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Dynamics of periodic structures has fascinated researchers for decades. Metamaterials are one of the exemplars of these periodic structures. Spatial periodicity of mechanical unit cells in artificially engineered metamaterials exhibits idiosyncratic physical properties like negative mass, negative Young’s modulus, and negative Poisson’s ratio. These extreme physical properties are beyond the properties found in the natural materials. This exceptional dynamic behaviour is frequency dependent, which in turn forms the attenuation and transmission band during wave transmission through these metamaterials. The frequency ranges in which a wave can transmit or attenuate along the length of the metamaterial are known as transmission and attenuation bands respectively. In this work, the band structure of piezo-embedded negative mass metamaterial is analysed using generalized Bloch theorem. The addition of the piezoelectric material at the resonating unit increases the damping and complexity of the solution. Bloch theorem is used to solve several periodic media and using this theory, the relationship between frequency and wavenumber can be established. Implementation of Bloch theorem has not been reported yet in the context of the piezo embedded mass-in-mass metamaterial. Therefore, wave propagation through finite units is studied through band structure. In addition, voltage and power produced by piezoelectric material are estimated. This research can be considered as the first step towards modelling an active metamaterial.
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