Eigenpairs of a coupled rectangular cavity and its fundamental properties.

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.