Component mode synthesis methods for non-proportionally damped systems

This paper presents several new methods of component mode synthesis (CMS) for non-proportionally damped systems. In contrast to existing CMS approaches, these methods are based upon a first-order state-space formulation which engenders complex-valued modal vectors, transformation matrices, and reduced structural matrices. Four new methods are presented. These are baseband and non-baseband versions of `constraint modes' and `residual flexibility' methods. The constraint modes methods are applicable when existing finite element matrices can be employed for analytical implementation. The residual flexibility methods are used within an experimentally-based implementation with test data. The experimentally-based methodology produces matrices that are compatible with the analytical matrices; thus, system models comprising both types of matrices can be analyzed as a single assembly. The performances of the new methods are assessed using a system of two coupled beams with non-proportional viscous damping. Good results are obtained for all methods, when compared to calculated results based on modeling the entire structure.