12 Temperature Effects on the Modal Properties of a Suspension Bridge 89 Table 12.2 Eigen-frequencies estimated from the measurement data using the SSI-COV algorithm in comparison to the values based on the SBM method and the Abaqus model SSI-COV SBM Abaqus Modes Hz Hz % Hz % HS1 0.136 0.130 4.41 0.128 6.19 HA1 0.444 0.442 0.45 0.431 2.90 HS2 0.577 0.556 3.51 0.533 7.56 HA2 0.626 0.597 4.61 0.583 6.81 HS3 0.742 0.830 11.90 0.833 12.31 HA3 1.011 1.000 1.03 0.974 3.69 VA1 0.223 0.205 8.10 0.214 3.91 VS1 0.294 0.319 8.35 0.302 2.72 VS2 0.408 0.439 7.63 0.407 0.25 VA2 0.587 0.585 0.39 0.583 0.68 VS3 0.853 0.864 1.31 0.856 0.34 VA3 1.163 1.194 2.72 1.191 2.36 TS1 1.237 1.215 1.78 1.238 0.026 TA1 2.184 2.186 0.09 2.122 2.85 the second asymmetric torsional mode shape. To increase the identification speed of the lower modes, the sampling frequency of the lateral and vertical acceleration records were reduced to 2 Hz. The sampling frequency of the torsional acceleration response remained at 20 Hz. This allowed the SSI-COV algorithm to be applied to more than 50;000 acceleration records of 10 min duration in less than half a day. A Finite element (FE) model created by Steigen [15], using the Abaqus software, and improved by Tveiten [17] was used to evaluate a numerical prediction of the mode shapes and eigen-frequencies of the Lysefjord Bridge. The eigenfrequencies and the mode shapes of the Lysefjord Bridge were also approximated by using harmonic series expansions following Sigbjörnsson and Hjorth-Hansen [12] for the lateral motion and Strømmen [16] for the vertical and torsional ones. In the following, the latter method is referred to as the “Simplified Bridge Model” denoted SBM. The eigen-frequencies evaluated using the two different models and the SSI-COV algorithm are listed in Table 12.2. 12.3 Results 12.3.1 Influence of Temperature Variations on the Eigen-Frequencies As stated by Xia et al. [19], a higher temperature leads in general to decreased values of vibration frequencies, mainly due to the temperature dependency of the materials Young’s modulus. Such variations of the eigen-frequencies are visible in Fig. 12.2, except for temperatures over 20ıC where the number of samples was probably too low to provide reliable results. The influence of temperature variations on the first lateral mode HS1 is rather small. The frequency drops from 0.139 to 0.135 Hz when the temperature increases from 0 to 20ıC. For a similar temperature change, the frequency associated with VA1 decreases only from 0.227 to 0.220 Hz. The most dramatic frequency change occurs for the mode TS1 where the frequency decreases from 1.25 to 1.23 Hz. The scatter of the eigen-frequencies observed on Fig. 12.2 is due to the influence of other parameters such as traffic and wind excitation. The daily fluctuations of the eigen-frequencies can be visualized by studying few days of data. This is done in Fig. 12.3, where 10 days of data recorded in October 2015 are displayed. The first lateral eigen-frequency HS1 fluctuates between 0.132 Hz for diurnal data and 0.145 Hz for nocturnal data. These fluctuations are relatively small compared to those from VA1 which ranges from 0.217 Hz during day time to almost 0.230 Hz during the night. For the torsional motion, TS1 fluctuates between 1.25 Hz down to 1.23 Hz. As suggested by Kim et al. [7], heavy traffic is likely to be responsible for a decrease in the estimated eigen-frequencies of the bridge deck. The effects of the temperature and traffic on the bridge eigen-frequencies are therefore expected to superimpose and be responsible for larger frequency variations. At night time, the lower temperature and the reduced traffic leads to higher eigen-frequencies whereas at day time, the increase of the temperature and traffic leads to lower eigenfrequencies. This appears clearly on Fig. 12.3, where a pseudo-period of 24 h is visible. The periodical pattern is clearly visible for the vertical bridge motion, but it is more noisy for the lateral and torsional motions. This can be partly explained by the higher signal to noise ratio measured for the vertical motion.
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