Smoothing experimental data in dynamic substructuring of built up systems Substructuring is performed using the dual domain decomposition: the coupling problem can be directly formulated from [12], while a similar formulation for the decoupling problem is developed and discussed in [3, 4] for collocated approach and in [16, 5] for non collocated approach. In the coupling problem, the FRF matrix of the component subsystems is assumed to be known at the coupling DoFs. With regard to the decoupling problem, the FRF matrix of the coupled system is assumed to be known at the coupling DoFs (standard interface). Information about the residual subsystem can consist either of measured FRFs or of a physical model. Here, the first assumption is considered. To circumvent ill-conditioning due to internal resonances of the residual subsystems with fixed interface, FRFs at some internal DoFs of the residual subsystem are used (extended interface) [2, 15, 4]. Since FRFs are curve-fitted from experimental tests, errors due to measurement inaccuracies and to identification can be expected. 2 Addition and subtraction of subsystems The coupled structural systemAB is assumed to be made by two subsystems (A and B) joined through a number of couplings (see Fig. 1). The degrees of freedom (DoFs) of the coupled system can be partitioned into internal DoFs (not belonging to the couplings) of subsystemA(a), internal DoFs of subsystemB(b), and coupling DoFs (c). If addition of subsystems (coupling problem) is considered, subsystems Aand B are assumed to be known whilst the FRF of the coupled systemABis unknown. If subtraction of subsystems (decoupling problem) is considered, the coupled structural systemAB and a residual subsystemB are assumed to be known whilst the FRF of subsystemAis unknown. 2.1 Addition of subsystems In the frequency domain, the equation of motion of a linear time-invariant subsystem r may be written as: Z(r)(ω) u(r)(ω) = f (r)(ω) + g(r)(ω) (1) where: [Z(r)] is the dynamic stiffness matrix of subsystemr; {u(r)} is the vector of degrees of freedom of subsystemr; {f (r)} is the external force vector; {g(r)} is the vector of connecting forces with other subsystems (constraint forces associated with compatibility conditions). 91
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