Wave propagation in three-component layered phonon crystals

This research work focuses on mathematical modeling of wave propagation phenomena in inhomogeneous media. In the framework of the one-dimensional approximation, the characteristics of waveguides and resonances in inhomogeneous one-dimensional periodic structures consisting of three different components were studied. To describe the dynamics of acoustic waves in such structures, stationary equations of pressure fluctuations in the medium and corresponding boundary conditions were applied, which include continuity conditions for pressure and velocity. As a result of this study, an analytical solution for the fundamental cell was found. The passbands for various waveguide modes were also identified and a dispersion relation describing the nature of wave modes in structures of this type was obtained. In addition, the dependence of the waveguide frequency on the linear concentrations of materials in the fundamental cell was determined.