-UPS, Université de Toulouse, 3 rue Caroline Aigle, 31400, Toulouse, France

    Zhenhang Wu, Sébastien Seguy & Manuel Paredes

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  1. Zhenhang Wu
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  2. Sébastien Seguy
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  3. Manuel Paredes
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Correspondence to Zhenhang Wu.

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The authors declare that all procedures performed in this study were in accordance with the ethical standards of COPE. This manuscript is only submitted to the journal ‘Nonlinear Dynamics’. The authors declare that this study is complete, unsplit and original.

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Wu, Z., Seguy, S. & Paredes, M. Qualitative analysis of the response regimes and triggering mechanism of bistable NES. Nonlinear Dyn 109, 323–352 (2022). https://doi.org/10.1007/s11071-022-07609-x

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