Fluid-structure coupled wave scattering in a shell-membrane cylindrical cavity embedded between rigid ducts

This paper examines fluid–structure coupled wave scattering by a flexible cylindrical shell cavity closed by elastic membrane discs at its inlet and outlet. A harmonic incident wave travels along a rigid upstream duct, interacts with the coupled shell–membrane cavity, and is transmitted into a rigid downstream duct. The cavity is filled with a compressible fluid, so the acoustic field is governed by the Helmholtz equation, while the shell motion is modelled using the Donnell–Mushtari equations. The interaction between the acoustic field and shell vibration generates non-orthogonal structural–acoustic modes, which are treated using generalised eigenfunction properties. In contrast, the membrane dynamics at the cavity ends are represented through an orthogonal modal expansion within a Galerkin projection. Enforcing continuity of acoustic pressure and normal velocity at all interfaces yields truncated linear algebraic systems for the modal amplitudes, which are solved numerically. Accuracy and convergence are assessed by reconstructing the imposed matching conditions and by verifying power balance. Parametric studies then quantify the effects of cavity geometry and shell parameters on scattering, energy redistribution, and transmission loss. The results provide guidance for designing and optimising shell–membrane configurations for acoustic enclosures and duct-silencer applications.