Elastic mechanical metamaterials are the exemplar of periodic structures. These are artificially designed structures having idiosyncratic physical properties like negative mass and negative Young’s modulus in specific frequency ranges. These extreme physical properties are due to the spatial periodicity of mechanical unit cells, which exhibit local resonance. That is why scientists are researching the dynamics of these structures for decades. This unusual dynamic behavior is frequency contingent, which modulates wave propagation through these structures. Locally resonant units in the designed metamaterial facilitate bandgap formation virtually at any frequency for wavelengths much higher than the lattice length of a unit. Here, we analyze the band structure of piezo-embedded negative mass metamaterial using the generalized Bloch theorem. For a finite number of the metamaterial units coupled equation of motion of the system is deduced, considering purely resistive and shunted inductor energy harvesting circuits. Successively, the voltage and power produced by piezoelectric material along with transmissibility of the system are computed using the backward substitution method. The addition of the piezoelectric material at the resonating unit increases the complexity of the solution. The results elucidate, the insertion of the piezoelectric material in the resonating unit provides better tunability in the band structure for simultaneous energy harvesting and vibration attenuation. Non-dimensional analysis of the system gives physical parameters that govern the formation of mechanical and electromechanical bandgaps. Optimized numerical values of these system parameters are also found for maximum first attenuation bandwidth. Thus, broader bandgap generation enhances vibration attenuation, and energy harvesting can be simultaneously available, making these structures multifunctional. This exploration can be considered as a step towards the active elastic mechanical metamaterials design.

弹性机械超材料是周期性结构的典范。这些是人工设计的结构，在特定的频率范围内具有特殊的物理特性，例如负质量和负杨氏模量。这些极端的物理特性归因于机械单元电池的空间周期性，该机械单元电池表现出局部共振。这就是为什么科学家几十年来一直在研究这些结构的动力学的原因。这种异常的动态行为是频率偶然的，它调制通过这些结构的波传播。设计的超材料中的局部共振单元实际上促进了在任何频率下的带隙形成，其波长远高于单元的晶格长度。在这里，我们使用广义布洛赫定理分析压电嵌入负质量超材料的能带结构。对于有限数量的超材料单元，考虑纯电阻式和并联电感器能量收集电路，推导出系统的运动方程。随后，使用后向替代方法计算压电材料产生的电压和功率以及系统的透射率。在谐振单元处添加压电材料增加了解决方案的复杂性。结果说明，在谐振单元中插入压电材料可在带结构中提供更好的可调谐性，以便同时进行能量收集和振动衰减。系统的无量纲分析给出了控制机械和机电带隙形成的物理参数。还找到了这些系统参数的最佳数值，以获得最大的第一衰减带宽。因此，更宽的带隙产生增强了振动衰减，并且可以同时进行能量收集，从而使这些结构具有多功能性。这种探索可被视为迈向主动弹性机械超材料设计的一步。