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

Abstract

Vibro-acoustic analysis of complex systems at higher frequencies faces two challenges: how to compute the response without using an excessive number of degrees of freedom (DOFs), and how to quantify the uncertainty of the response due to small spatial variations in geometry, material properties, and boundary conditions, which have a wave scattering effect? In this study, a general method of analysis is presented that provides an answer to both questions while overcoming most limitations of statistical energy analysis. The fundamental idea is to numerically compute an artificial ensemble of realizations for the components of the built-up system that are highly sensitive to small random wave scatterers. This can be efficiently performed because their eigenvalue spacings and mode shapes conform to Gaussian orthogonal ensemble spacings and Gaussian random fields, respectively. The DOFs of the overall system are therefore limited to those of the deterministic components and the interface DOFs of the random components. The method is extensively validated by application to plate structures. Good agreement between the predicted response probability distributions and the results of detailed parametric probabilistic models is obtained, also for cases of low modal overlap, single point loading, and strong subsystem coupling.

Microwave Studies of Three Chiral Ensembles in Chains of Coupled Dielectric Resonators

“…4. More specifically, we used the distribution for the couplings and the inverse of the corresponding fits from (19). For more details on the tworesonator measurements, see Appendix C. We chose σ = 36.3 MHz as this allowed us to use a range of d values in Fig.…”

“…For more details on the tworesonator measurements, see Appendix C. We chose σ = 36.3 MHz as this allowed us to use a range of d values in Fig. 5b leading to a good representation of the tails of the Gaussian couplings from (19). This σ led to a mean value of the distance of d = 5 mm between adjacent resonators.…”

“…11. The two resonance frequencies ν ± for every distance d can be used to extract the coupling a via (19). The dashed lines in Fig.…”

“…From the very beginning there had been the interest in experimental demonstrations of the predictions of random matrix theory, where the distribution of spacings of adjacent levels played a dominating role. For the Gaussian orthogonal ensemble there is an abundant number of realizations, including systems not quantum-mechanical in origin (for example [18,19] for vibro-acoustics, but see also Sect. 3.2 of [20]).…”

Acoustic Scattering in Duct With a Chaotic Cavity

“…In this case, due to huge complexity of the results, it is of great interest to get information about the statistics of the scattering. We can notice that, for the study of coupled structural vibrations, the statistical approach has been widely used, starting form the ideas of Statistical Energy Analysis [1,2,3,4,5,6].…”