In the high frequency limit, a vibrating panel subject to spatially-random temporally-broadband forcing is shown to have broadband power and directivity properties that can be expressed in simple analytical terms by a limited set of parameters. A lightly-loaded fixed-fixed membrane with a distribution of broadband uncorrelated drive points is analyzed. The theory is developed using classical modal methods and asymptotic modal analysis, assuming small damping. The power and directivity of the radiated pressure field are characterized in terms of structural wave Mach number, damping ratio, and dimensionless frequency. The relatively simple directivity pattern that emerges can be shown to arise from edge radiation. From the point of view of edge radiation, assuming a lightly damped reverberant structure, the same radiation formula and directivity pattern can be derived in a much simpler manner. Broadband radiation from structures with subsonic and supersonic flexural wave speeds is discussed and characterized in terms of a simple interpretation of the surface wavenumber spatial transform. The results show that the physical idea of interpreting edge radiation in terms of uncancelled volumetric sources is not correct, and the effect of higher order edge singularities is in fact very significant. The approach implies a relationship between radiation and structural power flow that is potentially useful in energy-intensity based prediction methods, and can be generalized to more complex structures with application to vehicle interior noise prediction.

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