Finite element simulations of surface effect on Rayleigh waves

Rayleigh waves influenced by surface effect are investigated by using finite element methods, in which eigenfrequency analysis are performed on a model composed of a half-space covered by the surface effect dominated domain. For a given wavelength, the frequency of the Rayleigh wave is obtained as the eigenfrequency of the model satisfying Floquet periodic boundary conditions. The thickness of the surface effect can be set to be infinitely small or a finite value in the finite element methods. The curvature-dependent out-of-plane force induced by surface tension as described by the generalized Young-Laplace equation is realized through geometric nonlinear analysis. The finite element simulations show that the assumptions of small curvature and infinitely small thickness of the surface effect widely used in theoretical approaches become invalid when Rayleigh waves are highly influenced by the surface effect. This work gives a more accurate insight into the surface effect on Rayleigh waves and provides a potential method for measuring the thickness of the surface effect from the dispersion curves of surface effect influenced Rayleigh wave velocities.