### ASA 124th Meeting New Orleans 1992 October

## 1pPAb2. Theoretical and numerical aspects of absorbing ducts with
asymmetrical lining.

**Martin Ochmann
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*Technische Fachhochschule Berlin, Fachbereich 2, Luxemburger Strasse 10,
W-1000 Berlin 65, Germany
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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.