Band-averaged variance prediction in hybrid deterministicstatistical-energy analysis of vibro-acoustic systems

© Proceedings of ISMA 2018 - International Conference on Noise and Vibration Engineering and USD 2018 - International Conference on Uncertainty in Structural Dynamics. All rights reserved. The hybrid deterministic - statistical energy analysis method is a versatile framework for vibro-acoustic analysis. Stiff system components are modelled deterministically, while the wave fields in flexible components are modelled as diffuse. In this paper, the hybrid method is extended such that the ensemble mean and variance of the band-averaged system response can be computed. The variance represents the uncertainty that is due to the assumption of a diffuse field in the flexible components of the hybrid system. After generalizing the diffuse field reciprocity relationship, explicit expressions are derived for the cross-frequency and band-averaged variance of the vibrational energies in the diffuse components and the cross spectrum of the response of the deterministic components. These expressions are extensively validated against detailed Monte Carlo analyses of coupled plate systems in which diffuse fields are simulated by randomly distributing small point masses across the flexible components, and good agreement is found.