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.

中文翻译：

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来自安装在管道中的柔性结构的辐射模式和声音辐射。

最初针对自由场问题提出的辐射模式概念已经在振动结构及其主动控制应用的声辐射分析中得到广泛应用。在本文中，通过基于能量的公式结合近场集成技术，研究了柔性结构的声辐射，该声辐射齐平地安装在2D和3D配置中的管道内部。首先根据模态辐射效率讨论结构辐射特性，该模态辐射效率相对于频率表现出明显的振荡行为，其中对称模式占优势，小声波数平滑变化。然后研究室内声辐射模式。结果表明，与自由空间相比，管道中的低阶辐射模式更敏感，并且从其截止频率开始就容易受到管道的影响。在截止频率及其倍频/谐波中，可以观察到辐射模式形状的剧烈变化。最后，分析扩展到耦合面板-管道系统。可以看出，与自由空间情况相反，低阶辐射模式沿管道长度方向显示出主要变化，这表明可能将3D配置简化为2D模式。