Validation of a Simple Empirical Model for Calculating the Vibration of Flat Plates Excited by Incompressible Homogeneous Turbulent Boundary Layer Flow

The vibration responses of three flat rectangular plates excited by turbulent boundary layer flow are calculated and compared to measured data. The measurements were made in three different facilities by Wilby at ISVR [1] (high speeds typical of aircraft), Han at Purdue University [2] (moderate speeds typical of automobiles), and Robin at University of Sherbrooke [3] (lowest speeds), spanning 50 years of time. The plates are different sizes, made from different materials, and have different boundary conditions. The boundary layers have different heights and flow speeds. The ratios of plate flexural and convective wavenumbers k_b/k_c over the three cases range from about 0.1 to 2. Plate vibrations are normalized by wall pressure fluctuation autospectra measured by the previous investigators. This wide range of structural and flow conditions and the use of plate vibration spectra normalized by wall pressure autospectra allows for an objective assessment of various TBL wall pressure fluctuation cross-spectral empirical models. Two cross-spectral models are considered: the widely used Corcos model [4] and the less well-known elliptical extension by Mellen [5]. Smolyakov’s empirical models for convection velocity and streamwise and spanwise surface pressure length scales [6] supplement the Corcos and Mellen models. Calculations using the Corcos cross-spectral model overestimate the vibrations by about an order of magnitude at lower speed (and lower k_b/k_c) conditions. Including Smolyakov’s convection velocity and length scale formulations improves accuracy at low frequencies. The Mellen cross-spectral pressure model, supplemented with Smolyakov’s empirical models for convective wave speed and streamwise and spanwise surface pressure length scales, is therefore well suited for calculating plate vibrations due to TBL flows with flow speed/flexural wave speed ratios ranging from 0.1 to 2.