5 Experimental Investigation of the Dynamic Characteristics of a Glass-FRP Suspension Footbridge 41 0 1 2 3 4 5 100 10−2 10−4 10−6 Frequency (Hz) ANPSD 1.08 1.55 2.19 2.47 2.58 3.20 4.19 Fig. 5.6 ANPSD for lateral acceleration records 0 1 2 3 4 5 50 100 150 200 Frequency (Hz) Model order Fig. 5.7 The stabilization diagram of one of the setups The vertical and lateral accelerations from all the sensors were used for modal parameter identification, with the model order parameter set to 200. The two channels corresponding to the reference stations (No. 55) were chosen as the reference channels. The stabilisation criteria were set to 1% for frequency, 5% for damping, 1% for modal assurance criterion and 0.8 for the low bound of the modal phase collinearity. Shown in Fig. 5.7 is a stabilisation diagram from one of the data set-ups, with the power spectral density of all the signals superimposed. Only the frequency content, up to 5 Hz, is presented in the figure, since this is the most relevant frequency range for pedestrian structures. Stable poles are presented by big red circles. It can be seen that the stable poles for natural frequencies are clearly identified, except for the one around 2.70 Hz. There are in total nine dominant modes identified, including three lateral bending, five vertical bending and one torsional mode. These nine mode shapes are illustrated in Figs. 5.8, 5.9, 5.10, 5.11, 5.12, 5.13, 5.14, 5.15 and 5.16. It can be observed that a majority of the modes found by the peak-picking method are identified by the SSI method. The only discrepancy is that two modes appear from peak-picking in the frequency range of 2.40–2.70 Hz, whereas Fig. 5.7 for SSI shows that there is only one consistent stable pole around 2.70 Hz. Moreover, the mode shapes of the identified lateral bending modes in Figs. 5.9, 5.11 and 5.16 are not very smooth. These findings might be due to the fact that the vertical acceleration signals are stronger than those in the lateral direction, and consequently the noise in vertical accelerations might be spoiling or hiding some lateral bending dominated modes [13]. The identified modes are summarised in Table 5.1. There is a relatively high mode density in the frequency range 0–5 Hz. From the first harmonic dynamic force generated from pedestrian walking the two vertical bending modes at the natural frequencies of 1.51 and 2.21 Hz and a lateral mode at 1.08 Hz are potentially excitable. The damping ratios of all vertical bending modes in Table 5.1 are not <0.96%, whilst the damping ratios of all lateral bending modes are >1%, except for
RkJQdWJsaXNoZXIy MTMzNzEzMQ==