Figure 1.
The Rheinbrücke Maxau bridge
Figure 2.
Basic dimensions of the Rheinbrücke Maxau bridge
Figure 3.
Schematic cross-section of the bridge deck slab [18]
Figure 4.
Location of the measurement points on the bridge girders during the tests
Figure 5.
Variability of the 10-min averaged values of the first three natural frequencies of the bridge-vehicle system recorded at the reference point
Figure 6.
Variability of the 10-min averaged values of the first three natural frequencies of the bridge-vehicle system recorded at the reference point
Figure 7.
10 min-averaged PSDs of daily traffic-induced vertical accelerations of the bridge
Figure 8.
10-min averaged RMS levels and kurtosis values of bridge accelerations recorded at the reference point
Figure 9.
Vertical acceleration time history and their 10-min averaged PSD at the reference point
Figure 10.
Charts of singular values of decomposed PSD matrices of traffic-induced bridge vibrations recorded at the reference point and points No. 3', 4', and 3"
Table 1.
Statistical data on modal frequencies of the bridge-vehicle system determined by the FDD method
| Mode No. | Mean modal frequency fFDD [Hz] | Range of modal frequencies fmin - f max [Hz] | Dominant [Hz] | Standard deviation σ [Hz] | Max. relative variation | Variability factor |
|---|---|---|---|---|---|---|
| 1 | 0.511 | 0.507-0.517 | 0.507 | 0.004 | 2.11 | 0.8048 |
| 2 | 1.038 | 1.032-1.047 | 1.035 | 0.013 | 1.46 | 1.2733 |
| 3 | 1.391 | 1.376-1.404 | 1.389 | 0.017 | 1.98 | 1.2172 |
| 4 | 1.480 | 1.471-1.489 | 1.489 | 0.046 | 1.24 | 3.0779 |
| 5 | 2.046 | 2.023-2.069 | 2.023 | 0.022 | 2.24 | 1.0929 |
Figure 11.
Normalized mode shapes, their theoretical approximation, and corresponding modal frequencies identified by the FDD technique
Table 2.
Natural frequencies of the bridge-vehicles system determined by the RDM method and statistical data of the modal damping ratios
| Mode No. | Mean modal frequency fRDM [Hz] | Mean damping ratio | Range of damping ratio ξmin- ξmax [%] | Standard deviation Σ | Max. relative variation | Variability factor |
|---|---|---|---|---|---|---|
| 1 | 0.514 | 2.35 | 1.84-2.69 | 0.32 | 36.17 | 13.62 |
| 2 | 1.032 | 1.62 | 1.44-1.94 | 0.17 | 30.78 | 10.49 |
| 3 | 1.377 | 1.42 | 1.29-1.55 | 0.10 | 18.35 | 7.04 |
| 4 | 1.494 | 3.61 | 2.90-4.13 | 0.42 | 34.12 | 11.63 |
| 5 | 2.046 | 1.68 | 1.25-1.98 | 0.32 | 43.45 | 19.13 |
Figure 12.
Normalized RD signatures of vertical bridge accelerations collected during a 60-min measurement cycle (first row) and linear regression on the extremes of these signatures (second row)
Table 3.
Comparison of the average natural (fFDD, fRDM) and forced (fPP) vibration frequency values of the bridge-vehicle system determined using different techniques
| Mode No. | Mean vibration frequency fPP [Hz] | Mean modal frequency fFDD [Hz] | Mean modal frequency fRDM [Hz] | Relative variation | Relative variation |
|---|---|---|---|---|---|
| 1 | 0.513 | 0.511 | 0.514 | -0.39 | 0.19 |
| 2 | 1.033 | 1.038 | 1.032 | 0.48 | -0.10 |
| 3 | 1.389 | 1.391 | 1.377 | 0.14 | -0.86 |
| 4 | 1.489 | 1.480 | 1.494 | -0.60 | 0.34 |
| 5 | 2.046 | 2.046 | 2.046 | 0.00 | 0.00 |