84 W. D’Ambrogio and A. Fregolent Fig. 8.4 Residual subsystem 8.3.1 Analysis of FRF and Transmissibility Indicators Since rotational DoFs at the junction between the residual subsystem and the unknown subsystem are not measured, an analysis of FRF and Transmissibility indicators is performed to select the optimal DoFs that should be used to substitute DoFs 11#x and 11#y. Figures 8.7 and 8.8 show the FRF indicators H11#x,i andH11#y,i computed by Eq. (8.13), showing the propensity of a force applied to DoFi to excite a rotation on Dofs 11#x and11#y respectively. From Fig. 8.8 it can be noticed that a force should be applied either to DoF 9z or toDoF10z in order to excite Dof 11#y: the effect of a force applied to a different DoF is several order of magnitude lower especially in the low frequency range. By applying a force either to DoF 9z or toDoF 10z, DoF 11#x is sufficiently excited, as confirmed by the observation of Fig. 8.7. The same conclusions can be drawn by observing Table 8.3 which shows the static FRF indicators: in order to excite DoF 11#y it is essential to apply a force either to DoF 9z or toDoF10z. Figures 8.9 and 8.10 show the Transmissibility indicators T11#x,i and T11#y,i, computed by Eq. (8.14), showing the propensity of a force applied to DoF i to produce a moment about Dofs 11#x and 11#y respectively. From Fig. 8.10 it can be noticed that a force should be applied either to DoF 9z or toDoF10z in order to produce a moment about DoF 11#y: the effect of a force applied to a different DoF is several order of magnitude lower. By applying a force either to DoF 9z or to DoF 10z, a significant moment about DoF 11#x is produced, as confirmed by the observation of Fig. 8.9. The same conclusions can be drawn by observing Table 8.4 which shows the static Transmissibility indicators: in order to produce a moment about DoF 11#y it is essential to apply a force either to DoF 9z or toDoF10z.
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