On the influence of a surface roughness on propagation of anti-plane short-length localized waves in a medium with surface coating

We discuss the propagation of localized surface waves in the framework of the linear Gurtin–Murdoch surface elasticity and taking into account a roughness of a free boundary. We derive a boundary-value problem for anti-plane motions with curvilinear boundary and surface stresses. Using the asymptotic technique developed earlier, we obtain the form of a localized wave and analyze its amplitude evolution. As the main result we present the dependence of the wave amplitude on the roughness magnitude. The presented results could be used for non-destructive evaluation of the surface microstructure using surface waves-based devices. In particular, measuring the decay rate with the depth one can estimate roughness of a surface and appearance of new surface defects.