Optimizing noise control in flexible shells using membrane discs and lining conditions

This study presents a novel approach for enhancing acoustic attenuation in duct systems by modeling and analyzing a waveguide equipped with elastic components at the boundaries of a sound-absorbent lining cavity. The proposed configuration includes flexible shells at both the inlet and outlet, which are capable of supporting structure-borne modes. These flexible shells are modeled using the Donnell–Mushtari equations to capture their vibrational response. The mathematical formulation involves solving a mixed-type boundary value problem, where the displacement of the circular membrane discs at the interfaces is described by a second-order differential equation with specific edge conditions. A mode-matching solution is developed by expanding the duct region eigenfunctions with undetermined mode amplitudes, ensuring continuity and coupling edge conditions at the interfaces. The Galerkin formulation is applied to model the vibrational response of the membrane discs, while the mode-matching method describes acoustic propagation within the duct system. Numerical results demonstrate that the proposed configuration significantly enhances acoustic attenuation within targeted frequency ranges and varying lining conditions, providing valuable insights for improving noise control strategies in industrial applications. • Models waveguide with membranes and lining for optimal attenuation. • Applies Donnell–Mushtari theory to capture shell vibration. • Uses mode-matching and Galerkin methods to model the fluid–structure coupled dynamics. • Achieves high attenuation across frequencies, aiding industrial noise control.