Abstract
To improve the efficiency of midfrequency analysis of built-up structure systems with interval parameters, the second-order interval and subinterval perturbation methods are introduced into the hybrid finite element/statistical energy analysis (FE/SEA) framework in this paper. Based on the FE/SEA for built-up structure systems and the second-order interval perturbation method, the response variables are expanded with the second-order Taylor series and nondiagonal elements of the Hessian matrices are neglected. Extreme values of the expanded variables are searched by using efficient search algorithm. For large parameter intervals, the subinterval perturbation method is introduced. Numerical results verify the effectiveness of the proposed methods.
Highlights
In the last two decades, predicting the response of a system with uncertainties has got more and more attention in the engineering design
The second-order interval perturbation method combined with FE-Statistical energy analysis (SEA) (SIPFEM/SEA) is proposed for the response prediction of the built-up structure systems with nonparametric and small interval parametric uncertainties; secondly, the subinterval perturbation method based on the SIPFEM/SEA is introduced to predict the response of the built-up structure systems with nonparametric and large interval parametric uncertainties
The subinterval perturbation method based on the SIPFEM/SEA is introduced
Summary
In the last two decades, predicting the response of a system with uncertainties has got more and more attention in the engineering design. To improve the efficiency of the midfrequency analysis of built-up structure systems with interval parametric uncertainty, the second-order interval perturbation method and subinterval analysis technique are introduced into the hybrid FE-SEA framework. Expand the interval response variables (EjI and SIqq) of the built-up structure system with the second-order Taylor series at the mean values of interval parameters, and for the sake of simplicity and efficiency, the nondiagonal elements of the Hessian matrices are neglected (equations (25)∼(26)). Because of the neglect of the higher order terms of Taylor series, SIPFEM/SEA is limited to the midfrequency analysis of the built-up structure systems with small interval parametric uncertainty. In order to predict the response of the built-up structure systems with large interval parametric uncertainty, the subinterval perturbation method based on SIPFEM/SEA is introduced . From the convergence condition of perturbation theory, we can see that if the number of the subintervals for each parameter is sufficiently large, the bounds of the response variables of the built-up structure systems with large interval parametric uncertainty will be predicted accurately
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