Direct decoupling of substructures using primal and dual formulation on the drive point rotational mobility at the coupling DoF is shown in Fig. 4 together with the FRF obtained after curve-fitting. Fig. 4 Drive point rotational mobility of the complete system at the coupling DoF: true (—), perturbed by noise (∗∗∗) and fitted (—) 0 20 40 60 80 100 120 140 160 180 200 10−5 100 105 Frequency [Hz] Magnitude [rad s−1/(N m)] 0 20 40 60 80 100 120 140 160 180 200 −4 −2 0 2 4 Frequency [Hz] Phase [rad] In the sequel, only FRFs perturbed by simulated noise will be considered. In fact, if noise-free FRFs of the coupled system are used, the FRF of the unknown subsystem is always predicted without errors (although the problem may be singular for several reasons, as stated in section 2.3, the use of smart inversion techniques completely removes the singularity). Furthermore, perturbed FRFs are not used in raw form but are smoothed through a curve fitting procedure. The rotational mobility of subsystemAcan be determined by using the procedure described in section 2. The compatibility condition is written generally as: [BC]{u}= B AB C u AB + BB C u B ={0} where uAB T = θ1 θ3 θ4 θ5 θ8 u B T = θB 1 θB 3 θB 4 θB 5 and [BAB C ] and [BB C] built as detailed afterwards. In non collocated approach, the compatibility and the equilibrium DoFs are not the same. Therefore, a localization matrix [LE] =[LC], where [LC] is the nullspace of [BC], is defined to enforce equilibrium of constraint forces. A matrix [BE] can be defined accordingly, such that [LE] T[BE] T =0. 4.1.1 Compatibility Compatibility is alternatively enforced: • only at the coupling DoFs (standard interface). In this case, it is: [BC]= θ1 θ3 θ4 θ5 θ8 0 0 0 1 0 BAB C | θB 1 θB 3 θB 4 θB 5 0 0 0 −1 BB C 63
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