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Statistical energy analysis
Statistical energy analysis (SEA) is a method for predicting the transmission of sound and vibration through complex structural acoustic systems. The method is particularly well suited for quick system level response predictions at the early design stage of a product, and for predicting responses at higher frequencies. In SEA a system is represented in terms of a number of coupled subsystems and a set of linear equations are derived that describe the input, storage, transmission and dissipation of energy within each subsystem. The parameters in the SEA equations are typically obtained by making certain statistical assumptions about the local dynamic properties of each subsystem (similar to assumptions made in room acoustics and statistical mechanics). These assumptions significantly simplify the analysis and make it possible to analyze the response of systems that are often too complex to analyze using other methods (such as finite element and boundary element methods).
==History==
The initial derivation of SEA arose from independent calculations made in 1959 by Richard Lyon 〔LYON, R.H.; MAIDANIK, G.: Power Flow Between Linearly Coupled Oscillators, ''Journal of the Acoustical Society of America''; 34, pp.623–639, 1962〕 and Preston Smith 〔Smith, P. W. "Response and radiation of structural modes excited by sound." The Journal of the Acoustical Society of America 34.5 (1962): 640-647.〕 as part of work concerned with the development of methods for analyzing the response of large complex aerospace structures subjected to spatially distributed random loading. Lyon's calculation showed that under certain conditions, the flow of energy between two coupled oscillators is proportional to the difference in the oscillator energies (suggesting a thermal analogy exists in structural-acoustic systems). Smith's calculation showed that a structural mode and a diffuse reverberant sound field attain a state of 'equipartition of energy' as the damping of the mode is reduced (suggesting a state of thermal equilibrium can exist in structural-acoustic systems). The extension of the two oscillator results to more general systems is often referred to as the modal approach to SEA.〔Lyon, Richard H. Statistical energy analysis of dynamical systems: theory and applications. 1975.〕 While the modal approach provides physical insights into the mechanisms that govern energy flow it involves assumptions that have been the subject of considerable debate over many decades.〔Fahy, F J., "Statistical energy analysis: a critical overview." Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences 346.1681 (1994): 431-447.".〕 In recent years, alternative derivations of the SEA equations based on wave approaches have become available. Such derivations form the theoretical foundation behind a number of modern commercial SEA codes and provide a general framework for calculating the parameters in an SEA model 〔Shorter, P. J., and Langley R. S., "Vibro-acoustic analysis of complex systems." Journal of Sound and Vibration 288.3 (2005): 669-699.〕
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