On the peculiarities of anti-plane surface waves propagation for media with microstructured coating

We discuss new type of surface waves which exist in elastic media with surface energy. Here we present the model of a coating made of polymeric brush. From the physical point of view the considered model of surface elasticity describes a highly anisotropic surface coating. Here the surface energy model could be treated as 2D reduced strain gradient continuum as surface strain energy depends on few second spatial derivatives of displacements. From the mechanical point of view the proposed model relates to 2D coating made of long fibers undergoing stretching and bending deformations. We consider here anti-plane surface waves. The dispersion relation is derived and its dependence on the material parameters is analysed.