The non-unique existence of Rayleigh waves in nonlocal elastic half-spaces

It is well known that for the local isotropic elastic half-spaces, there always exists a unique Rayleigh wave. However, as shown in this paper, for the nonlocal isotropic elastic half-spaces, the existence picture of Rayleigh waves is more complicated. It contains the domains (of the material and nonlocality parameter) for which only one Rayleigh wave can propagate, the domains that support exactly two Rayleigh waves and the domains where three Rayleigh waves are possible. When two or three Rayleigh waves exist, one wave is the counterpart of the local (classical) Rayleigh wave, the other waves are new Rayleigh modes. Remarkably, the new modes can travel with high velocity at small wave numbers. The existence results are proved by employing the complex function method. The formulas for the wave velocity of Rayleigh waves have also been derived and they will be useful in various practical applications.