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Elastic mechanical metamaterials exhibit unusual frequency contingent properties like negative mass, negative Young’s modulus, and negative Poisson’s ratio in a particular band of the excitation frequency. Locally resonant units in the designed metamaterial enable bandgap formation virtually at any frequency for wavelengths much higher than the lattice length of the unit. Due to out of phase motion of multiple resonating units with lattice, there is a change in the dynamic properties (stiffness or mass or density) of the material as these properties become frequency-dependent.On another side, at higher frequencies for wavelengths equal to the lattice size of the medium, the Bragg scattering phenomenon occurs, which also helps in the bandgap formation. Therefore, these extreme frequency contingent physical properties modulate wave propagation through designed metama- terials. In this research, the band structure of piezo-embedded negative stiffness metamaterial is derived using generalized Bloch theorem. Bloch theorem is used to solve various periodic media problems in different fields. The relationship between frequency and wave number can be established using this theory. The results elucidate that the insertion of the piezoelectric material in the resonating unit can provide not only better tunability but also several unusual band structures that can be perceived. The attenuation bandwidth of the designed metamaterial can be tailored through critical parameters derived from the extensive non-dimensional study of the system. This research can be considered as a contribution towards designing the active elastic mechanical metamaterials.
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