The Acoustic Field in a Closed Space Behind a Rectangular Simply Supported Plate Excited by Boundary Layer Turbulence

Abstract

AD analytic tolutloo U obtained for the acouitlc premre ttatlttlci In a clowd rectangular ibaped cavity behind a limply supported, rectangular plate excited by boundary layer turbulence. The connlbutioo of the cavity acouKie prenure U neglected at contributing tc the plate excitation, leaving only the turbulent preiture fluctuation! at the exciting force. The mathematical model for the turbulent premre rutlnlci U baied on that of Corcot, which agrees well with experiment. A byproduct of thli analyiii it an analytic tolution for the turbulent flow excited plate vibration velocity itatlitici. The plate velocity and cavity acounic prenure RatUtici are exprenedin the form of cron power spectral densities and power spectral densities. Dimensionless forms of the plate velocity spectral density and cavity acounic pressure spectral density ate developed. The dlmensionless plate velocity spectral density and dlmenslonless cavity acoustic pressure spectral density were computed, by means of a digital computer, for selected values of dlmenslonless input parameters. From these computed dlmensionless specca, the effects of major parameters on the plate velocity spectral density and the cavity acoustic pressure spectral density were determined. A 'peak spectrum," constructed by connecting the major spectral peaks in the plate velocity or cavity acoustic pressuri .»lectra, proved to be a useful engineering concept. Knowledge of the 'peak »pectrum' is equivalent to knowledge of the maximum plate velocity or cavity acoustic pressure spectral levels for a particular set of input parameters. Based on the computed dlmenslonless spectra, mathematical expressions are derived for the dlmenslonless plate velocity "peak spectral density" and the cavity acoustic pressure "peak spectral density" over a limited range of dlmensionless frequency. The computed simply supported plate velocity "peak spectrum' compares well with the plate velocity "peak spectrum" constructed from experimental measurements on a fixed edge plate above the first plate natural frequency. No experimental data exists for the cavity acoustic pressure. Comparison of the computed dlmensionless cavity acoustic pressure spectral density at the plate and the dlmensionless turbulent pressure qwctral density allowed formulation of criteria under which the cavity acoustic pressure wasnegligible compared to the turbulent pressure. As this analysis assumed the cavity acoustic pressure to be negligible compared to the turbulent pressure, the aforementioned criteria are, in effect, limits of applicability of this analysis. ADMINISTRATIVE INFORMATION This study was originally prepared as a dissertation in partial fulfillment of the requirements for the degree Doctor of Philoropby in Applied Mechanics at the University of Connecticut. The work was accomplished under USL Proj'jct No. 7-1-052-00-00 and the Navy Subproject and Task No. ZR 011 01 01.