Time analysis of immersed waveguides using the finite element method

The propagation of acoustic waves in immersed waveguides has been previously studied with the help of the finite element method, using the ATILA code [A. C. Hladky-Hennion et al., J. Sound Vib. 200, 519–530 (1997)]. But this method, which is a modal analysis, essentially concerns the case of rectilinear, infinite, and uniform waveguides. Thus this paper deals with another way of solving the problem of wave propagation along waveguides, with the help of a time analysis using finite elements. First, the theoretical formulation is presented for immersed structures. Then, Plexiglas and brass wedge guides, of different apex angles, are considered. When immersed in water, these wedges generate either propagating or radiating wedge waves. The finite element results, using a time analysis, are compared to the previous finite element results, using a modal analysis and to the experiments, leading to a good agreement. Thus the approach can be easily extended to other waveguides whatever their cross sections.