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Active tunability of band gaps for a novel elastic metamaterial plate

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Abstract

A novel active elastic metamaterial plate is proposed, with tunable vibration band-gap characteristics is by using the periodically placed piezoelectric actuator and sensor pairs along one direction of the plate. Active control strategies are employed to actively adjust the band-gap properties of the metamaterial plate. Displacement and acceleration feedback control methods are applied to design the controllers so that the positive active stiffness and inertia for the elastic metamaterial plate can be provided. The dynamic responses of the finite plate with periodic piezoelectric actuator/sensor pairs are calculated using the spectral element method (SEM), and the calculation accuracy of the SEM is validated by the finite element method. The present results reveal that zero-frequency band gaps can be generated for the elastic metamaterial plate, and the band-gap characteristics in the medium and high frequency ranges can be significantly enhanced by using the acceleration feedback control. Moreover, very wide band gaps for the elastic metamaterial plate can be obtained by using the active acceleration control, and the starting frequencies of the first band gap under the acceleration control can be reduced by increasing the acceleration control gain. The widths of the zero-frequency and Bragg-type band gaps for the elastic metamaterial plate can be amplified by increasing the displacement feedback control gain. The control voltages to be applied on the actuators for the elastic metamaterial plate are also calculated and discussed.

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Acknowledgements

This research work is supported by the National Natural Science Foundation of China (Project-Nos. 11761131006, 11572007, 11402067), the German Research Foundation (DFG, Project-No. ZH 15/30-1) and the Basic Research Foundation of Chinese University (Project-Nos. 3072019CFJ0205, HEUCFJ180203).

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Authors and Affiliations

  1. College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin, 150001, People’s Republic of China

    Tao Ren, Chunchuan Liu & Fengming Li

  2. Department of Civil Engineering, University of Siegen, 57068, Siegen, Germany

    Chuanzeng Zhang

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  1. Tao Ren
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Correspondence to Chunchuan Liu or Fengming Li.

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Ren, T., Liu, C., Li, F. et al. Active tunability of band gaps for a novel elastic metamaterial plate. Acta Mech 231, 4035–4053 (2020). https://doi.org/10.1007/s00707-020-02728-1

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  • DOI: https://doi.org/10.1007/s00707-020-02728-1

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