Interval sensitivity analysis of joint dynamics in complex built-up structures

Abstract

The dynamic properties of joints, or inter-component connections, are a principal source of uncertainty when modelling complex built-up structures. In the present paper, we propose an interval-based sensitivity analysis (SA) to establish the contribution, or influence, of a structure’s uncertain joint dynamics towards the uncertainty of its coupled admittance. We choose an interval SA as it overcomes the limitations of conventional local and global methods; accuracy and computation efficiency, respectively. Furthermore, it avoids the need for detailed probabilistic data to describe each joint, which is often unavailable. The proposed interval SA is based on the dual formulation of the sub-structuring problem and utilises the Sherman–Morrison formula to factor out the contribution of an individual joint. A complex interval is used to represent the uncertain joint stiffness and damping, and precise bounds on the assembly’s complex admittance (also operational response) are determined following an application specific algorithm. The relative change between input (joint stiffness and damping) and output (complex admittance) interval area is chosen as a sensitivity metric and used to rank order the uncertain influence of each joint. The method is illustrated by numerical example.

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