Technische Fachhochschule Berlin, Fachbereich 2, Luxemburger Strasse 10, W-1000 Berlin 65, Germany
The propagation loss of absorbing ducts will be calculated with the aim to find the optimal design of the absorber for a specific problem. An infinite, rectangular duct lined with locally reacting absorbers will be considered. The impedances of the lining surfaces could be different, so that the asymmetrical case is included. To calculate the propagation loss due to absorption the boundary value problem of the wave equation in the absorbing channel has to be solved and the eigenfunctions (or modes) and eigenvalues have to be determined numerically. It can be shown that these modes are biorthogonal and that it is possible to expand a prescribed incident wave field into a sum of absorber modes. Since the underlying mathematical boundary problem is non-self-adjoint it is not possible to derive the expansion theorem by using the usual Sturm--Liouville theory. Instead of this Cauchy's integral formula has to be used for the series expansion in connection with Green's function. The eigenvalue problem will be solved numerically by using Muller's method. Numerical results for different absorber configurations will be presented and discussed.