Modeling and Analysis of a Nonlinear Locally Resonant Metamaterial with Inductance Shunt

This paper investigates a weakly nonlinear metamaterial with electromechanical local resonators coupled to a resistance-inductance shunt circuit. An analytical solution is developed for the system using the perturbation method of multiple scales, and validated through direct numerical integration. Linear and nonlinear band structures are used for parametric analysis of the system, focusing on the effect of system parameters on band gap formation and vibration attenuation. In addition, the effects of nonlinearity and the interaction with shunt parameters are examined. Results describe multiple methods of tuning band gaps and pass bands of the system through various parameters, demonstrating the flexibility and potential of the examined metamaterial.