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

In this article, we substantiate the appositeness of the 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 tailored-Galerkin approach that 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 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. Furthermore, it appears that the transmission loss and structural vibration attenuation in the expansion chamber may be improved by adjusting chamber dimensions and excitation modes.