Elastic guided waves in plates with surface roughness. I. Model calculation

This paper reports analytical research on the effect of surface roughness on ultrasonic guided waves in plates. The theoretical model is constructed by exploiting the phase-screen assumption that takes advantage of the Kirchhoff approximation, where, on a local scale, the roughness degrades only the signal phase. The effect of the rough surface on the guided wave is treated by decomposing the wave modes into their constituent partial waves and considering individually the effect of the roughness on the partial wave components as they reflect from the plate surfaces. An approximate dispersion relation is derived for the traction-free rough waveguide that is formally identical to the conventional Lamb wave equation, but incorporating the roughness parameter as a complex plate thickness. A more accurate version of the model calculation is generalized to fluid-immersed plates having only a single rough surface either on the same, or opposite, side of the plate as the incident ultrasonic field. Calculations of the reflection coefficients in the presence of roughness serve to illustrate the phenomena for the case of the guided waves.