96 P. Singh and A. Sadhu 0.018 0.016 0.014 0.012 0.01 0.008 0.006 0.004 0.002 0 0 1 2 3 4 5 6 f (Hz) X (f ) 7 8 9 10 Fig. 10.3 FFT of vehicle acceleration response at a speed of 40 km/h 0.05 0.15 0.15 0.2 0.1 0.1 8 ×10−3 ×10−3 7 6 5 4 3 2 1 0 6 4 2 0 0.05 0.05 0 0 0.04 0.03 0.02 0.01 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 0 0 5 10 15 0 5 10 15 0 5 10 15 0 5 10 15 0 5 10 15 0 5 10 15 X (f ) X (f ) X (f ) X (f ) X (f ) X (f ) f (Hz) f (Hz) f (Hz) f (Hz) f (Hz) f (Hz) Fig. 10.4 WPT coefficients of vehicle acceleration response at a speed of 40 km/h experiment. The bridge is subjected to forced vibrations using a shaker table from underneath, shown in Fig. 10.8. Forced vibrations are used to mimic the ambient vibrations of a bridge that may be caused due to wind excitations. Figure 10.9 shows the FFT results for the bridge and vehicle acceleration response. Two bridge frequencies directly measured from the bridge deck, which can be seen in Fig. 10.9a, are mentioned in the first column (fdirect) of Table 10.2. Using the analytical formula to calculate the bridge frequency pair, the frequency pair values are calculated and are shown in the second column (fanalytical pair) of Table 10.2. The measured values of the frequency pair are shown in Fig. 10.9b and are tabulated in the third column (fmeasured pair) of Table 10.2. By averaging the frequency pair values from column 3 of Table 10.2, the bridge frequencies are calculated for the indirect method and are shown in column 4 (findirect) of Table 10.2. It can be seen that the values from column 1 and column 4 of Table 10.2 are close to each other and indirect monitoring can be used as a reliable way of measuring the natural frequencies of a bridge. Figure 10.10 shows the WPT coefficients for the vehicle acceleration response from Fig. 10.9b. It shows that the various frequency components from Fig. 10.9b can be well separated by the WPT algorithm and can be classified using a TF method. Further studies are undergoing to differentiate between these frequencies separated by the WPT algorithm.
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