2022/12/19 by Afzal, Muhammad, Bilal, Hazrat, Ahmed, Naveed +1
#Analysis of PDEs (math.AP) #Classical Physics (physics.class-ph) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2212.10364
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 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 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.