Dynamics of Piezo-Embedded Negative Stiffness Mechanical Metamaterials: A Study on Electromechanical Bandgaps

Abstract

Dynamics of periodic materials and structures have a profound historic background starting from Newton’s first effort to find sound propagation in the air to Rayleigh’s exploration of continuous periodic structures. This field of interest has received another surge from the early 21st century. Elastic mechanical metamaterials are the exemplars of periodic structures that exhibit interesting frequency-dependent properties like negative Young’s modulus, negative mass and negative Poisson’s ratio in a specific frequency band due to additional feature of local resonance. In this research, we present the modeling of piezo-embedded negative stiffness metamaterials by considering a shunted inductor energy harvesting circuit. For a chain of a finite number of metamaterial units, the coupled equation of motion of the system is deduced using generalized Bloch’s theorem. Successively, the backward substitution method is applied to compute harvested power and the transmissibility of the system. Additionally, through the extensive non-dimensional study of this system, the proposed metamaterial band structure is investigated to perceive locally resonant mechanical and electromechanical bandgaps. The results explicate that the insertion of the piezoelectric material in the resonating unit provides better tun-ability for vibration attenuation and harvested energy.