Localized Frequency Shift and Attenuation of Rayleigh Waves Due to Surface Roughness
Paper 904
This paper will be presented in the session Acoustic Materials and their Characterization.
Full paper (PDF format).
Abstract
The local effect of small two-dimensional roughness corrugation on the Rayleigh wave frequency and attenuation is studied using Rayleigh method. The case considered is a semi-infinite isotropic elastic media. Fourier transform is applied on the differential equations governing the normal modes of vibration and the dispersion relation is derived for stress-free boundary conditions at roughness surface. Up to second order terms are kept in the equation. The dispersion relation is then solved numerically to calculate the local effect of roughness on the wave’s frequency.
Result are checked with zero roughness height and show complete agreement with the traditional problem of smooth surface. As the height increases then the wave speed decrease until it totally demolishes. One should note that this is the local effect of the roughness and not the global one. In general the wave might still be propagate but these results mean that the wave will be severely slowed down at roughness heights more than that. On the other hand calculations demonstrate the effect of wave spacing as measured by the parameter a which is related to roughness wave no. When a =0 then the surface is flat and the same value of the wave speed is calculated. As a increases the wave speed decreases in a semi-linear fashion except around the values when a is near to the wave number, at this case a resonance phenomenon occurs and the wave speed increases in this vicinity. However, as the corrugation wave number increases beyond that the wave speed decreases. Similar behavior was found for the random three dimensional wave in the calculations of . Eguiluz, and Maradudin [Physical Review B, Vol. 28, No. 2, (1983), p. 728.]. This also in agreement with the physical behavior of such waves.