Abnormal wave propagation behaviors in two-dimensional mass–spring structures with nonlocal effect

Abstract

This paper considers the propagation of elastic waves in periodic two-dimensional mass–spring structures with diagonal springs. The second-neighbor interactions in non-diagonal directions are included to account for the nonlocal effect. The influences of the spring stiffness in the diagonal directions and the nonlocal effect on the propagation characteristics of elastic waves are then scrutinized. Through the dispersion relation curve and the equi-frequency contours, it is seen that when the diagonal spring stiffness increases, the slope of the second curve in the –M direction will not always be positive, meaning that the negative group velocity occurs. Therefore, an incident wavevector with a chosen angle to the negative group velocity can lead to the negative refraction phenomenon in the two-dimensional mass–spring structure. Another interesting phenomenon called directional radiation of elastic waves can also be achieved by adjusting the nonlocal effect. Within a certain range, the stronger the nonlocal effect in a specific direction is, the more obviously the elastic waves propagate along this direction. In this paper, we theoretically analyze and numerically simulate the phenomena of negative refraction and directional wave propagation by choosing a proper set of parameters of the two-dimensional mass–spring structure.