An innovative special class of tunable periodic metamaterials is designed, suitable for realizing high-performance acoustic filters. The metamaterial is made up of a phononic crystal coupled to local resonators. Such local resonators consist of masses enclosed into piezoelectric rings, shunted by either dissipative or non-dissipative electrical circuit. By tuning the impedance/admittance of such electrical circuits, it is possible to fully adjust the constitutive properties of the shunting piezoelectric material. This feature paves the way for unconventional behaviours, well beyond the capabilities achievable with classical materials. It follows that the acoustic properties of the periodic metamaterial can be adaptively modified, in turn, opening new possibilities for the control of pass and stop bands. By exploiting a generalization of the Floquet–Bloch theory, the in-plane free wave propagation in the tunable metamaterial is investigated, by varying a certain tuning parameter, to show the efficiency of the proposed shunting piezoelectric system as a wave propagation control device. Particular attention is devoted to the determination of the in-plane constitutive equations of the shunting piezoelectric phase in the transformed Laplace space. Finally, broad design directions of tunable acoustic filters aiming to a changing performance requirement in real-time, is also provided.

设计了一种创新的特殊类型的可调周期超材料，适用于实现高性能的声学滤波器。超材料由耦合到本地谐振器的声子晶体组成。这样的局部谐振器由包裹在压电环中的质量组成，这些质量被耗散或非耗散电路分流。通过调节这种电路的阻抗/导纳，可以完全调节并联压电材料的本构特性。此功能为非常规行为铺平了道路，远远超出了传统材料可以实现的功能。因此可以周期性地修改周期性超材料的声学特性，从而为控制通带和阻带开辟了新的可能性。通过利用Floquet-Bloch理论的推广，通过改变一定的调谐参数，研究了可调谐超材料中面内自由波的传播，以证明所提出的并联压电系统作为波传播控制装置的效率。特别注意确定变换后的拉普拉斯空间中并联压电相的平面本构方程。最后，还针对实时变化的性能要求提供了可调谐声滤波器的广泛设计方向。特别注意确定变换后的拉普拉斯空间中并联压电相的平面本构方程。最后，还针对实时变化的性能要求提供了可调谐声滤波器的广泛设计方向。特别注意确定变换后的拉普拉斯空间中并联压电相的面内本构方程。最后，还针对实时变化的性能要求提供了可调谐声滤波器的广泛设计方向。