Component mode synthesis as a framework for uncertainty analysis

Component mode synthesis (CMS) is a well-established technique for the vibration analysis of built-up structures. It was originally developed as a method for reducing the size of a finite element model, hence reducing computational cost. CMS also offers an appealing framework for the analysis of the dynamics of uncertain structures. The benefits concern the numerical costs, the way uncertainty is included, quantified and propagated. This paper reviews and discusses these issues. The fixed-interface (Craig–Bampton) method is described, while the number of interface degrees of freedom (dofs) can be further reduced using characteristic constraint modes. Quantification and propagation of uncertainty is discussed. Uncertainties in properties can be naturally and straightforwardly introduced at the component level, either in terms of the component physical properties or the component modal properties, while the individual components are typically statistically independent, being made by different manufacturing processes. CMS methods are also amenable to the inclusion of experimentally measured variability data, quantifying it in terms of component modal properties. An example is given. The application of perturbational techniques is considered. The CMS framework is particularly amenable to propagation of uncertainty through one or more of the analysis paths at component or at global level using perturbations. Finally, qualitatively different uncertainty descriptions can be combined, with some components being described probabilistically, some possibilistically, the descriptions then being unified at the global level. Numerical examples are presented. Overall, CMS methods offer a strong physical insight into the analysis of structures with non-deterministic properties.