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Published: 1966

Total Pages: 75

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The concepts and relations which form the theoretical foundation of the statistical energy approach to vibration analysis are delineated. The utility of this approach for dealing with complex systems is discussed, and its range of applicability is indicated. The important properties of the modes of vibrating systems are reviewed and used to exhibit relations between modal responses and average responses of total systems. It is demonstrated that under some conditions, which are often approximated in actual systems, the average rate of flow of energy from one mode to another is proportional to the difference in the modal energies. It is also shown that under some conditions the average rate of flow of energy between two sets of modes (representing groups of modes of two coupled systems in a given frequency band) is proportional to the difference in the set-average modal energies. Examples are presented which indicate how these relations permit one to obtain approximate solutions to complex problems simply, on the basis of energy conservation considerations. Available extensions of the major concepts developed in detail are mentioned, and references to the current literature are given.