Discretized subregion variational principle for dynamic substructuring

The purpose of this paper is to derive and apply the relationships of the dynamic substructure synthesis method, based on the subregion variational principle of elastodynamics in discrete form. Two theorems are derived for discretized systems and are used to demonstrate the interface compatibility condition of dynamic substructure synthesis. This enables the dynamic substructure synthesis method to be derived from the subregion variational principle. A complete modal expansion is used to derive the residual modes for both the free and fixed interface methods. The alternative formulations of the hybrid, free interface, and fixed interface methods, as well as Guyan-Irons reduction, are shown by coordinate transformations to be degenerate cases. These cases are all reasonable representations of the Rayleigh-Ritz method, and if they use constraint modes and/or attachment modes, good convergence can be assured because the static modes are included in the substructure reduction. The relationships between these cases are explored, and illustrative examples are solved.