  This paper extends the inverse substructuring (IS) approach to the
state-space domain and presents a novel state-space substructuring (SSS)
technique that embeds the dynamics of connecting elements (CEs) in the Lagrange
Multiplier State-Space Substructuring (LM-SSS) formulation via compatibility
relaxation. This coupling approach makes it possible to incorporate into LM-SSS
connecting elements that are suitable for being characterized by inverse
substructuring (e.g. rubber mounts) by simply using information from one of its
off diagonal apparent mass terms. Therefore, the information obtained from an
in-situ experimental characterization of the CEs is enough to include them into
the coupling formulation. Moreover, LM-SSS with compatibility relaxation makes
it possible to couple an unlimited number of components and CEs, requiring only
one matrix inversion to compute the coupled state-space model (SSM). Two
post-processing procedures to enable the computation of minimal-order coupled
models by using this approach are also presented. Numerical and experimental
substructuring applications are exploited to prove the validity of the proposed
methods. It is found that the IS approach can be accurately applied on
state-space models representative of components linked by CEs to identify
models representative of the diagonal apparent mass terms of the CEs, provided
that the CEs can be accurately characterized by the underlying assumptions of
IS. In this way, state-space models representative of experimentally
characterized CEs can be found without performing decoupling operations. Hence,
these models are not contaminated with spurious states. Furthermore, it was
found that the developed coupling approach is reliable, when the dynamics of
the CEs can be accurately characterized by IS, thus making it possible to
compute reliable coupled models that are not composed by spurious states.
