Wave transmission through nonlinear impacting metamaterial unit

Abstract

Metamaterials are an increasingly well-known type of generalized composites that can exhibit unconventional behaviors and responses due to its exciting frequency dependent properties which are not commonly encountered in natural materials. Elastodynamic metamaterials based on mechanical structures have a range of potential applications of importance in sound, vibration and seismic engineering. However, the effectiveness of metamaterials is limited to a relatively narrow frequency band as they are generally based on linear resonance mechanisms. These linear metamaterials do not perform well when under the broadband excitation spectra that are common in real life applications. Mathematically, the 1-D metamaterial is represented by a series of periodic resonating spring and mass lattice structures. In this paper, the bandwidth of a metamaterial is examined by introducing nonlinearity in the resonating frequency. The performance of nonlinear metamaterial is well investigated in the field of electromagnetic wave propagation although the existing literature on nonlinear mechanical metamaterial is very limited and investigated only bistable and monostable type resonating metamaterial. Till date, any research on the impacting resonating metamaterial has not been reported, in spite of its excellent vibration insulation and resonating bandwidth enhancement properties. Therefore, as a first step towards exploring the impacting metamaterial, we have analytically estimated the bandwidth enhancement of a one dimensional impacting mechanical metamaterial unit over a linear metamaterial. First, the steady state response of an impacting system is computed analytically and then the transmission loss in the frequency domain is estimated using MATLAB. From the analysis, it is found that the resonating bandwidth of an impacting system is wider than that of an equivalent linear system. Therefore, it can be effectively used as a wideband mechanical filter, acoustic insulator or shield.