The Sound Power Radiated by Some Axisymmetric Vibration Modes of a Guided Annular Plate

Abstract

The problems of measuring and identifying the sound fields generated by some vibrating flat circular annular plates, which satisfy some different axisymmetric or asymmetric boundary conditions and which are characterised by different excitation behaviours, are still of considerable interest both from theoretical and practical points of view. Therefore, some approximate methods to deal with the sound radiation by some selected plates have seldom been presented in the literature. The equivalent surface area method was used to estimate the radiation efficiency of a clamped circular plate by Czarnecki, Engel and Panuszka. 1 The authors also make use of the correlation method for some near field measurements of the sound power of a flat circular plate. 2 A comprehensive approach to find the radiation efficiency of a spinning annular disk was proposed by Lee and Singh. 3 A closed path integral technique was used to derive the radiation efficiency of a clamped circular plate by Levine and Leppington. 4 The technique was applied by Rdzanek to provide some very precise estimates for the sound power of an individual mode and a mode pair valid for the high frequencies. 5 The technique was later used by Rdzanek and Engel to deal with the magnitudes valid for an annular plate. 6,7 So far, no theoretical analysis of the complex self power of a guided annular plate has been carried out and no high frequency asymptotics have been presented. Therefore, the aim of this paper is to provide some elementary formulations for the magnitude which would be useful for some highly efficient engineering computations of the total sound power radiated by a guided plate excited in an acoustic fluid.