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History[ edit ] The initial derivation of SEA arose from independent calculations made in by Richard Lyon [1] and Preston Smith [2] 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.

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. Lyon mentioned the use of such methods in his initial SEA text book in but a number of alternative derivations have been presented over the years [7] [8] [9] [10] Method[ edit ] To solve a noise and vibration problem with SEA, the system is partitioned into a number of components such as platesshells, beams and acoustic cavities that are coupled together at various junctions.

Each component can support a number of different propagating wavetypes for example,the bendinglongitudinal and shear wavefields in a thin isotropic plate.

From an SEA point of view, the reverberant field of each wavefield represents an orthogonal store of energy and so is represented as a separate energy degree of freedom in the SEA equations. The energy storage capacity of each reverberant field is described by a parameter termed the 'modal density', which depends on the average speed with which waves propagate energy through the subsystem the average group velocityand the overall dimension of the subsystem.

The transmission of energy between different wavefields at a given type of junction is described by parameters termed 'coupling loss factors'. Each coupling loss factor describes the input power to the direct field of a given receiving subsystem per unit energy in the reverberant field of a particular source subsystem.

The coupling loss factors are typically calculated by considering the way in which waves are scattered at different types of junctions for example, point, line and area junctions.

Strictly, SEA predicts the average response of a population or ensemble of systems and so the coupling loss factors and modal densities represent ensemble average quantities. To simplify the calculation of the coupling loss factors it is often assumed that there is significant scattering within each subsystem when viewed across an ensemble so that direct field transmission between multiple connections to the same subsystem is negligible and reverberant transmission dominates.

In practical terms, this means that SEA is often best suited for problems in which each subsystem is large compared with a wavelength or from a modal point of view, each subsystem contains several modes in a given frequency band of interest.

The SEA equations contain a relatively small number of degrees of freedom and so can be easily inverted to find the reverberant energy in each subsystem due to a given set of external input powers.

The ensemble average sound pressure levels and vibration velocities within each subsystem can then be obtained by superimposing the direct and reverberant fields within each subsystem. Applications[ edit ] Over the past half century, SEA has found applications in virtually every industry for which noise and vibration are of concern.

Interior noise prediction and sound package design in automotive, aircraft, rotorcraft and train applications Interior and exterior radiated noise in marine applications Prediction of dynamic environments in launch vehicles and spacecraft Prediction of noise from consumer goods such as dishwashers, washing machines and refrigerators Prediction of noise from generators and industrial chillers Prediction of air-borne and structure-borne noise through buildings Design of enclosures etc.

Several commercial solutions for Statistical Energy Analysis are available: Statistical energy analysis of dynamical systems: Oxford University Press, Physical and Engineering Sciences ∙ Khuzd û l ∙ 9.

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