Perturbation theory about SAW dispersion and application

The perturbation theory of Auld, which describes the effect of a subsurface gradient on the velocity dispersion of surface waves has been modified to a simpler form, by an approximation using a newly defined velocity gradient for the case of isotropic materials. The modified theory is applied to the wear-in procedure in AISI 1045 steel with various residual stress distributions. The frequency dependency of the Rayleigh surface wave is investigated indirectly by measuring the angular dependency of the backward radiation of the incident ultrasonic wave in the scuffing specimens, and then compared to the perturbation theory. It was concluded that Break-in procedure in order to elongate the safety life reduce g, fractional change in velocity per unit stress by 20-30%.