## 2 Dynamic Tests of the Real Structure  
In situ dynamic tests were performed to investigate the structural vibration characteristics of the aqueduct under the natural wind excitation. Velocity transducers were installed on the top surface of the bottom slabs of the U-shaped flumes at locations of 1/4, 1/2 and 3/4 spans for span 6, 8, 10 and 14 (see Figure 2). A three-directional transducer layout, as shown in Figure 3, was adopted at the 1/2 span along the lateral, longitudinal and vertical directions, whereas only lateral and longitudinal transducers were placed at 1/4 and 3/4 spans. The 4 spans were tested individually. A sampling frequency of 20 Hz, which corresponds to a sampling interval of 50 ms, was set, and the total sampling time was fixed as 10 min. In the final data processing, an FFT point of 4096, Hanning window and 1/2 data-segment overlap were chosen, which gave rise to a 0.005 Hz resolution in the frequency domain spectra. Under the aforementioned testing setups and analysis parameters, the velocity spectra in the frequency domain for all transducers in three directions of the 4 spans are shown in Figures 4-7. To better show the consistency of test results, two typical spectra obtained from 3 lateral sensors (@ 1/4, 1/2 and 3/4 span) on span #8 and #10 are also provided (see Figures 8 and 9). On the velocity spectrum of each span, the peak amplitude frequencies obtained from the data collected by more than 2 transducers in the same direction (lateral or longitudinal) but at different locations well coincide with one another.  
Figure 3: Transducer layout inside U-shaped flumes.  
Figure 2: Full-scale 3D FE model of the aqueduct.  
Figure 4: Velocity spectrum in frequency domain of span #6.  
Figure 5: Velocity spectrum in frequency domain of span #8.  
Figure 6: Velocity spectrum in frequency domain of span #10.  
Figure 8: Velocity spectrum of 3 lateral transducers for span #8.  
Figure 7: Velocity spectrum in frequency domain of span #14.  
Figure 9: Velocity spectrum of 3 lateral transducers for span #10.  
It is obvious that the lateral vibration of the aqueduct is dominant among three directions, with its velocity amplitudes being higher than those along the longitudinal and vertical directions. Span 6 and span 8 essentially demonstrate the same lateral vibration feature in which the frequencies of the first, second and third lateral modes stand at 0.97\(-\)0.975 Hz, 1.02 Hz and 1.06 Hz, respectively, and the first mode has much higher velocity amplitude than the other two. Span 10 has the same lateral mode frequencies with span 6 and span 8, but contrary to the two former spans, the velocity amplitude of the first mode is lower than those of the second and third modes. Span 14 does not show the first lateral mode at 0.97 Hz on the velocity spectrum, but two other peak amplitudes appear at 1.04 Hz and 1.10 Hz, which are quite close to the second and third lateral modes of the other three spans. Although the four sets of results cannot be compared with one another directly since dynamic tests were conducted individually for each span, a general trend can still be observed that the lateral velocity amplitudes of span 6 and span 8 are much higher than those corresponding values of span 10 and span 14.  
The longitudinal vibration of the aqueduct basically exhibits two main modes on the four velocity spectra. The frequencies of the first longitudinal modes locate consistently at 1.495\(-\)1.50 Hz, while the second longitudinal modes fluctuate within a very small range of 1.885\(-\)1.935 Hz. Unlike the lateral and longitudinal vibrations, the vertical vibration of the aqueduct only manifests a single peak frequency around 5.285\(-\)5.395 Hz on the velocity spectra of all four spans, with the velocity amplitudes maintaining at almost the same magnitude.  
From those field test findings, the dynamic characteristics of the whole aqueduct can be summarized in Table 1.