Responses of finite baffled plate to turbulent flow excitations

Formulations for estimating dynamic and acoustic responses of a finite baffled plate subject to turbulent boundary-layer excitations are presented. In deriving the formulations, the effects of structural nonlinearities induced by in-plane forces and shearing forces due to stretching of plate bending motion are considered. The excitation force due to turbulent flow is expressed in terms of a sum of two components. One component corresponds to a fluctuating pressure field due to acoustic radiation, which is determined analytically for both supersonic and subsonic flows. The other component corresponds to a fluctuating pressure field due to a turbulent boundary layer, which is determined experimentally. The cross-power spectra of the plate flexural displacement and the radiated acoustic pressure are shown to be directly related to that of the turbulent boundary layer. In addition to the plate dynamic and acoustic responses, a stability analysis is given using the basic existence-uniqueness theorem. In particular, stable conditions for a linearized system are obtained via the Routh algorithm. It is shown that temporal instability can be induced by the added stiffness due to acoustic radiation in the presence of mean flow. The effect of the added stiffness increases quadratically with the mean flow speed.