Analysis of a Nonlinear Locally Resonant Metamaterial With Resistance-Inductance Shunt

Abstract The study of metamaterials for simultaneous vibration control and energy harvesting is a subject with considerable recent interest. This paper investigates a weakly nonlinear meta-material with electromechanical local resonators coupled to a resistance-inductance shunt circuit, a system with no previous examination in the literature. The nonlinear band structure of the system is presented to demonstrate the effect of an inductor in the shunt circuit, including the influence on softening and hardening nonlinearity effects. The system is then excited by a transient wavepacket and simulated numerically to further explore the features of nonlinear wave propagation in the proposed structure for multiple inductance values. Particularly, the system’s voltage response is studied through spatial profiles to observe the effects of shunt inductance, nonlinearity, and any potential interaction between the two. Focus is given to the potential for vibration control and energy harvesting by this metamaterial, including comparisons to previously investigated similar systems with resistance-only shunt circuit. For certain parameters including high electromechanical coupling, the band structure of this system is shown to include three mode branches instead of the two-mode band structure observed in the absence of shunted inductor. Strong vibration attenuation is observed in the frequency range around the central mode branch. The effects of the inductor on wave propagation and harvested voltage are also shown.