Novel energy exchange behaviors and mechanisms in nonlinear acoustic metamaterials with multiple nonlinear resonators

Abstract Wave-wave interactions in a nonlinear metamaterial or structure with two propagating waves can induce energy exchange within the nonlinear systems. The effects of nonlinear resonators on these interactions and energy exchanges in a nonlinear acoustic metamaterial have not been extensively studied in the literature. In this paper, a nonlinear monatomic acoustic metamaterial with multiple nonlinear resonators (NMAM-MNR) is constructed to investigate the new behaviors and mechanisms introduced by these nonlinear resonators. Stability analyses reveal that stability can be tuned by adjusting the number of nonlinear resonators and by selecting different intensities or masses of the resonators and the chain. Additionally, direct numerical simulations are performed to study the novel energy exchange behaviors and mechanisms in NMAM-MNR systems. The results demonstrate that the degree and frequency of energy exchange can be tuned by altering the mass ratios, stiffness ratios, intensities, and natural frequencies of the nonlinear resonators and the chain. The influence of mass and stiffness ratios on the time taken for the B-wave magnitude to first reach its maximum value in NMAM-MNR systems is also studied, showing that the rate of energy exchange induced by wave-wave interactions can be tuned by changing the stiffness and mass ratios of multiple nonlinear resonators. These properties have potential applications in the fields of energy harvesters, waveguides, and resonant energy transfer mechanisms.