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Stability analysis of inerter-based n-DOF vibration systems containing semi-active switched elements

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Abstract

This paper investigates the stability problem of inerter-based semi-active n-degree-of-freedom (n-DOF) vibration systems containing semi-active switched elements, where the results can be applied to the design of many vibration control systems, such as building vibrations, vehicle suspensions, isolators, etc. Since introducing switched elements to n-DOF vibration systems may lead to instability, it is theoretically and practically meaningful to investigate the stability of n-DOF vibration systems containing semi-active switched elements. Necessary and sufficient conditions for the global asymptotic stability of a single-degree-of-freedom (SDOF) system containing at most one switched spring, one switched inerter, and one switched damper are derived, by solving the explicit solutions of the system states and analyzing the properties of energy functions. Based on the Lyapunov approach, a series of asymptotic stability conditions for the multi-degree-of-freedom (MDOF) system containing one semi-active switched inerter or one semi-active switched spring are derived. Finally, numerical simulation examples are presented to illustrate the stability results.

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Data Availibility Statement

The datasets analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grants 62373166, 61873129, the Natural Science Foundation of Jiangsu Province under Grant BK20211234, the China Postdoctoral Science Foundation under Grant 2022M71136.

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Authors and Affiliations

  1. Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), School of Internet of Things Engineering, Jiangnan University, Wuxi, 214122, China

    Wei Xu & Kai Wang

  2. School of Automation, Nanjing University of Science and Technology, Nanjing, 210094, China

    Michael Z. Q. Chen

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  1. Wei Xu
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  2. Kai Wang
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  3. Michael Z. Q. Chen
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Correspondence to Kai Wang.

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Xu, W., Wang, K. & Chen, M.Z.Q. Stability analysis of inerter-based n-DOF vibration systems containing semi-active switched elements. Nonlinear Dyn (2024). https://doi.org/10.1007/s11071-024-09573-0

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