Responses of a finite baffled plate subject to turbulent and mean flow excitations

摘要

Formulations for predicting dynamic and acoustic responses of a finite plate flush-mounted on an infinite baffle subject to turbulent and mean flow excitations are presented. In deriving these formulations, the effects of stretching due to in-plane force and coupling between structural vibration and acoustic radiation are taken into account. The resulting equation governing plate vibration contains cubic nonlinearities. To obtain an approximate solution, the plate flexural displacement is expanded into orthogonal base functions. The unknown coefficients associated with base functions are determined by solving a set of coupled nonlinear integral equations using Galerkin's method. A stability analysis is given using the basic existence-uniqueness theorem. In particular, stable conditions for a linearized system are obtained using the Routh algorithm. It is shown that structural instabilities can be induced by fluid loading and mean flow. Two unstable mechanisms are found to be attributable to added damping and stiffness due to acoustic radiation. The effect of added damping increases linearly, while that of added stiffness increases quadratically with the Mach number of mean flow. Finally, the cross-power spectral density functions of plate flexural vibration and radiated acoustic pressure are derived and expressed in terms of the cross-power spectral density function of turbulent flow.