Gaussian orthogonal ensemble modeling of built-up systems containing general diffuse components and parametric uncertainty

Abstract

Built-up vibro-acoustic systems may contain components whose vibration field is sensitive to uncertainty from small spatial variations in geometry, material properties, or boundary conditions, which have a wave scattering effect. Such components can be modeled as diffuse. Statistical energy analysis (SEA) and related approaches are frequently employed for analyzing built-up systems with diffuse components, but their scope is limited because subsystems must be weakly coupled, the displacement fields are not modeled but only the total energies, the joint response probability density function is not available, and the computational efficiency decreases when there is additional parametric uncertainty. Recently, a method of analysis was presented that overcomes those limitations. It is a computationally efficient Monte Carlo method in which the subsystem displacement fields rather than the total energies are modeled. The method relies on the fact that the undamped eigenvalues of a diffuse wave field conform to those of a Gaussian Orthogonal Ensemble (GOE) matrix, while the mode shapes are Gaussian random fields. In this paper, the method is generalized such that diffuse components that are not homogeneous and isotropic, and that have a non-constant modal density, can be analyzed. This is achieved by transforming the GOE eigenvalue spacings to conform to the modal density of a diffuse component, and by relating its mode shape correlation function to the Green’s function of the corresponding unbouded subsystem. Parametric uncertainty is included in a straightforward way. The accuracy and computational efficiency of this field-based method is investigated by comparison with the energy-based (hybrid deterministic-)SEA method and with a detailed Monte Carlo method, where the diffuse field assumption is not made and local random wave scatterers are explicitly modeled. It is found that the new approach is more accuracte than SEA and also more computationally efficient when there are several or many uncertain parameters.