Journal
JOURNAL OF SOUND AND VIBRATION
Volume 275, Issue 3-5, Pages 823-846Publisher
ACADEMIC PRESS LTD ELSEVIER SCIENCE LTD
DOI: 10.1016/S0022-460X(03)00780-6
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This paper is concerned with the ensemble statistics of the response to harmonic excitation of a single dynamic system such as a plate or an acoustic volume. Random point process theory is employed, and various statistical assumptions regarding the system natural frequencies are compared, namely: (i) Poisson natural frequency spacings, (ii) statistically independent Rayleigh natural frequency spacings, and (iii) natural frequency spacings conforming to the Gaussian orthogonal ensemble (GOE). The GOE is found to be the most realistic assumption, and simple formulae are derived for the variance of the energy of the system under either point loading or rain-on-the-roof excitation. The theoretical results are compared favourably with numerical simulations and experimental data for the case of a mass loaded plate. (C) 2003 Elsevier Ltd. All rights reserved.
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