Propagation of elastic waves in a plate with rough surfaces

Propagation of Lamb waves in plates with rough surfaces is important to practical problems of nondestructive evaluation and study of seismic waves and, however, is very diffcult that the research till now has been limited to the approximate techniques such as phase screen model. The problem is studied in this paper by the stochastic theory and the elevation variation of the rough surfaces is considered as a stochastic procedure. The dispersive relation of the stochastic average of the Lamb wave, Rayleigh-Lamb equation is deduced based on the assumptions that the variation is small and the multi-reflections are independent from each other. The attenuation of the Lamb waves caused by the surface roughness is analyzed by the equation and it is found that the attenuation is approximately proportional to the variance of the roughness and is independent from its correltion length. Experimental measurement is carried out to verify the theoretical predictions.