On nonlocal surface elasticity and propagation of surface anti-plane waves

We discuss the nonlocal model of surface elasticity that is the model with surface energy density which depends on first and higher gradients of displacements. To demonstrate the peculiarities of the model we consider the propagation of antiplane surface waves in an elastic halfspace with the surface energy. Using the least action principle we derive the governing equations for the problem. Analyzing the anti-plane deformations we obtain the dispersion relation and analyze its dependence on surface elastic moduli and on the order of considered gradients