High order approximate low frequency theory of elastic anisotropic lining and coating

A problem of the dynamic behavior of an elastic layer coupled to one or two thick elastic solids is considered. All the materials may possess a general anisotropy and the layer is assumed to be thin enough with respect to the characteristic wavelength. Introducing the asymptotic power series with respect to the thickness-over-wavelength ratio for the main quantities and using the asymptotic integration method the displacements and stresses on the layer surfaces are related. Thus, the so-called impedance boundary conditions (IBC) are deduced for three cases--for a coated substrate with given displacements or with given stresses on the surface and for two substrates with a layer in between. In contrast to previous papers these IBC are obtained for the most general situation with the asymptotic accuracy up to the sixth order, uniform with respect to the representation of the displacements and stresses. Presented theory can be used for studying the surface and interface phenomena as well as for calculating fields and spectra of layered solids. The results are validated numerically and compared with those of other authors.