Hybrid finite element/statistical energy method for mid-frequency analysis of structure−acoustic systems with interval parameters

Abstract

The hybrid Finite Element/Statistical Energy Analysis (FE-SEA) model for mid-frequency analysis consists of two parts: the FE components and the SEA components, which are called as the master system and the subsystem respectively. The hybrid Finite Element/Statistical energy analysis approach is established on the assumption that the FE components have fully deterministic properties, while the SEA subsystems have a high degree of randomness. This method has been recently extended to allow the properties of the FE components of built-up structures to be uncertain like interval or probabilistic, and the hybrid model with parametric and non-parametric uncertainties is obtained. By dealing with the non-parametric uncertainty analytically and the parametric uncertainty with Monte Carlo Simulations, the distribution of the responses of the hybrid model can be obtained. In this paper, the interval parametric uncertainty is introduced into the hybrid FE–SEA framework for structure−acoustic systems, and the interval dynamic equilibrium equations are established, thus a hybrid model with non-parametric and interval parametric uncertainties for structure−acoustic systems is obtained; to improve the computational efficiency, the second-order interval perturbation finite element method is introduced into the hybrid FE-SEA framework and the second-order interval perturbation finite element/statistical energy analysis (SIPFEM/SEA) method is proposed. For the structure−acoustic system with interval parameters modeled by FE-SEA, the parameters of FE components are considered as interval parameters instead of deterministic ones, thus the expectations of the second order quantities such as the vibrational energy and the response cross-spectrum in the FE-SEA framework become interval variables, too. In the SIPFEM/SEA, the expectations of the second order response quantities of a structure−acoustic system are expanded with the second-order Taylor series at the nominal values of interval parameters, and for the sake of simplicity and efficiency, the non-diagonal elements of the Hessian matrices are neglected; then by searching the target positions of interval parameters that maximize or minimize the objective functions, the bounds of the vibrational energy and the response cross-spectrum can be obtained. Because of the neglect of the higher order terms of Taylor series, SIPFEM/SEA is limited to the interval analysis with narrow parameter intervals. For larger parameter intervals, the sub-interval perturbation method based on the SIPFEM/SEA is introduced. The proposed methods are illustrated by applications to two example structure−acoustic systems in which the acoustic cavities are modeled by using the interval FE method and the structures are modeled by using the SEA. Reference comparisons are made with the Monte Carlo simulations of the hybrid FE/SEA model. The numerical results verify the accuracy and efficiency of the proposed methods.