Dynamical behavior of fluid–structure interaction in ducts with rigid and flexible interfaces: Modeling and analysis

This study investigates the propagation of fluid–structure coupled waves in a duct featuring both rigid and flexible interfaces. Two cases are considered: in the first case, with a rigid interface, the truncated form of solution preserves the conservation law, while in the second setting, the power balance is not preserved initially, but is rectified as the number of modes, denoted as N, approaches infinity. The discrepancy is explained by specific equations and the presence of delta functions to enforce edge conditions on the membrane at the interface. The Galerkin approach is adopted to address this issue, expressing the membrane's displacement using a generalized Fourier series. The investigation establishes a framework for modeling higher-order boundary conditions within a duct, employing the mode-matching (MM) method. The study also delves into the scattering components of power, which vary significantly for the two cases. These findings have implications for noise control devices, particularly in active noise control measures utilizing flexible components to dampen both noise and structural vibrations.