Modes coupling due to nonhomogeneously shaped walls in duct acoustics

Abstract

The acoustic pressure field inside finite or infinite, fluid-filled waveguides with surfaces having distributed small deviations (corrugation, roughness, facade irregularities in streets and so on) from the regular shape (smooth surface) is studied, using an approach called shape profile model. In this approach, the acoustic field is obtained from the coupling between Neumann modes of the regularly shaped surface that bounds outwardly the perturbed surface of the waveguide (i.e. on outer side of the perturbed surface). The effect of the rough boundaries on the acoustic field is modelled by an operator acting on the acoustic pressure, which takes into account both the depth and the slopes of the profile. Two coupling mechanisms are identified, namely the “bulk” or “global” modal coupling and the “boundary” or “local” modal coupling. This model departs from those available until now because it does not make use of the so-called multimodal approach: it lies on the integral formulation in the frame of a modal approach using a unique set of eigenfunctions, in order to obtain the pressure field inside the wave guide as a coupling between modes.