Several solution methods for the generalized complex eigenvalue problem with bounded uncertainties

Qiu, Zhiping; Wang, Xiaojun

doi:10.1016/j.ijsolstr.2004.09.043

Cited by 12 publications

(2 citation statements)

References 7 publications

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“…Uncertainty analysis involving interval quantities can be carried out using direct interval arithmetic, which may, however, cause large overestimations known as the wrapping effect. Intrusive interval methods such as the interval Taylor approach and perturbation method [29,30] can often get relatively tight response bounds, but they are difficult to adapt to different problems as the mathematic formulation is complex and modifications should be made to the original solvers. The Chebyshev inclusion function (CIF) [31], which controls well the overestimations, has the advantages of transparency and simplicity in concept.…”

Section: Introductionmentioning

confidence: 99%

Response analysis of an accelerating unbalanced rotating system with both random and interval variables

Yang

et al. 2020

Journal of Sound and Vibration

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This paper investigates the accelerating up transient vibrations of a rotor system under both the random and uncertain-but-bounded uncertainties. The Polynomial Chaos Expansion (PCE) coupled with the Chebyshev surrogate method is used to analyses the propagations of the two categorizes of uncertainties. The output responses will possess the characteristics of both bounded quantities and statistical moments. As a hybrid non-intrusive uncertainty quantification (UQ) procedure, the deterministic rotor model is taken as a black box and will only be executed at specific parameter points. A number of uncertain physical parameters are studied and the corresponding transient responses are presented. The accuracy and efficiency are verified by the Monte Carlo simulations (MCS) in combination with the scanning scheme and also other hybrid analysis framework. It will provide guidance for the accurate transient dynamic analysis of engineering problems with hybrid uncertainties.

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Section: Introductionmentioning

confidence: 99%

Response analysis of an accelerating unbalanced rotating system with both random and interval variables

Yang

et al. 2020

Journal of Sound and Vibration

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“…Currently, the literatures on dynamic response of linear system with interval parameters are relatively inadequate. Qiu et al [12][13] presented a new algorithm to evaluate the dynamic response range of structures with uncertainties on the basis of the parameter perturbation method and interval mathematics.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Response Analysis for Structures with Interval Parameters Based on Affine Arithmetic

Zhu

Chen

2008

AMR

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This paper aims to study the uncertainty of the MDOF structural dynamic response, taking not only the interval characteristics of structural physical parameters and geometric dimension, but also the interval characteristics of applied load simultaneously . By means of the description of the interval parameters of uncertain structure with affine forms, the interval structural dynamic equation is studied, and an improved affine arithmetic based on interval division is presented, where correlations between the interval elements in eigenvalue and responses equations are considered, independent uncertain parameters are transformed to affine forms, and the solution of eigenvalue and response equations are transformed into the corresponding certain ones. With general affine arithmetic, the eigenvalue of each order and response bounds are determined by searching for the maximum and minimum in the solutions. Finally, some mathematical examples and a further engineering application confirm the feasibility and validity of this approach.

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Reliability-based topology optimization for freely vibrating continuum structures with unknown-but-bounded uncertainties

Xia

Qiu

Wang

2021

Struct Multidisc Optim

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Several solution methods for the generalized complex eigenvalue problem with bounded uncertainties

Cited by 12 publications

References 7 publications

Response analysis of an accelerating unbalanced rotating system with both random and interval variables

Response analysis of an accelerating unbalanced rotating system with both random and interval variables

Dynamic Response Analysis for Structures with Interval Parameters Based on Affine Arithmetic

Reliability-based topology optimization for freely vibrating continuum structures with unknown-but-bounded uncertainties

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