Vertex combination approach for uncertainty propagation analysis in spacecraft structural system with complex eigenvalue

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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.