Dispersion Equation for Longitudinal Waves in a Layered Medium with Inhomogeneous Boundary Conditions in Different Propagation Directions

We study the propagation of longitudinal waves in a layered medium with inhomogeneous boundary conditions for two versions of wave propagation geometry-parallel and perpendicular to structure layers. The dispersion equations for a longitudinal wave are derived for the considered cases of propagation. The dispersion equations are solved for the wavenumber to determine dependences of effective longitudinal wave velocities on relative layer thickness and material parameters. The resulting dependences are used in the problems of determining the physical and mechanical characteristics of the medium based on acoustic measurements.