Nonlocal interactions on dynamic growth of an inclusion in locally resonant elastic wave metamaterials

In this work, the influences of nonlocal interactions on the growing inclusion are studied which are embedded in an elastic wave metamaterial with local resonators. The nonlocal interactions between main resonators are considered as linear springs connected to the second nearest neighboring ones. In addition, the inclusion is supposed that particle masses change along a straight line. Based on the Wiener–Hopf method, the ratio of the tip to end displacements of the inclusion is derived. Furthermore, the dynamic effective mass and stop band frequency are discussed. Numerical results show that in comparison with the system without nonlocal interactions, the new periodic structure can make the displacement ratio tend to the case of homogeneous lattices for high-speed regions. It indicates that more powerful resistance can be created by nonlocal springs during the inclusion growth.