Mechanical metamaterials are uniquely engineered form of periodically arranged unit cells that exhibit interesting frequency-dependent physical properties like negative effective mass, Young’s modulus and Poisson’s ratio. These extreme engineering properties are beyond the natural properties of a material, which can modulate the propagation of wave. In this article, a mechanical realization of one of these uncommon properties called negative stiffness is emulated through analytical simulation. Wave propagation in metamaterials is contingent on frequency, which in turn results in transmission and attenuation bands. Simultaneous vibration control and energy harvesting can be executed by embedding energy harvesting smart material within the resonating units of the metamaterial. However, this needs careful design studies to outline the range of parameters. In this work, first, the band structure of a piezo-embedded negative stiffness metamaterial is studied using generalized Bloch’s theorem. Subsequently, harvested power along with the transmissibility is computed for a chain of finite number of metamaterial units by using backward substitution method. The results of the parametric studies elucidate that piezo-embedded negative stiffness metamaterial can enhance the performance in terms of vibration attenuation and harvested energy.

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.

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