Flexural instability and sound amplification of a membrane-cavity configuration in shear flow

The scattering of sound by a membrane-covered cavity in a duct with shear flow is calculated with a linear model based on the multimodal method. The model is verified by comparison against the previous experiments focused on sound suppression of a stable system with high-tension membranes and a low-speed flow. It is shown in this paper that such a situation is drastically changed when the flow velocity is larger than the in vacuo flexural wave speed of the membrane. One of the neutral hydrodynamic modes can be destabilized under certain conditions, and this flexural instability can lead to sound amplification. For a given flow profile, the axial growth rate of the instability increases with the mean flow velocity but saturates at high velocities. For a given mean flow velocity, there is an optimum boundary layer thickness for the instability. Increasing the structural damping tends to stabilize the instability and thus inhibit the sound amplification.