Impedance transition and slow-wave modulation in a bladder-type attenuator under overcharge conditions

Bladder-type attenuators are widely used in pipeline noise control due to their compact configuration and broadband low-frequency attenuation capability. However, when the pre-charge pressure inside the bladder exceeds the operating fluid pressure (overcharged condition), a drastic deterioration of transmission loss is frequently observed, while the underlying physical mechanism remains insufficiently understood. In this study, an equivalent impedance framework is developed to characterize the coupled bladder-perforated structure under overcharge conditions. The tensioned bladder membrane is modeled as a stretched circular membrane and connected in series with the perforated pipe, leading to a composite surface impedance formulation. The derived impedance is incorporated into a one-dimensional transfer-matrix model, yielding analytical expressions for both transmission loss and axial wave dispersion. The results reveal a clear stiffness-mass transition in the composite impedance spectrum. Increasing overcharge pressure significantly raises the effective boundary stiffness, shifts the stiffness-mass transition toward higher frequencies, and suppresses the slow-wave effect. Both finite element simulations and experimental measurements validate the proposed model within the plane wave regimen. The analysis demonstrates that the degradation of acoustic performance under overcharge conditions originates from an impedance transition that drives the duct toward a rigid-wall limit, thereby eliminating the slow-wave-induced reflection mechanism.