468 T. Kalaycıog˘lu and H.N. Özgüven Table 46.1 Physical parameters Element Number (i) mi [kg] ki [N/m] ci [Ns/m] 1 2.5 1500 0.15 2 3 2000 0.20 3 2 2100 0.21 4 3 1900 0.19 5 2.5 2200 0.22 Exact Polluted Curve Fitted Log( I H22 [m/N] I ) 10-6 10-4 10-2 100 Frequency [Hz] 1 2 3 4 5 6 7 8 9 Fig. 46.3 Driving point FRF of the coupled system at the 2nd DoF: true (solid black line), polluted (blue asterisks) and curve fitted (red dashed lines) Exact Eq.(17) Log( I HU 22 [m/N] I ) 10-6 10-4 10-2 100 Frequency [Hz] 1 2 3 4 5 6 7 8 9 FRAC = 0.99708 Fig. 46.4 Driving point FRF at the 2nd DoF of the unknown subsystem: true (solid black line), predicted using Eq. (46.17) (magenta asterisks) In order to simulate the measured FRFs of the coupled system, first the exact FRFs of the coupled system (Hˆ ) are calculated by using the physical parameters given in Table 46.1 and then they are polluted by simply adding complex random variables as shown below: Hij .!k/ DbHij .!k/ Cpij,k Ci qij,k (46.26) Here, pij,k and qij,k are independent random variables with Gaussian distribution, zero mean and a standard deviation of 5 10 5 m/N. The effect of such a pollution on the driving point FRF at the 2nd DoF (the coupling DoF) of the coupled system is shown in Fig. 46.3 together with the FRF obtained after curve fitting. Then, by using the curves fitted to the polluted FRFs of the coupled structure, driving point FRF at the coupling DoF of the unknown subsystem is calculated using the proposed formulations, and the results are given in Figs. 46.4 and 46.5. Figures 46.4 and 46.5 show that both approaches predict the unknown subsystem FRF satisfactorily. If the performances of both approaches are compared with each other around resonances, the predicted FRF via Eq. (46.24) seem to fit better to the true FRF by visual inspection. However, in order to make a reliable and sound comparison, it is required to use a metric rather than making visual inspection. For that purpose, the Frequency Response Assurance Criterion (FRAC) [22] is used. The FRAC values calculated for FRFs calculated by using Eqs. (46.17) and (46.24) are 0.99708 and 0.99791, respectively. So, it can be said again that, at least for the example case given here, both equations can successfully be used for decoupling, and Eq. (46.24) gives slightly better results compared to Eq. (46.17).
RkJQdWJsaXNoZXIy MTMzNzEzMQ==