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

Bastien Mallaroni (1) , Pierre-Olivier Mattei (1) , Jean Kergomard (1)

1 LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]

The pressure field inside a flanged duct of finite length radiating on one side in an infinite medium can be described from the knowledge of a radiation matrix impedance, as proposed by Zorumski. In order to calculate the resonance frequencies (which are complex because of the energy loss by radiation), 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 purposes a development of the Green's function which is valid for all frequencies. The results are applied to the calculation of the complex resonance frequencies of a flanged duct of finite length, by using a formulation of the internal pressure based upon cascade impedance matrices. It presents and discusses the influence of higher order duct modes and the results for several duct radius/length ratios.

Mots clés: radiation; resonance frequencies; zorumski

Domaines: Acoustique [physics.class-ph]; Acoustique [physics.class-ph]

Bastien Mallaroni, Pierre-Olivier Mattei, Jean Kergomard. Complex resonance frequencies of a finite, circular radiating duct with an infinite flange. 2009. ⟨hal-00402870v1⟩