Abstract
This paper presents a method, based on matched eigenfunction expansions, for the determination of the frequencies of the acoustic resonances that can occur in a circular cylindrical waveguide in the presence of a number of thin radial fins of finite length in the axial direction. The fins are evenly distributed around the guide and we find that there are significant differences in the possible modes depending on whether the number of fins is even or odd and also that the qualitative behaviour of the mode frequencies changes when the number of fins passes a certain critical value. Simple approximate formulas are derived for the low-frequency modes under the assumption that the number of fins is large. The implications of our results are discussed for the case when the circular cross-section is replaced by an annular one, a situation of practical importance in the design of turbomachinery.
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