带无限大凸缘的有限长圆形辐射管道的复共振频率
Complex resonance frequencies of a finite, circular radiating duct with an infinite flange
摘要：
固体或流体的辐射可以通过共振模式来表征。由于辐射造成的能量损失，它们很复杂，谐振频率也很复杂。对于管道，它们可以根据辐射阻抗矩阵的知识来计算。对于有限长的法兰管道在无限介质中的一侧辐射的情况，Zorumski使用管道模式的分解给出了该矩阵的表达式。为了计算共振频率，必须修改Zorumski理论中使用的公式，因为它对复频率无效。分析发展的格林函数在自由空间中使用的Zorumski取决于积分的贝塞尔函数成为发散的复杂频率。本文首先提出了一个发展的格林函数，这是有效的所有频率。结果被施加到计算复杂的共振频率的法兰管道，通过使用配方的内部压力的基础上级联阻抗矩阵。几个系列的共振模式被发现，每个系列被证明是相关的主导管道模式。高阶管道模式的影响和几种流体密度的结果，并进行了讨论。
英文摘要：
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.
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