Replacement of unobservable coupling DoFs in substructure decoupling

In this paper, suitable criteria are sought for an optimal replacement of unobservable coupling DoFs when performing substructure decoupling, that is the identification of a dynamic model of a substructure embedded in a known structure. The need arises since coupling DoFs are often difficult to observe, either because they cannot be easily accessed or because they include rotational DoFs. The substitution must be carried out both to preserve the information that would be lost when some coupling DoFs are not taken into account, and to avoid or minimize ill-conditioning problems. As shown in previous papers, coupling DoFs can be effectively replaced by internal DoFs for the sake of substructure decoupling. Furthermore, criteria for an appropriate selection of the internal DoFs used to replace unobservable coupling DoFs are sketched, which involve either the Frequency Response Function (FRF) or the transmissibility between internal and coupling DoFs. Here, previously introduced FRF and transmissibility criteria are combined with the condition number of the interface flexibility matrix to develop a procedure to optimally replace some coupling DoFs with a subset of internal DoFs. The procedure is tested using both simulated and experimental data of a tree structure (known structure), made by a cantilever beam with two offset short arms, coupled to another beam (structure to be identified).