Spectro-spatial analysis of elastic wave propagation in nonlinear elastic metamaterial systems with damping

Different from the linear counterpart, elastic wave propagation in nonlinear elastic metamaterials with damping (EMD) systems has much more novel behaviors. It is little work that reveals the nonlinear wave propagation mechanism in the nonlinear EMD in the literature. In this paper, nonlinear EMD systems with different configurations for the nonlinear elements are constructed to study the nonlinear wave propagation characteristics based on the analytical formulation. Nonlinear wave propagation attenuation characteristics in nonlinear EMD systems are studied in the frequency-domain. Spectro-spatial characteristics of nonlinear traveling wave packet in space- and time-domain are also analyzed to reveal space frequency-domain characteristics. Influences of different configurations for the nonlinear elements on wave propagation in nonlinear EMD systems are discussed. Results shown that locations of band structures can be tuned by changing intensities of nonlinearities in the nonlinear EMD systems, which are not found in the linear system. Moreover, different configurations for the nonlinear elements can lead to localization feature emerged in a nonlinear EMD system, which indicates solitary waves causing from the interaction between dispersion and nonlinearity exist in the nonlinear systems. This interesting wave propagating properties can be used to design new devices for acoustic switches, energy harvesting, and broadband vibration control.