On the modeling of modes coupling in dissipative fluid-filled waveguide with corrugated surfaces

Abstract

This paper aims at providing an alternative analytical model, which would be more suitable than a previous one [C. Potel and M. Bruneau, J. Sound Vib. 313, 738 (2008)], to describe the mode coupling due to scattering on small one-dimensional irregularities (parallel ridges) of the surfaces of a fluid-filled waveguide. Both models rely on standard integral formulation and modal analysis, the acoustic field being expressed as a coupling between eigenmodes of a regularly shaped waveguide, which bounds outwardly the corrugated waveguide considered. But the model presented here departs from the previous one essentially because it starts from the integral formulation for the acoustic pressure field, the solution relying on a modal expansion, whereas the previous one starts from the inner product of the set of differential equations (which govern the acoustic pressure field) and the appropriate eigenfunctions, the solution being obtained from using a one-dimensional integral formulation. Substituting this alternative model for the previous one clearly accelerates convergences (even permits to avoid divergences) of the iterative process used to solve the problem. Finally, complex eigenfunctions are introduced here in order to account for the dissipative effects due to thermoviscous phenomena (through an impedancelike boundary condition), which is of importance at the cut-off frequencies.