Dispersive behavior of high frequency Rayleigh waves propagating on an elastic half space

Abstract: When the wavelength of Rayleigh wave is comparable with nanometers, Rayleigh wave will become dispersive. Such an interesting phenomenon cannot be predicted by the classical theory of elastodynamics. In order to reveal the internal mechanism and influencing factors of the dispersion, a model of Rayleigh wave propagating on an elastic half space is established and analyzed by a new theory of surface elastodynamics, in which the surface effect characterized by both the surface energy density and surface inertia is introduced. Two intrinsic nano-length scales, including the ratio of bulk surface energy density to bulk shear modulus and the ratio of surface mass density to bulk mass density, are achieved. It is found that when the wavelength of Rayleigh wave is comparable with the two intrinsic nano-lengths, the surface effect becomes significant. As a result, dispersion of Rayleigh wave happens and even two Rayleigh waves with different wave speeds may appear. Furthermore, it is found that the effect of surface energy density would enhance the wave speed, while that of surface inertia would reduce it. With the increase of wavelength, both effects gradually disappear and the Rayleigh wave speed degenerates to the classical one. The results of this paper are not only helpful to understand the dispersive mechanism of elastic waves, but also helpful for the fine design and measurement of nanowave devices. Graphic abstract: [Figure not available: see fulltext.]