Abstract
Frequency-dependent fluctuations in the power transmissibility of a reverberant elastic body are measured and compared with theoretical estimates. Wideband (0.1–2 MHz) transient sources are applied to aluminum blocks of dimensions of the order of 3 cm (greater than typical wavelengths) and found to generate signals with durations of the order of 100 ms. At low frequencies the power spectra of these waveforms, found by FFT, show the usual distinct resonance peaks that allow unambiguous mode counting. At higher frequencies, where modal overlap is significant, mode counting is more difficult. Nevertheless, modal density is, in principle, recoverable by analysis of the variance of the power spectra. An improved theory for the relative variance is presented, which includes the effects of variations in modal widths and includes the effects of spectral rigidity. The theory assumes that modal amplitudes are Gaussian random numbers, as is predicted by random matrix theory. The method consistently overestimates modal densities, by about 50%. After elimination of other causes, the discrepancy is attributed to the assumption on modal amplitude statistics.
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