MODES IN LINED WEDGE-SHAPED DUCTS

✍ Scribed by F.P. Mechel

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 333 KB
• Volume: 216
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1998.1705

✦ Synopsis

The computation of sound fields in wedge-shaped spaces with an absorbing boundary (the seabed) is a classical problem of underwater acoustics, covered by a large number of publications. All known solutions are approximations which are restricted to very small wedge angles q 0 , typically less than 3°. In underwater acoustics is is further assumed that k 0 r 1. The background of the present paper is the performance of lined conical duct sections in silencers. There the wedge angle can attain values around 45°, and the assumption k 0 r 1 cannot be made. The absorber of the lined boundary here is supposed to be locally reacting (for reasons of simplicity); it can be characterized by a normalized surface admittance G 0 . The problems of the analysis arise from the fact, that the fundamental field solutions (modes) can no longer be separated in the cylindrical co-ordinates r, q if a boundary is absorbing. This paper describes analytical solutions for the construction of modes in lined wedge-shaped ducts; they can be applied for wedge angles up to about 15°(a subsequent paper will describe a method for angles up to about 45°but only moderate k 0 r values). In the solutions, use is made of ''fictitious modes'', which satisfy the boundary conditions and solve a part of the wave equation. They must be completed by a ''modal rest'' to satisfy approximately the full wave equation. In the first solution, the rest is synthesized by fictitious modes; in the second solution, a separate function is introduced for the rest. Modes for typical underwater acoustics conditions will arise as side products.