In this paper, an active control strategy is employed to actively tune the vibration and wave propagation properties in a piezoelectric metamaterial beam. The piezoelectric actuator and sensor are periodically arranged along the piezoelectric metamaterial beam. By using the extended Hamilton principle, the governing equations for the fully coupled piezoelectric metamaterial beam are obtained. The negative proportional feedback control strategy is introduced to achieve the periodical active stiffness for the piezoelectric metamaterial beam. The band structures and natural frequencies of the proposed periodic structure are derived by the transfer matrix method, and the spectral element method is applied as numerical validation. The influences of the feedback control gain ratio, length ratio, and the number of the unit cells on natural frequencies and bandgaps are discussed. Results indicate that the natural frequencies of the system are reduced with the increase in the feedback control gain ratio and length ratio. In addition, multiple bandgaps can be generated by using the negative proportional feedback control strategy. It is found that bandwidths can be obviously broadened by selecting the proper feedback control gain ratio and length ratio. The theoretical and numerical results show that the vibration and wave propagation properties of the proposed piezoelectric metamaterial beam can be controlled by using the negative proportional feedback control strategy.

中文翻译：

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压电超材料梁中弹性波传播的主动调谐

在本文中，采用主动控制策略来主动调整压电超材料梁中的振动和波传播特性。压电致动器和传感器沿压电超材料梁周期性排列。利用扩展的哈密顿原理，得到了全耦合压电超材料梁的控制方程。引入负比例反馈控制策略来实现压电超材料梁的周期性主动刚度。所提出的周期结构的能带结构和固有频率是通过传递矩阵方法推导出来的，并应用谱元方法作为数值验证。反馈控制增益比、长度比、讨论了固有频率和带隙上的晶胞数。结果表明，随着反馈控制增益比和长度比的增加，系统的固有频率降低。此外，使用负比例反馈控制策略可以产生多个带隙。发现通过选择合适的反馈控制增益比和长度比可以明显拓宽带宽。理论和数值结果表明，所提出的压电超材料梁的振动和波传播特性可以通过使用负比例反馈控制策略来控制。此外，使用负比例反馈控制策略可以产生多个带隙。发现通过选择合适的反馈控制增益比和长度比可以明显拓宽带宽。理论和数值结果表明，所提出的压电超材料梁的振动和波传播特性可以通过使用负比例反馈控制策略来控制。此外，使用负比例反馈控制策略可以产生多个带隙。发现通过选择合适的反馈控制增益比和长度比可以明显拓宽带宽。理论和数值结果表明，所提出的压电超材料梁的振动和波传播特性可以通过使用负比例反馈控制策略来控制。