Dispersive surface waves propagating through a continuous elastic medium with local rotation

Abstract

Elastic metamaterials are man-made materials engineered with the purpose of inducing atypical bulk elastic properties. To model a type of elastic metamaterial with local rotational effects, a new two-dimensional continuum model which incorporates local rotation as a scalar field superposed on the translational displacement fields is utilized. This paper provides a comprehensive study of surface wave propagation in this new continuous medium. Unlike the classical Rayleigh wave, the surface wave in this new medium is dispersive. An explicit dispersion relation is obtained, and a closed-form solution of the dispersion curve is derived. The dispersion relation is then used to evaluate the general behaviour of the surface wave. It is found that even for the cases where the effect of local rotation is relatively weak, the surface wave still clearly shows dispersion. The phase velocity of the surface wave falls mostly between the classical Rayleigh wave and the shear wave, especially for cases where the effect of local rotation is weak. In addition to the classical Rayleigh wave, there exists another surface wave which possesses a wavespeed depending only on local rotational parameters. It was also found that particles residing on the free surface of the material move in an elliptical fashion similar to that of classical Rayleigh wave propagation.