Improved model of a layered medium with slip on the contact boundaries

The continuum equations of a layered medium with slip taking into account second-order terms with respect to a small parameter of the layer thickness are obtained on the basis of the asymptotic homogenization method. A linear slip condition is used that relates the jumps in the tangential displacements at the interlayer boundaries to the shear stresses. The equations obtained are also an asymptotically complete unification of several models of a layered media based on engineering approaches or approximate hypotheses on the nature of the layers deformation's, The wave properties of the system of equations obtained are investigated and dispersion relations are written out for harmonic waves. The solution of a problem of a Rayleigh-type surface wave on the boundary of an elastic layered half-space is constructed.