8. Optimal Replacement of Coupling DoFs in Substructure Decoupling

Substructure decoupling consists in the identification of a dynamic model of a structural subsystem, starting from an experimental dynamic model (e.g. FRFs) of the assembled system and from a dynamic model of a known portion of it (the so-called residual subsystem). The degrees of freedom (DoFs) of the assembled system are partitioned into internal DoFs (not belonging to the couplings) and coupling DoFs. To achieve decoupling, a negative structure opposite to the residual subsystem is added to the assembled system, and compatibility and equilibrium conditions are enforced at interface DoFs. Interface DoFs can include coupling DoFs only (standard interface), additional internal DoFs of the residual subsystem (extended interface), subsets of coupling DoFs and internal DoFs (mixed interface), or a subset of internal DoFs only (pseudo interface). As shown in previous papers, the use of a mixed interface allows to replace some coupling DoFs (e.g. rotational DoFs) with a subset of internal DoFs. Furthermore, qualitative criteria for an appropriate selection of the internal DoFs used to replace unwanted coupling DoFs are stated. In this paper, a procedure to optimally replace coupling DoFs with internal DoFs is developed, using either the Frequency Response Function (FRF) or the transmissibility between internal and coupling DoFs. The procedure is tested on an assembled structure made by a cantilever column with two staggered short arms (residual substructure) coupled to a horizontal beam (unknown substructure).