90 E. Cheynet et al. (HS1) 0.135 0.14 0.13 0.3 0.295 0.29 0.42 0.41 0.4 1.26 1.24 1.22 f (Hz) f (Hz) f (Hz) f (Hz) f (Hz) (HA1) 0.46 0.45 0.44 0.43 (HS2) 0.59 0.58 0.57 (HA2) 0.64 0.63 0.62 0.23 0.223 0.215 0.6 0.59 0.58 2.21 2.18 2.16 (VS1) (VA1) (VS2) (VA2) (TS1) 5 10 15 20 (TA1) T(°C) 5 10 15 20 T(°C) Fig. 12.2 Evolution of the first four lateral and vertical and the first two torsional eigen-frequencies with the temperature. The data set comprises 6 months of acceleration and temperature records (July–December 2015) Temperature fluctuations seem to have a larger influence on the variation of the eigen-frequencies than the traffic loading. The attenuation of the daily periodicity of the eigen-frequency in November and December (Fig. 12.4) cannot simply be explained by a reduction of heavy traffic for example. The periodicity pattern appears to be almost entirely modulated by temperature changes. For example, we observed that the sinusoidal pattern was elongated at the bottom part in July (longer day) but elongated at the top part in October (shorter day), without strong variations in the amplitude of the fluctuations. 12.3.2 Influence of Temperature Variations on the Modal Damping Ratios The estimation of the modal damping ratios is one of the most crucial step in studying accurately the buffeting response of a suspension bridge. Unfortunately, such studies are a rarity in full scale. In general, the aerodynamic damping ratios are obtained with a large dispersion in full-scale [2, 13]. This requires a statistically significant amount of data, which is rarely presented in the literature. In this subsection, the total damping is considered for various wind conditions, using a considerable amount of data. The evolution of the modal damping ratios with the mean wind velocity has been described in e.g. Cheynet et al. [4] and is therefore not recalled here. Temperature effects on the modal damping ratios remain mostly unexplored and are therefore briefly investigated in the following. The variation of the modal damping ratios with temperature is displayed in Fig. 12.5, for the first four lateral and vertical modes as well as the first two torsional modes.
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