Eigenpairs of a coupled rectangular cavity and its fundamental properties.
Eigenpairs of a coupled rectangular cavity and its fundamental properties.
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DOI：
10.1121/1.3682046
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发表时间：
2012-03
期刊：
影响因子：
--
通讯作者：
N. Tanaka;Y. Takara;H. Iwamoto
中科院分区：
文献类型：
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作者：
N. Tanaka;Y. Takara;H. Iwamoto
本文研究了在许多文献中经常使用的由五个刚性墙和一个柔性板组成的耦合矩形腔的特征值问题。本文的目的是显式地推导出耦合腔的本征对，这些本征对尚未找到。首先，导出特征对需要满足的耦合正交性条件，从而使得能够验证新寻找的或已经存在的特征对。利用耦合正交性条件，得到了耦合腔系统的振型方程，从而可以处理耦合腔的强迫响应。结果表明，控制声场动力学的本征函数可表示为简并本征函数的无穷和。然后导出了特征矩阵方程，描述了耦合腔的本征对。为了研究所得到的本征对的基本性质，进行了数值分析，发现除了传统的驻波模式外，还存在着消逝模式。最后，进行了实验，验证了本文所得到的特征对的有效性。
This paper deals with the eigenvalue problem of a coupled rectangular cavity comprising five rigid walls and one flexible panel frequently employed in much literature. It is the purpose of this paper to derive explicitly the eigenpairs of the coupled cavity, which are yet to be found. First, the coupling orthogonality conditions the eigenpairs need to satisfy are derived, thereby enabling the verification of the eigenpairs newly sought or already existent. Using the coupling orthogonality conditions, the modal equation of the coupled cavity system is then obtained, permitting one to deal with a forced response of the coupled cavity. It is shown that the eigenfunctions governing the dynamics of the sound field are expressed as the infinite sum of degenerate eigenfunctions. The characteristic matrix equation is then derived, specifying the eigenpairs of the coupled cavity. In order to investigate the fundamental properties of the eigenpairs derived, a numerical analysis is conducted, revealing the presence of evanescent modes in addition to the conventional standing wave modes. Finally, an experiment is carried out, verifying the validity of the eigenpairs derived in the article.