## 7 Signal Processing:
### Two-Degree-of-Freedom Acceleration Response  
The 2 DOF acceleration response was obtained using the same sensor setup as the SDOF tests, allowing the bridge section to oscillate in both vertical and torsional DOF. Two setups were prepared for 2 DOF experiments, and two testing arrangements were considered to record the coupled motion. The first arrangement was with initial displacement in the vertical DOF (called \"vertical-dominant coupled motion\"), and the second was with initial displacement in the torsional DOF (called \"torsional-dominant coupled motion\"). The acceleration responses for the 2 DOF tests for both vertical- and torsional-dominant motions are shown in Figure 15. The response dampened faster at 10 m/s wind speed than at 0 m/s due to added aerodynamic damping from the wind flow on the section.  
The FFTs of the vertical- and torsional-dominant motions are plotted in Figure 16 in which red circle shows the peak value. The vertical-dominant motion has more noise contributions compared with the torsional-dominant motion. At 10 m/s, the high-frequency noise overshadowed the vertical-dominant frequency.  
Figure 14: Time history: (**a**) vertical at \(U\) = 0 m/s; (**b**) vertical at \(U\) = 10 m/s; (**c**) torsional at \(U\) = 0 m/s; (**d**) torsional at \(U\) = 10 m/s.  
Figure 13: Filtered response of SDOF pitch response: (**a**) filtered acceleration time history at \(U\) = 0 m/s; (**b**) filtered acceleration time history at \(U\) = 10 m/s.  
Similarly, vertical- and torsional-dominant responses from Setup 2 are shown in Figure 17. The corresponding frequency spectrum is shown in Figure 18 in which red circle shows the peak value.  
Figure 16: FFTs of the dominant coupled responses from Setup 1: (**a**) vertical response at \(U=0\) m/s; (**b**) vertical response at \(U=10\) m/s; (**c**) torsional response at \(U=0\) m/s; (**d**) torsional response at \(U=10\) m/s.  
Figure 15: Dominant coupled response from Setup 1: (**a**) vertical at \(U=0\) m/s; (**b**) vertical at \(U=10\) m/s; (**c**) torsional at \(U=0\) m/s.  
The vertical-dominant response from Setup 1 was more affected by noise than Setup 2, indicating that the vertical bearings were a major source of noise. The torsional-dominant responses from both setups were less affected by noise. The vertical- and torsional-dominant responses from Setup 1 decayed regularly, while those from Setup 2 decayed irregularly, possibly due to the presence of unrestricted rocking motion. The frequency spectrum analysis of Setup 2 responses showed three dominant modes at 0 m/s wind speed, with the frequency of 3.202 Hz representing the vertical mode, 5.04 Hz the torsional mode, and 4.41 Hz the unrestricted motion, which was more prominent in the vertical dominant response. The FFT of the torsional-dominant response from Setup 1 showed no contribution  
Figure 17: Dominant coupled responses from Setup 2: (**a**) vertical response at \(U=0\) m/s; (**b**) vertical response at \(U=10\) m/s; (**c**) torsional response at \(U=0\) m/s; (**d**) torsional response at \(U=10\) m/s.  
Figure 18: FFTs of dominant coupled responses from Setup 2: (**a**) vertical response at \(U=0\) m/s; (**b**) vertical response at \(U=10\) m/s; (**c**) torsional response at \(U=0\) m/s; (**d**) torsional response at \(U=10\) m/s.  
from the vertical mode, while the FFT of the torsional dominant response from Setup 2 showed a small peak representing the vertical frequency.