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

TL;DR

This paper develops and compares two mode-matching-based methods to analyze acoustic scattering in waveguides with elastic plates and flexible joints, highlighting the impact of joint conditions on scattering and transmission.

Contribution

It introduces two novel mode-matching schemes incorporating tailored-Galerkin and modal approaches for elastic waveguides with flexible joints, enabling detailed analysis of scattering effects.

Findings

Edge conditions significantly influence scattering energies.

The proposed methods effectively incorporate various joint constraints.

Numerical results show the impact of joint types on transmission loss.

Abstract

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.