Acoustic scattering from a wave-bearing cavity with flexible inlet and outlet

In this article, we substantiate the appositeness of the \emph{mode-matching technique} to study the scattering response of bridging elastic plates connecting two flexible duct regions of different heights. We present two different solution schemes to analyze the structure-borne and fluid-borne radiations in the elastic plate-bounded waveguide. The first scheme supplements the mode-matching technique with the so-called \emph{tailored-Galerkin approach} which uses a solution ansatz with homogeneous and integral parts corresponding to the vibrations of the bridging elastic plate and the cavity, respectively. In the second scheme, we supplement the mode-matching technique with the \emph{modal approach} wherein the displacement of the bridging elastic plate is projected onto the eigenmodes of the cavity. To handle the non-orthogonality of the eigenfunctions, we invoke generalized orthogonality relations. An advantage of the proposed mode-matching schemes is that they provide a convenient way of incorporating a variety of edge conditions on the joints of the plates, including clamped, pin-joint, or restraint connections. The numerical analysis of the waveguide scattering problems substantiates that edge connections on the joints have a significant impact on the scattering energies and transmission loss.