Effect of interaction of adjacent unit-cells on wave propagation in coupled mass-in-mass metamaterials

This paper aims to study the effect of the interaction of adjacent unit-cells in coupled mass-in-mass metamaterial on wave behaviors, which enables us to achieve a wavy dispersion relationship. Elastic wave propagation in a coupled mass-in-mass metamaterial is investigated to clarify the effect of the interaction of adjacent unit-cells on the dispersion relation and wave velocity. Elastic wave behavior based on an infinite system is studied in terms of the band structure and group velocity. The dynamic responses in frequency domain and time domain of the finite mass-in-mass lattice are calculated by using Laplace transform and numerical methods. The band structures and transmittances show that the coupled mass-in-mass metamaterial has a bandgap, which can be used to suppress and isolate vibration. The parameter study shows that changing the stiffness and location of the coupled springs can adjust the distribution of the bandgap. Importantly, we also calculate the ratio of group velocity to phase velocity that indicates the negative group velocity appearing in the wavy dispersion relation of coupled mass-in-mass metamaterials. These results show that the interaction of adjacent unit-cells plays a crucial role in the wave behavior of the coupled mass-in-mass metamaterial.