Radiation modes and sound radiation from a flexible structure mounted in a duct

The concept of the radiation modes, originally proposed for free-field problems, has found its widespread use in sound radiation analyses of vibrating structures and their active control applications. In this paper, the sound radiation of a flexible structure, flush-mounted inside a duct in both 2D and 3D configurations, is investigated via an energy-based formulation in conjunction with the near-field integration technique. The structural radiation characteristics are first discussed in terms of modal radiation efficiency, which exhibits obvious oscillating behavior with respect to frequencies, in which symmetric patterns are dominant with smooth variations for small acoustic wavenumbers. Then the interior sound radiation modes are investigated. It is shown that, as compared with their free-space counterparts, the lower-order radiation modes in a duct are more sensitive and prone to be affected by the duct starting from its cut-on frequency. Drastic changes in the radiation mode shapes are observed around the cut-on frequency and each of its multiples/harmonics. Finally, analyses are extended to a coupled panel-duct system. It is observed that, contrary to the free-space case, lower-order radiation modes exhibit predominant variations along the duct length direction, suggesting a possible simplification of the 3D configuration into a 2D one.