TURBULENT-FLOW-EXCITED VIBRATION OF A SIMPLY SUPPORTED RECTANGULAR FLAT PLATE

An analytic solution is obtained for the plate velocity statistics of a turbulent flow excited, simply supported, rectangular flat plate. The radiated acoustic pressure is neglected as contributing to the plate excitation, leaving only the turbulent boundary layer pressure fluctuations as the exciting force. The mathematical model for the turbulent boundary layer pressure statistics is based on that of Corcos, which agrees well with experiment. Plate velocity statistics are expressed in the forms of dimensionless cross power spectral and power spectral densities. Plate velocity spectral and cross spectral densities were obtained with a digital computer for selected flow and plate parameters. From these computed dimensionless spectra, effects of major parameters on the plate velocity statistics were determined. A “peak spectrum,” constructed by connecting major spectral peaks of the plate velocity spectral density, proved to be a useful engineering concept, inasmuch as knowledge of the “peak spectrum” is equivalent to knowledge of the maximum plate velocity spectral density for a given set of input parameters. The computed dimensionless plate velocity “peak spectrum” compares well with “peak spectra” constructed from available experimental data. © 1969, Acoustical Society of America. All rights reserved.