Response variance prediction in the statistical energy analysis of built-up systems

Abstract

In the statistical energy analysis (SEA) of high frequency noise and vibration, a complex engineering structure is represented as an assembly of subsystems. The response of the system to external excitation is expressed in terms of the vibrational energy of each subsystem, and these energies are found by employing the principle of power balance. Strictly the computed energy is an average taken over an ensemble of random structures, and for many years there has been interest in extending the SEA prediction to the variance of the energy. A variance prediction method for a general built-up structure is presented here. Closed form expressions for the variance are obtained in terms of the standard SEA parameters and an additional set of parameters alpha(k) that describe the nature of the power input to each subsystem k, and alpha(ks) that describe the nature of the coupling between subsystems k and s. The theory is validated by comparison with Monte Carlo simulations of plate networks and structural-acoustic systems.

Accurate extreme-value-based frequency response bounding for structures with a small number of highly random parameters

“…Because the SEA theory for an L-shaped plate is spread over a number of sources i.e. [6][22] [24] and [32], this appendix serves to bring the results together. SEA involves splitting the system into subsystems enabling the mean and variance to be obtained with computational efficiency.…”

“…The most accurate method for built-up structures is given in [24]. The energy variance can be written in the form: …”

“…Importance or Line Sampling [19][20] can speed-up the process (as available in the software COSSAN [21]) but accuracy is not guaranteed. High frequency methods apply to structures with vibration wavelengths much shorter than component dimensions for which SEA is most successful [22][23][24][25][26]. SEA takes no account of differing levels of parameter variability because randomness is assumed to be sufficiently high for knowledge of variability not to be needed.…”

Sensitivity studies of friction-induced vibration

“…Within room acoustics, and somewhat more recently in structural vibration theory, statistical methods have been developed to analyse the ensemble mean response of uncertain systems (e.g., Cremer and Muller, 1982;Lyon and de Jong, 1995). In recent years these techniques have been extended to allow ensemble variance of complex coupled systems to be predicted as well (Langley and Cotoni, 2004). Hybrid models combining these statistical methods consistently with deterministic approaches such as Finite Element methods have been developed (Langley and Bremner, 1999).…”

An efficient probabilistic approach to vibro-acoustic analysis based on the Gaussian orthogonal ensemble

“…Langley and Cotoni extended the SEA method to predicting the variance of the energy by introducing an additional set of parameters that describe the nature of the external power input to each subsystem and the coupling between the different subsystems. 6 Very recently the marginal probability density function (PDF) of a subsystem's total energy has been characterized for some special but important cases. Under the additional assumption of moderately high modal overlap and for certain loading cases, the energy is approximately lognormally distributed.…”