Active tunability of band gaps for a novel elastic metamaterial plate
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O R I G I NA L PA P E R
Tao Ren · Chunchuan Liu Chuanzeng Zhang
· Fengming Li ·
Active tunability of band gaps for a novel elastic metamaterial plate
Received: 18 April 2019 / Revised: 4 February 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
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. 1 Introduction The elastic wave propagation and vibration band-gap characteristics of periodic structures have been investigated for a long time [1–4]. When the frequencies of the elastic waves are in the frequency band gaps, they will attenuate near the excitation locations and cannot freely propagate through the periodic structures [5,6]. Generally speaking, the elastic wave band-gap mechanisms for periodic structures can be classified into the Bragg scattering and local resonance mechanisms [7,8]. For periodic structures with Bragg scattering mechanism, the band gaps are induced by the periodically arranged scatterers, and the band-gap locations generally appear in the medium and high frequency ranges [1,9]. For the local resonance-type periodic structures, the frequency ranges of the band gaps can be determined by the local resonance frequencies of the resonators, and the band-gap locations can appear in the low frequency range [10–12]. Therefore, the vibration suppression T. Ren · C. Liu (B) · F. Li (B) College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin 150001, People’s Republic of China C. Liu E-mail: [email protected] F. Li E-mail: [email protected] C. Zhang Departmen
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