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.

中文翻译：

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新型弹性超材料板带隙的主动可调性

提出了一种新型主动弹性超材料板，通过使用沿板的一个方向周期性放置的压电致动器和传感器对，具有可调振动带隙特性。采用主动控制策略来主动调整超材料板的带隙特性。应用位移和加速度反馈控制方法来设计控制器，从而为弹性超材料板提供正主动刚度和惯性。使用谱元法（SEM）计算了具有周期性压电执行器/传感器对的有限板的动态响应，并通过有限元方法验证了SEM的计算精度。目前的结果表明，弹性超材料板可以产生零频带隙，使用加速度反馈控制可以显着提高中高频范围内的带隙特性。此外，采用主动加速控制可以获得非常宽的弹性超材料板带隙，通过增加加速控制增益可以降低加速控制下的第一带隙的起始频率。弹性超材料板的零频和布拉格型带隙的宽度可以通过增加位移反馈控制增益来放大。还计算和讨论了施加在弹性超材料板致动器上的控制电压。采用主动加速控制可以获得非常宽的弹性超材料板带隙，通过增加加速控制增益可以降低加速控制下的第一带隙的起始频率。弹性超材料板的零频和布拉格型带隙的宽度可以通过增加位移反馈控制增益来放大。还计算和讨论了施加在弹性超材料板致动器上的控制电压。采用主动加速控制可以获得非常宽的弹性超材料板带隙，通过增加加速控制增益可以降低加速控制下的第一带隙的起始频率。弹性超材料板的零频和布拉格型带隙的宽度可以通过增加位移反馈控制增益来放大。还计算和讨论了施加在弹性超材料板致动器上的控制电压。弹性超材料板的零频和布拉格型带隙的宽度可以通过增加位移反馈控制增益来放大。还计算和讨论了施加在弹性超材料板致动器上的控制电压。弹性超材料板的零频和布拉格型带隙的宽度可以通过增加位移反馈控制增益来放大。还计算和讨论了施加在弹性超材料板致动器上的控制电压。