Discretized subregion variational principle for dynamic substructuring

The purpose of this paper is to derive and apply the relationships of the d ynamic substructure synthesis method, based on the subregion variational pr inciple of elastodynamics in discrete form. Two theorems are derived for di scretized systems and are used to demonstrate the interface compatibility c ondition of dynamic substructure synthesis. This enables the dynamic substr ucture synthesis method to be derived from the subregion variational princi ple. A complete modal expansion is used to derive the residual modes for bo th the free and fixed interface methods. The alternative formulations of th e hybrid, free interface, and fixed interface methods, as well as Guyan-Iro ns reduction, are shown by coordinate transformations to be degenerate case s. These cases are all reasonable representations of the Rayleigh-Ritz meth od, and if they use constraint modes and/or attachment modes, good converge nce can be assured because the static modes are included in the substructur e reduction, The relationships between these cases are explored, and illust rative examples are solved.