Dispersion analysis of a three-layered waveguide with finite element and matrix methods

The study of sound wave propagation in multilayered plate structures represents an important part of acoustics. In this paper, we compare two different modeling techniques based on the finite element method (FEM) and the matrix methods using an example of a three-layered waveguide with a middle liquid layer. First, the theory of the matrix methods is summarized with a focus on multilayered waveguides containing liquid layers. Furthermore, we present a numerical procedure for obtaining modal solutions, and we discuss sample solutions for the three-layered waveguide. Second, FEM is applied to simulate the waveguide setup including real-world transducers mounted on wedges. We introduce a 2D model of the setup and a procedure for obtaining group velocity dispersion diagrams. The model is validated using theoretical and experimental results. In addition, the effect of discretization error is demonstrated. We present sample dispersion diagrams and compare them to those obtained with the matrix methods. Finally, we utilize the FEM simulation results to depict the displacement profiles across the waveguide. We show that the results of both modeling techniques are in good agreement and that they provide interesting insights into the wave mechanics of the three-layered waveguide.