## 4 Buffeting Response Analysis
### Buffeting-Induced Resonances of Stay Cables  
The internal resonance of stay cables arises from frequency-matching characteristics between the cables and primary structural components. To simulate the geometric nonlinearity of the cables under wind loads, each stay cable was discretized into 10 segmented link10 elements [27], resulting in the dynamic behavior illustrated in Figure 13.  
The upper end of the cable is connected to the pylon, while the lower end is anchored to the deck. Here, \(U_{i}(t)\) denotes the mean wind velocity acting on the cable nodes, and \(u(t)\) represents the turbulent wind component. Due to the broadband frequency characteristics of wind-induced buffeting, which distributes energy across a wide spectrum, the cables experience multi-directional vibrations \(x\), \(y\), and \(z\) at their upper, midpoint, and lower nodes when exposed to turbulent flow fields. This significantly elevates the risk of exciting resonant vibrations [28]. Based on the dynamic analysis results, the vertical and lateral displacement responses at the midpoints of all the windward-side stay cables in the left span were extracted. Figure 14 compares the RMS values of these responses between the two schemes. Distinct peaks were observed at J1, J4, and J13 in the steel cable scheme, whereas the CFRP cable scheme exhibited more uniform and smoother response distributions. Figure 14: RMS values of vertical and lateral displacements at center of the stay cables for the two schemes. Figure 13: Diagram of overall wind-induced deformation in stay cables. As shown in Figure 15, the three-dimensional motion trajectories of the stay cable midpoints were plotted using the lateral response (\(x\)-axis), longitudinal response (\(y\)-axis), and vertical response (z-axis). By observing their projections on the x-y, y-z, and x-z planes, the following can be noted: For steel cables J01, J03, and J13, the lateral motion trajectories exhibited a more scattered distribution than the vertical component, with isolated points at the edges of the projected point clouds. This indicates the occurrence of abnormal lateral oscillations in the steel cables. In contrast, the CFRP cable midpoint trajectories displayed more concentrated circular distribution patterns across all three projection planes, reflecting smaller vibration amplitudes. These observations will be further discussed through spectral analysis. A spectral analysis was performed on the vertical and lateral displacement responses at the upper, lower, and midpoint nodes of the stay cables for both the schemes. Vertical excitation at the upper pylon connection was excluded due to negligible displacement magnitudes. The results in Figures 16 and 17 show that, while the steel cable scheme exhibited no significant amplitude amplification from frequency coupling in the vertical component, minor amplitude peaks occurred near the dominant frequencies of the main girder (0.12-0.25 Hz) due to the proximity of the cables' fundamental frequencies to the girder frequencies. In the lateral component, steel cables J04 and J13 showed resonant peaks at 0.15 Hz and 0.18 Hz. These peaks originate from weak excitation components at the upper end, despite the absence of corresponding frequency content at the lower deck connection. The lower fundamental frequency of the steel cables leads to denser higher  
Figure 15: Motion trajectories at the center of stay cables induced by buffeting: (**a**) No. J01 steel cable; (**b**) No. J04 steel cable; (**c**) No. J13 steel cable; (**d**) No. J01 CFRP cable; (**e**) No. J04 CFRP cable; (**f**) No. J13 CFRP cable. mode frequency distributions, causing frequent mode shape transitions under turbulent excitation and resulting in multiple closely spaced spectral peaks. For the CFRP cables, the resonance peaks in the vertical response spectrum aligned with the main girder's fundamental frequency range (0.15-0.2 Hz). However, these peaks  
Figure 16: Vertical response spectra of the stay cables for the two schemes: (**a**) No. J01 steel cable; (**b**) No.