Approximate high-order dynamic theory of a fluid layer in between two thick solids

A thin layer of heavy fluid with bound faces is considered first. For the sake of simplicity, the effects of vortex and viscosity are neglected. Two cases of compressible and incompressible fluids are treated, assuming that a thickness-over-wavelength ratio is a small parameter. For the internal state of medium the relations between the quantities on the layer surfaces are deduced. In contrast to the standard approach, which expands the propagator matrix into power series of a small wave number, the asymptotic integration of 3D equations and boundary conditions of fluid dynamics is performed. Respective relations are represented in a recurrent form and permit one to obtain the high-order components of the displacements and pressure rather simply. When considering two thick solids with a fluid in between, this result is used to derive the so-called "impedance boundary conditions" (IBC) with a relative asymptotic error up to tenth order. Tests show their validity until the first quasiresonance frequency of a layer, so, the analysis is not just long wave but essentially low frequency. Thus, these IBC are applicable to reduce the dimension in the analysis of challenged multicomponent system of fluid-coupled solids in a reasonable frequency range.