Long non-linear strain waves in layered elastic half-space

Elastic strain wave propagation in a thin non-linearly elastic layer superimposed on non-linearly elastic half-space is studied. Two layer-half-space contact models are considered. It is found that the Benjamin-One equation can be derived for description of longitudinal non-linear strain waves, when the contact between the layer and the half-space is provided only by means of the normal stresses and displacements. When the full contact problem is considered the more complicated integro-differential equation is derived. It is found that long non-linear periodical and solitary strain waves as well as envelope waves may exist in the first case, while only envelope wave solutions are found to the full contact problem. Linear wave analysis shows that the Korteveg-de Vries equation, often usable, is unlikely to be an adequate model for longitudinal surface strain waves. Application of the results obtained to experiments devoted to superconductivity threshold control in thin metal films as well as to generation of acoustic solitons in layered half-space is discussed.