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Perturbation solution for the interaction of Lamb waves with localized surface defects

We present an analytical solution of the transmitted and reflected wave fields due to the interaction of Lamb waves with localized, small-scale defects on late surfaces. The surface defect is represented by a distribution of surface sources, and the overall solution is obtained as a superposition of the incident wave field plus the 'small' wave field associated with the surface sources. The reflection and transmission coefficients of various Lamb modes are also determined. It is shown that the scattered field consists of a superposition of various possible modes at the frequency of the incident mode. For the fundamental modes, it is found that the reflection coefficients are periodic functions of the defect width with the period and magnitude being dependent on the surface defect profile. The transmission coefficient for the converted mode is also found to be a periodic function of the defect width while that corresponding to the incident mode does not deviate significantly from unity. A parametric study has also shown that to this approximation the numerical values of the reflection and transmission coefficients are not sensitive to the maximum slope of the defect profile.