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.

我们讨论线性Gurtin-Murdoch表面弹性框架中局部表面波的传播，并考虑到自由边界的粗糙度。我们导出了具有曲线边界和表面应力的反平面运动的边界值问题。使用较早开发的渐近技术，我们获得了局部波的形式并分析了其幅度演化。作为主要结果，我们提出了波幅对粗糙度幅值的依赖性。提出的结果可用于使用基于表面波的设备对表面微观结构进行无损评估。特别地，用深度测量衰减率可以估计表面的粗糙度和新的表面缺陷的出现。