Surface effects on the propagation of shear horizontal waves in thin films with nano-scalethickness

This paper aims at the theoretical analysis of the propagation of shear horizontal waves in an ultra-thin plate-like film with nano-scale thickness via the surface elasticity theory. Both the surface and the bulk of the material are assumed to be isotropic and linearly elastic. The governing equations with non-classical boundary conditions are derived. Numerical calculations are performed for the first few symmetric and antisymmetric modes of shear horizontal waves. It is found that the surface effects become significant with the decrease of the film thickness. In contrast to the classical case, all the modes in the thin film at nano-scale are dispersive. A special symmetric mode appears and stays close to the descending first antisymmetric mode. They may escape and stop propagating above certain frequencies.