Statistical Analysis of Power Injection and Response in Structures and Rooms

Abstract

The calculation of input power and response of simple models of rooms and structures is described. The approach is essentially statistical. Random variations in time are not considered; these fluctuations are averaged out. Randomness is introduced into the system models by considering basic parameters such as resonance frequencies and observation position to be selected statistically. Simplifying assumptions on the damping and mode shapes are made. The average and variance of power injected by point sources are calculated. The statistics of response near and away from the driving point are also found. It has not been possible to calculate the exact forms for the response distributions. Accordingly, in order to find confidence coefficients for estimation intervals, a distribution is chosen ad hoc. The selected one, the gamma distribution, has several desirable features. It is, in fact, exact for some important cases. Two kinds of estimation intervals are derived and applied to some simple examples. Finally, an interesting alteration of the frequency-spacing statistics, inspired by nuclear spectroscopy, is explored. It is found that a “level-repulsion” phenomenon causes small separations in resonance frequency to be less probable. This can smooth the multimodal response of systems in some important, practical instances.

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