Figure 1. Schematic of a Nite Plate Subject to Turbulent and Mean Ow Excitations. Vi. Concluding Remarks

\Flutter of a buckled plate as an example of chaotic motion of a deterministic autonomous system," 22 References 1. Ludwig, G. R., \An experimental investigation of the sound generated by thin steel panels excited by turbulent ow (boundary layer noise)," U. 21 be found. The formulation given by Eq. (63) represents a new way of estimating the radiated acoustic pressure from an elastic plate excited by turbulent ow. In deriving Eq. (63), the eeects of coupling among structural modes, radiated acoustic pressure, and turbulent ow are all taken into account. The cross-power spectral density function of the radiated acoustic pressure from a nite plate subject to turbulent ow is obtained and expressed in terms of the cross-power spectral density function of the turbulent boundary layer in an explicit form. In deriving this formulation, the eeects of stretching due to in-plane force and those of coupling between structural vibration and acoustic radiation are taken into account. A general stability analysis is given by using the basic existence-uniqueness theorem. In particular, the stable conditions for a linearized system are derived by using the Routh algorithm. Two sources of instabilities are found to be attributable to the added damping and stiiness due to uid loading and ow. The eeects of the added damping and stiiness increase with the Mach number of the mean ow, the former increasing linearly and the latter increasing quadratically.