22 R. Fagiani et al. applied to obtain the FRFs matrix of the coupled structure HRS. Since only the degrees of freedom corresponding to points 1 and 2 are coupled and the connections are modelled as rigid, becomes Eq. (2.7) HRS DHR CHS. The accelerance matrix GRS of the coupled structure can be also rewritten explicitly in terms of GS and GR using the Woodbury matrix identity as shown in [11, 13, 14] GRS DGR GR.GR CGS/ 1GR (2.8) Due the symmetry of the structure, the matrices are expected to be symmetric and the elements on the diagonal corresponding to point 1 and 2 are expected to be the same. 2.3.1 Experimental Case Study The accelerance matrices of the single beams and of the coupled structure have been measured by impact testing (impact hammer PCB 086C03) in the nearby area of the triaxial accelerometers (PCB M352C66) placed at points 1 and 2. The points correspond to the connection points of the coupled structure (Figs. 2.2, 2.3, and 2.4). All data were sampled at 6400 Hz. Fig. 2.3 Experimental case study: (a) source, (b) coupled structure 0 500 1000 1500 2000 2500 3000 10-3 10-2 10-1 100 101 102 |a1/F1| [m/s2/N] Frequency [Hz] Ge RS Ge Fig. 2.4 Experimental case study. Comparison between measured FRF for the coupled structureGe and those obtained coupling the FRF matrices of the source and the receiver GeRS using Eq. (2.12)
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