Review of statistical energy analysis hypotheses in vibroacoustics

Abstract

This paper is a discussion of the equivalence between rain-on-the-roof excitation, diffuse field and modal energy equipartition hypotheses when using statistical energy analysis (SEA). A first example of a simply supported plate is taken to quantify whether a field is diffuse or the energy is equally distributed among modes. It is shown that the field can be diffuse in a certain region of the frequency-damping domain with a single point force but without energy equipartition. For a rain-on-the-roof excitation, the energy becomes equally distributed, and the diffuse field is enforced in all regions. A second example of two plates coupled by a light spring is discussed. It is shown that in addition to previous conclusions, the power exchanged between plates agrees with the statistical prediction of SEA if and only if the field is diffuse. The special case of energy equipartition confirms this observation.

Coupling strength assumption in statistical energy analysis

“…Figure 6 shows the positions of the plates in the dimensionless wavelength-damping loss factor plane. The isovalue lines indicate the relative standard deviation of the repartition of energy in plates observed by a reference calculation conducted on a single plate (see [10] for details). All plates are confined in the zone where the value of the relative standard deviation is less than 0.3, meaning that the local fluctuations of energy within the plates are less than 30%.…”

“…For multi-degree of freedom subsystems, the coupling power proportionality is still valid (but now with the difference in modal energies) but requires further assumptions (rain-on-the-roof excitations, light damping, large number of resonant modes). The reader may refer to [5][6][7][8][9][10][11] for reviews of SEA and discussions on the required hypotheses.…”

Automatic subsystem identification in statistical energy analysis

“…The analysis, however, is not performed directly on the energy densities. The most important variable is not the energy itself but the normalised difference between the energy at each cell and the averaged energy of the system, as defined by [15] or [24] in order to study the energy equipartition in SEA problems. Therefore, a new map is produced, computing for each cell i and mode j the value ofẽ ij as…”

Entropy in sound and vibration: towards a new paradigm

“…Of course, there are several constraints for this result to be valid (the above list of assumptions). A careful study of these assumptions leads to establishing that all subsystems must be in diffuse field state (homogeneous and isotropic repartition of energy, see [17]). This state of diffuse field may be interpreted as an equilibrium state with a constant temperature.…”