Damping influence on dynamic propagation of inclusions in elastic wave metamaterials with local resonators

Damping can be found in all materials in nature, and it is an intrinsic property of materials and structures. In this work, the influence of damping on a growing inclusion embedded in an elastic wave metamaterial with local resonators is studied. It is assumed that the resonator masses vary along a straight line at a constant speed. Using an approach based on the Wiener–Hopf method, the ratio of tip to end displacements of the inclusion is derived. Numerical results show that powerful damping will reduce the instability of inclusion growth and shift it to a stable and slow propagation mode in low-speed regions. In addition, damping can make the displacement ratio tend to the case without inclusion in high-speed regions. These results indicate that more powerful resistance can be created by damping during inclusion growth.