On a Nonlinear Locally Resonant Metamaterial with Resistance-Inductance Shunt

Numerous recent works have established the potential of various types of metamaterials for simultaneous vibration control and energy harvesting. In this paper, we investigate a weakly nonlinear metamaterial with electromechanical local resonators coupled to a resistance-inductance shunt circuit, a system with no previous examination in the literature. An analytical solution is developed for the system using the perturbation method of multiple scales, and validated through direct numerical integration. The resulting linear and nonlinear band structures are used for parametric analysis of the system, focusing on the effect of resonator and shunt circuit parameters on band gap formation and vibration attenuation. This band structure analysis informs further study of the system through wavepacket excitation as well as spectro-spatial analysis. The voltage response of the system is studied through spatial profiles and spectrograms to observe the effects of shunt inductance, nonlinearity and their interactions. Results describe the impact of adding a shunted inductor, including significant changes to the band structure; multiple methods of tuning band gaps and pass bands of the system; and changes to wave propagation and voltage response. The results demonstrate the flexibility of the proposed metamaterial and its potential for both vibration control and energy harvesting, specifically compared to a previously studied system with resistance-only shunt.