MODAL ANALYSIS IN LINED WEDGE-SHAPED DUCTS

✍ Scribed by F.P. Mechel

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 437 KB
• Volume: 216
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1998.1706

✦ Synopsis

It has been suggested to describe the sound field in a wedge-shaped duct in a cylindrical co-ordinate system in which the boundaries of the wedge lie in a co-ordinate surface. This suggestion was developed in a companion paper [1]. The wave equation can be separated only if the boundaries are ideally reflecting (rigid or soft). Two solutions were proposed in reference [1] for absorbing boundaries. In the first solution, the sound field is composed of ''ideal modes'' (modes in a wedge with ideally reflecting boundaires); the boundary condition at the absorbing boundary then leads to a system of equations for the mode amplitudes. The problem with this method lies in the fact that there is no radial orthogonality of the ideal modes so that the precision of the field synthesis by ideal modes is doubtful. In the second method in reference [1] one defines ''fictitious modes'' which satisfy the boundary conditions at the flanks exactly and which are based on hypergeometric functions as radial functions, but which produce a ''rest'' in the wave equation. It was described how this rest can be minimized; this procedure leads to slow numerical integrations. In the present paper, the wedge is subdivided into duct sections with parallel walls (the boundary is stepped); the fields in the sections are composed of duct modes (modes in a straight lined duct); the mode amplitudes are determined from the boundary conditions at the section limits. The advantages of the present method are (analytically) the duct modes are orthogonal across the sections, so the mode amplitudes can be determined with the usual precision of a modal analysis, and (numerically) no numerical integrations are needed.