| Abstract: | An approach to obtaining the dispersion equation of surface acoustic waves (SAWs) on a stress-free, randomly rough surface of an anisotropic elastic medium is suggested. The problem is solved in the approximation of a weakly rough surface using Green′s function technique. The dispersion and attenuation of sagittally and shear horizontally (SH) polarized SAWs are investigated both analytically and numerically for a three-dimensionally (3D) and a two-dimensionally (2D) rough surface of an isotropic medium. The results for 2D roughness are shown to be contained in the more general expressions for the 3D case, and the connection between the results for the 3D and the 2D cases is pointed out. Dispersion relations are derived for SAWs of both polarizations propagating in an arbitrary direction along a 2D rough surface. The SAW attenuation mechanisms are investigated at various incidence angles. It is concluded that all three mechanisms (viz. scattering into bulk transverse, longitudinal, and Rayleigh surface acoustic waves) are involved for the Rayleigh and SH polarized SAWs at certain incidence angles, whereas at the other angles only some of the mechanisms are. The criterion for the existence of SH polarized SAWs on a rough surface is considered. A possible increase of the SAW phase velocity on a rough surface compared with that for a flat boundary is discussed. In the limit λ a (where a is the roughness correlation length) simple explicit expressions for the phase velocities of Rayleigh and SH polarized SAWs are derived. A comparison of the results obtained herein with those of other workers is presented. |
