An efficient method for evaluating the natural frequencies of structures with uncertain-but-bounded parameters

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

“…In this method, the interval matrices and the interval vectors were expanded to a first order Taylor series. To improve the accuracy of the IPM, an interval perturbation method based on the second-order Taylor expansion (SIPM) was recently developed [20,21]. Because of the neglect of the higher order terms of Taylor series, IPM is limited to the interval analysis with narrow parameter intervals.…”

The Influence of Uncertainty of Design Parameters on Dynamic Characteristics of Structure With Dampers

“…The computational cost in this approach is very high, especially for high numbers of the interval parameters. Therefore, a simplification of the above method was proposed in [3]. In that paper, the non-diagonal elements of the Hessian matrix are neglected.…”

“…Some researchers [3,7] proposed an approximation of the objective function ( ) p F using the second-order Taylor series expansion around the middle values of parameters p c : …”

“…It assumes that the lower and upper bounds of the objective function should be calculated as the end-point combination of the design interval parameters. The method is also used in [3]. However, when the number of interval design parameters is large, the computational cost of the combination of all the parameters is very high.…”

“…The method was extended in paper [6] and its application to optimization was shown. In [3,7], the authors improved the method using the second-order Taylor series expansion. In [7], Fujita and Takewaki introduced an application of the method to the analysis of structures with passive dampers.…”