Vibrations of plates with clamped and free edges excited by low-speed turbulent boundary layer flow

Abstract

Plate vibrations due to turbulent boundary layer (TBL) excitation can depend strongly on the plate boundary conditions, especially when the flow convects over the plate at speeds much slower than those of the bending waves in the plate. The vibration response of a TBL excited baffled flat rectangular plate is analyzed with two sets of boundary conditions: (a) all four edges clamped, and (b) three edges clamped and one edge free, with the flow direction perpendicular to the free edge. A finite element model with discretization sufficient to resolve the convective wavenumbers in the flow excitation field is used for the study. Three TBL wall pressure excitation models are applied to the plates to represent the cross-spectra of the wall pressures: (i) a modified Corcos model, which includes all wavenumber components of excitation; (ii) a low-wavenumber excitation model previously derived by one of the authors, which only models the wavenumber-white region of the modified Corcos model; and (iii) an equivalent edge force model which only models the convective component in the modified Corcos model. The TBL wall pressure autospectrum is approximated using the model derived by Smolyakov and Tkachenko. The results obtained from applying models (ii) and (iii) to the clamped and free edge plates are compared to those generated using model (i). For the completely clamped boundary conditions, the low-wavenumber and Modified Corcos models yield nearly identical vibration spectra, indicating that surface interactions dominate the response of fully clamped plates excited by TBL pressures. For the free edge boundary condition, the vibrations predicted using the equivalent edge force and modified Corcos models match very well, showing that edge interactions between TBL pressures and structural modes dominate the vibrations of plates with free edges excited by TBL flow.