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Vibration Reduction for an Asymmetric Elastically Supported Beam Coupled to an Inertial Nonlinear Energy Sink

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Abstract

Purpose

The present paper addresses the vibration reduction for an elastic beam with an asymmetric boundary condition that is clamped at one end and elastically supported at the other end. An inertial nonlinear energy sink (NES) is installed on the elastic support end to suppress the beam's vibration.

Methods

The nonlinear terms introduced by the NES are transferred as the external excitations acting on the beam. The motion equations of the beam with an NES are derived according to Hamilton's principle and the Galerkin truncation method. The beam's natural frequencies and corresponding mode shapes are analytically obtained and verified with the results of the finite element method. The responses of the beam are numerically and analytically solved by the fourth order Runge–Kutta method and the harmonic balance method (HBM), respectively.

Results

The good agreement among the results validates the present derivation of the theoretical model and numerical solutions. The steady-state responses of the beam with and without the NES are compared and analyzed in the time domain.

Conclusions

The results demonstrate that adding the inertial enhanced NES can effectively reduce the resonance amplitude of the beam. Furthermore, a parametric optimization is conducted for NES to improve its performance. The results of this paper contribute to the application of NESs on the boundaries of elastic structures.

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Acknowledgements

The work described in this paper was fully supported by the National Natural Science Foundation of China (Grant No. 12102015), the General Program of Science and Technology Development Project of Beijing Municipal Education Commission (Project No. KM202110005030), and grants from the Fundamental Research Program of Shenzhen Municipality (Project No: JCYJ20170818094653701).

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Authors and Affiliations

  1. Faculty of Materials and Manufacturing, Beijing University of Technology, Beijing, 100124, People’s Republic of China

    Wei Zhang, Zhi-Yong Chang & Jie Chen

  2. Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Structures, Beijing, 100124, People’s Republic of China

    Wei Zhang, Zhi-Yong Chang & Jie Chen

  3. Architecture and Civil Engineering Research Center, City University of Hong Kong Shenzhen Research Institute, Shenzhen, 518057, People’s Republic of China

    Jie Chen

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  1. Wei Zhang
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  2. Zhi-Yong Chang
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Correspondence to Jie Chen.

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Zhang, W., Chang, ZY. & Chen, J. Vibration Reduction for an Asymmetric Elastically Supported Beam Coupled to an Inertial Nonlinear Energy Sink. J. Vib. Eng. Technol. 11, 1711–1723 (2023). https://doi.org/10.1007/s42417-022-00666-x

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  • DOI: https://doi.org/10.1007/s42417-022-00666-x

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