Vibrations of infinite plates and the mean value vibrations of finite plates excited by turbulent boundary layer flows

Abstract

The vibration response of a turbulent boundary layer (TBL) excited flat plate is analyzed using a finite-element model and infinite plate theory. For the finite-element models, discretization sufficient to resolve the convective fluctuations in the flow excitation field is used for the study. Clamped boundary conditions are assumed for the finite-element models and analyses are conducted at a variety of flow speeds and structural loss factors. Two equivalent TBL wall pressure excitation models are applied to the plates: (1) a modified Corcos cross-spectrum model for the finite-element models, and (2) a wave-vector-frequency spectrum model (the Fourier transform of the modified Corcos cross spectra) for the infinite plate theory. The TBL wall pressure autospectrum is approximated using the model derived by Smolyakov and Tkachenko. The infinite plate predicts the mean value response of the finite plate very well for all speeds and loss factors considered, showing consistency with Skudrzyks mean value theory and its usefulness for generating sound and vibration estimates.