Statistical energy analysis

Statistical Energy Analysis (SEA) is a technique for predicting the transmission of sound and vibrations through complex structural acoustic systems. The method is particularly suitable as a forecasting method in the early planning phase of a product and for forecasting at higher frequencies. In an SEA, a system is represented as a series of coupled subsystems, from which a series of linear equations can be derived which describe the input, storage, transmission and dissipation of energy within each subsystem. For the parameters in the SEA equations, certain statistical assumptions are made about the local dynamic properties of each subsystem (similar to the assumptions in room acoustics or statistical mechanics ). These assumptions considerably simplify the analysis and enable the calculation of systems which are often too complex to analyze using other methods (such as finite element method and boundary element method ).

history

The initial derivation of SEA resulted from independent calculations by Richard Lyon in 1959 and Preston Smith in the context of the development of methods for analyzing the response of large and complex aerospace structures to spatially distributed random loading. Lyon's calculation revealed that, under certain conditions, the flow of energy between two coupled oscillators is proportional to the difference in the oscillator energies (which is based on a thermal analogy in structural acoustic systems). Smith's calculation showed that a structural mode and a diffusely reverberant sound field achieve a state of "equal distribution of energy" as the attenuation of the mode is reduced (comparable to the state of thermal equilibrium as it exists 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. While the modal approach provides physical insights into the mechanisms involved in the flow of energy, it is about assumptions that have dominated the subject of considerable debate for many decades. In recent years, alternative derivatives of the SEA equations based on wave approaches have become available. Such derivations form the theoretical basis behind a number of modern commercial SEA codes and a general framework for calculating the parameters in an SEA model.

method

To solve a sound and vibration problem with SEA, the system is divided into a number of components (such as panels, shells, beams and acoustic cavities) which are coupled together at different nodes. Each component can support a number of different wave types (for example, the bending , longitudinal, and shear wave fields in a thin isotropic plate). From the SEA's point of view, the reverberation of each wave field represents an orthogonal energy store and thus forms a separate energy degree of freedom in the SEA equation. The energy storage capacity of each reverberant field is described by a parameter, the so-called "modal density", which depends on the average speed at which the waves propagate energy through the subsystem (the average group speed and the overall size of the subsystem). The energy transfer between different wave fields is described by parameters so-called “coupling loss factors” according to the type of connection. Each coupling loss factor describes the input power to the direct field of a given receiving subsystem per unit of energy in the reverberation field of a particular source subsystem. The coupling loss factors are usually calculated taking into account the manner in which waves are scattered at different types of connections (e.g. points, lines and surface transitions). Strictly speaking, SEA gives a forecast of the average reaction of a collection or connection of systems and thus the coupling loss factor and modal densities, which represent the total of the average quantities. To simplify the calculation of the coupling loss factors it is often assumed that there is significant dispersion in each subsystem (when viewed across an ensemble) so that direct field transmission between multiple connections to the same subsystem is negligible and the reverberation transmission dominates. In practice this means that SEA is often best suited for problems in which each subsystem is large compared to a wavelength (or from a modal point of view each subsystem contains several modes in a certain frequency band which are of interest). The SEA equations contain a relatively small number of degrees of freedom and so can easily be reversed to find the reverberant energy in each subsystem due to a given amount of external input powers. The (overall average) sound pressure level and vibration velocities within each subsystem can then be obtained by superimposing the direct and reverberation fields within each subsystem.

Applications

Over the past half century, SEA applications have established themselves in almost all industries in which noise and vibrations are essential. Typical applications are:

• Interior noise forecast and sound package design in automotive, aircraft, rotorcraft and rail applications
• Indoor and outdoor interference radiation in marine applications
• Predict dynamic environments in launch vehicles and spacecraft
• Predict the noise of consumer products such as dishwashers, washing machines and refrigerators
• Prediction of noise from generators and industrial chillers
• Prediction of airborne and structure-borne noise through buildings
• Design of enclosures etc.

Further examples can be found in the course of conferences such as INTERNOISE, NOISECON, Euronoise, ICSV, NOVEM, SAE N & V.

Software implementations

Several commercial solutions for statistical energy analysis are available:

• SEAM, SEAM 3D from Cambridge Collaborative Inc. USA,
• VA One SEA Module (previously AutoSEA) from ESI Group , France,
• GSSEA-Light from Gothenburg Sound AB, Sweden,
• SEA + from InterAC, France distributed by LMS International.

Freeware:

• Statistical Energy Analysis Freeware,

Open source solutions:

• SEAlab - open code in Matlab / Octave from Applied Acoustics, Chalmers, Sweden

Individual evidence

1. ↑ LYON, RH; MAIDANIK, G .: Power Flow Between Linearly Coupled Oscillators, Journal of the Acoustical Society of America ; 34, pp. 623-639, 1962
2. ^ Smith, PW: Response and radiation of structural modes excited by sound. The Journal of the Acoustical Society of America 34.5 (1962): 640-647.
3. ^ Lyon, Richard H. Statistical energy analysis of dynamical systems: theory and applications. 1975.
4. ^ Le Bot, A., "Foundation of statistical energy analysis in vibroacoustics. Oxford University Press, 2015.
5. ↑ 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.
6. ^ Shorter, PJ, and Langley RS: Vibro-acoustic analysis of complex systems. Journal of Sound and Vibration 288.3 (2005): 669-699.
7. ↑ Archived copy ( memento of the original from July 16, 2011 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. 
8. ↑ http://www.esi-group.com/products/vibro-acoustics/va-one/core-modules/sea-module
9. ↑ http://www.gothenburgsound.se/products/Software/GSSEA-Light/index.html
10. ↑ http://www.interac.fr
11. ↑ http://www.free-sea.de/
12. ↑ Archived copy ( memento of the original from October 7, 2011 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice.