Nonlinear Metamaterials with Multiple Local Mechanical Resonators: Analytical and Numerical Analyses

Abstract

This paper examines the role of stiffness nonlinearity on a periodic one-dimensional chain with multiple local resonators. The cells of the chain consist of lumped masses connected through nonlinear springs. Each cell is embedded with multiple local resonators having different parameters. In one case the local resonators are assumed to be linear and in another case they are nonlinear. The dispersion equation for the system is derived analytically by the method of multiple scales (MMS). The results are validated via comparison with those in the literature and numerically via Matlab. The nonlinearity shows enhancement in the bandgap regions, especially with increasing number of local resonators.