Complex resonance frequencies of a finite, circular radiating duct with an infinite flange

TL;DR

This paper develops a new Green's function formulation valid for all frequencies to accurately compute complex resonance frequencies of a finite, flanged duct radiating into an infinite medium, accounting for energy loss due to radiation.

Contribution

It introduces a modified Green's function approach that handles complex frequencies, enabling precise calculation of resonance modes in radiating ducts with infinite flanges.

Findings

Multiple series of resonance modes identified, each linked to a dominant duct mode.

Higher order duct modes influence resonance frequencies significantly.

Resonance frequencies vary with fluid density, affecting duct radiation characteristics.

Abstract

Radiation by solid or fluid bodies can be characterized by resonance modes. They are complex, as well as resonance frequencies, because of the energy loss due to radiation. For ducts, they can be computed from the knowledge of the radiation impedance matrix. For the case of a flanged duct of finite length radiating on one side in an infinite medium, the expression of this matrix was given by Zorumski, using a decomposition in duct modes. In order to calculate the resonance frequencies, the formulation used in Zorumski's theory must be modified as it is not valid for complex frequencies. The analytical development of the Green's function in free space used by Zorumski depends on the integrals of Bessel functions which become divergent for complex frequencies. This paper proposes first a development of the Green's function which is valid for all frequencies. Results are applied to the calculation of the complex resonance frequencies of a flanged duct, by using a formulation of the internal pressure based upon cascade impedance matrices. Several series of resonance modes are found, each series being shown to be related to a dominant duct mode. Influence of higher order duct modes and the results for several fluid densities is presented and discussed.