8 F. Trainotti et al. Fig. 1.4 Layout of impacts and responses at the interface for VPT. Red: Impacts; Blue: Responses; Green: Virtual Point. (a) Component A—Piezo. (b) Component A—Laser. (c) Component B—Piezo. (d) Component B—Laser 1.4.2 Virtual Point Reduction The dynamics of the interface is condensed into a virtual point that is located in the center of the hole on the connecting surface of the two substructures. The placement and number of impacts and responses around the virtual point is chosen to ensure the observability of the entire set of selected virtual DoFs and a high quality transformation for both case studies [9, 11]. In the measurement campaign with the triaxial sensors the interface dynamics is reduced into a subspace composed by six rigid IDMs (three translations and three rotations). For this purpose, three sensors and eight excitation points are located on the interface of both substructures (Fig. 1.4a, c). The mono-dimensional nature of the available laser vibrometer, on the other hand, leads to the choice of a single-plane measurement campaign. Indeed, the FRFs are acquired exclusively along the vertical axis and consequently only the dynamics related to the vertical translational DoF and the two out-of-plane rotations is retained in the transformation. A total of six output signals and six impacts are used to describe the virtual point DoFs for each subcomponent (Fig. 1.4b, d). 1.4.3 Coupling Results The transformed FRF admittances YA qm and Y B qm are coupled according to LM-FBS (Eq. 1.8). An effective comparison between the two measurement campaigns is achieved by coupling only the dynamics associated with the translational DoF along the vertical axis. The experimental coupled FRF is plotted together with the correspondent assembly validation FRF for both case studies. To assess the accuracy of the experimentally coupled FRF, a cross-validation is performed by comparing the data with simulated results, in which only the vertical translation over the interface area is coupled. The outcome in magnitude and phase is shown in Fig. 1.5a,b. A focus on lower frequencies is depicted in Fig. 1.6a,b.
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