140 O. Avci Fig. 18.1 Laboratory structure, 2.2 m 9.2m Table 18.1 First bending mode natural frequencies and damping ratios for the footbridge [15] First bending mode frequency, fn (Hz) Modal damping ratio ( ) Stage Individual FRF Curve fitting of vibration data (MEScope) FEmodel (SAP2000) Half-power method (Individual FRF) Curve fitting of vibration data (MEScope) Time domain decay curves (filtered to capture first mode only) 1 8.00 8.08 7.99 0.00284 0.00451 0.01300 2 6.95 6.95 7.03 0.00453 0.00448 0.02200 Fig. 18.2 Mode shapes with commercial FE software of the first mode is higher than the Stage 2 natural frequency which means the bottom chord extensions provided stiffness to the structure. From Table 18.1, it can be observed that the curve fitted MEScope and FE model (SAP2000) frequency predictions are in very good agreement (within 2%). Moreover, according to Table 18.1, the frequency domain methods for the prediction of modal damping ratio (half-power method and MEScope curve fits) do not agree [22]. The time domain method (simple decay curves) results in a higher damping ratio than the frequency domain method predictions. As a result of the inconsistency in the modal damping ratio values of Table 18.1, it is not clear what to use for the damping values in the FE models. In order to overcome the modal damping ratio inconsistency, sinusoidal excitations are applied to the structure to put the system in resonance. By doing so, the effective mass procedure can be followed for the structure in resonance to find the modal damping ratios. FE model mode shapes are shown in Fig. 18.2. 18.3 Resonance of the Structure 18.3.1 Stage 1 Configuration For Stage 1, the structure was put in resonance by a shaker placed at the midspan, at three levels of excitation amplitudes. The results are shown in Table 18.2.
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