Tunable acoustic scattering in composite duct structures with elastic membrane discontinuities

This study investigates acoustic wave scattering in a composite duct structure incorporating a rigid annular shell connected to a flexible cylindrical shell via an embedded elastic membrane disc. The presence of the membrane introduces a vibratory discontinuity that significantly influences acoustic propagation and scattering characteristics. We develop a semi-analytical framework combining the Mode Matching (MM) technique for rigid-fluid interfaces with a Galerkin-based approach to model the elastic membrane vibrations. The formulation enforces continuity of pressure and axial velocity at the fluid-structure interfaces through truncated modal expansions, with convergence rigorously verified. By varying membrane edge constraints (spring-like, clamped, free) and geometric parameters, we identify distinct scattering regimes and demonstrate how structural and boundary variations can enhance or suppress acoustic reflection. Under spring-like conditions, a transmission loss of 13.5 dB is achieved, with subsequent variations governed by changes in scattering powers due to different parametric settings and edge conditions. The findings provide insights for the design of advanced tunable acoustic devices, including silencers and metamaterial waveguides, where controlling wave scattering is critical.