Vertex combination approach for uncertainty propagation analysis in spacecraft structural system with complex eigenvalue. (June 2020)

• Record Type: Journal Article
• Authors: Qiu, Zhiping; Lyu, Zheng
• Is Part Of: Acta astronautica. Volume 171(2020)
• Page Start: 106
• Page End: 117
• Publication Date: 2020-06
• Subjects: Vertex combination approach -- Uncertainty propagation analysis -- Spacecraft structural system -- Complex eigenvalue -- Convex set theory; Astronautics -- Periodicals; Outer space -- Exploration -- Periodicals; Astronautics; Periodicals; 629.405
• DOI: 10.1016/j.actaastro.2020.02.054
• Languages: English
• ISSNs: 0094-5765

Abstract

Abstract: Uncertainty propagation analysis is crucial to the safety and optimal design of spacecraft structural system in which high accuracy modelling is required. In consideration of convex uncertainties, a vertex combination approach based on the convex set theory is proposed to evaluate the influence of uncertain parameters on the complex eigenvalue of spacecraft structural system with non-proportional damping. The uncertain parameters are dealt with as a closed and bounded convex set. In the proposed method, complex eigenvalue problem with convex uncertainties can be converted into a family of equivalent eigenvalue problems without uncertainties, and the bound evaluation of eigenvalue is conducted by determining the extreme values of the deterministic complex eigenvalue problems. The advantage of this work is easy to integrate with existing codes for large-scale structural system, which allows us to carry out the extension of such deterministic finite element codes to deal with uncertain structural system with complex eigenvalue. Three numerical examples are performed to demonstrate the effectiveness and the accuracy of the proposed method. Highlights: Uncertainty modelling for spacecraft structural system with complex eigenvalue is conducted. Novel proof of vertex solution theorem is given to solve uncertain structural complex eigenvalue model. Vertex combination approach is proposed to predict the sharp bounds of spacecraft structural eigenvalue. Novel idea is to transform complex eigenvalue problem with uncertainties into a series of equivalent deterministic problems.