About the Realization of the Cremer Admittance of Locally Reacting Duct Linings

L. Cremer has shown that the least attenuated mode in ducts with locally reacting linings of a duct of (half) width h has its highest attenuation if U = k ₀ hZ ₀ G of the surface admittance G of the lining lies in the branch point U_b between the first two symmetrical duct modes. This is the highest possible attenuation of not too short silencers for a general modal excitation. A number of authors have tried to realize the Cremer admittance. This is not very difficult in single sharp resonance peaks. This paper describes how a number of attenuation peaks can be combined in a frequency curve, like that of a comb filter, by multi-layer linings (the resonating layers arranged in series), and that the individual peaks can be broadened in a side by side arrangement (in parallel) of resonating absorbers. It will be shown that many realizations are possible, so that technical aspects of the lining can be taken into account. Besides examples of absorbers with a Cremer admittance which were designed by trial and error along plausible guidelines, a numerical algorithm is developed for absorbers in parallel arrangement which optimizes the parameters of one of the partial absorbers.