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Dynamic Identification of A Cable-Stayed Bridge Induced by Random Traffic Flow Cover

Dynamic Identification of A Cable-Stayed Bridge Induced by Random Traffic Flow

Architecture, Civil Engineering, Environment
Volume 18 (2025): Issue 3 (September 2025)
By: Monika NAPIERAJ and  Piotr GÓRSKI  
Open Access
|Sep 2025

Figures & Tables

Figure 1.

The Rheinbrücke Maxau bridge
The Rheinbrücke Maxau bridge

Figure 2.

Basic dimensions of the Rheinbrücke Maxau bridge
Basic dimensions of the Rheinbrücke Maxau bridge

Figure 3.

Schematic cross-section of the bridge deck slab [18]
Schematic cross-section of the bridge deck slab [18]

Figure 4.

Location of the measurement points on the bridge girders during the tests
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
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
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
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
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
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"
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"

Figure 11.

Normalized mode shapes, their theoretical approximation, and corresponding modal frequencies identified by the FDD technique
Normalized mode shapes, their theoretical approximation, and corresponding modal frequencies identified by the FDD technique

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)
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)

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 fmax-fminfFDD[%]{{{{\rm{f}}_{\max }}{\rm{ - }}{{\rm{f}}_{\min }}} \over {{{\rm{f}}_{{\rm{FDD}}}}}}[\% ]Variability factor σfFDD[%]{\sigma \over {{{\rm{f}}_{{\rm{FDD}}}}}}[\% ]
10.5110.507-0.5170.5070.0042.110.8048
21.0381.032-1.0471.0350.0131.461.2733
31.3911.376-1.4041.3890.0171.981.2172
41.4801.471-1.4891.4890.0461.243.0779
52.0462.023-2.0692.0230.0222.241.0929

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 ξ¯[%]\bar \xi [\% ]Range of damping ratio ξmin- ξmax [%]Standard deviation ΣMax. relative variation ξmax−ξminξ[%]{{{\xi _{\max }} - {\xi _{\min }}} \over \xi }[\% ]Variability factor σξ[%]{\sigma \over \xi }[\% ]
10.5142.351.84-2.690.3236.1713.62
21.0321.621.44-1.940.1730.7810.49
31.3771.421.29-1.550.1018.357.04
41.4943.612.90-4.130.4234.1211.63
52.0461.681.25-1.980.3243.4519.13

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 fFDD−fPPfPP·100[%]{{{{\rm{f}}_{{\rm{FDD}}}} - {{\rm{f}}_{{\rm{PP}}}}} \over {{{\rm{f}}_{{\rm{PP}}}}}}\cdot100[\% ]Relative variation fRDM−fPPfPP·100[%]{{{{\rm{f}}_{{\rm{RDM}}}} - {{\rm{f}}_{{\rm{PP}}}}} \over {{{\rm{f}}_{{\rm{PP}}}}}}\cdot100[\% ]
10.5130.5110.514-0.390.19
21.0331.0381.0320.48-0.10
31.3891.3911.3770.14-0.86
41.4891.4801.494-0.600.34
52.0462.0462.0460.000.00
DOI: https://doi.org/10.2478/acee-2025-0040 | Journal eISSN: 2720-6947 | Journal ISSN: 1899-0142
Journal RSS Feed
Language: English
Page range: 191 - 203
Submitted on: May 11, 2025
|
Accepted on: Aug 24, 2025
|
Published on: Sep 30, 2025
Published by: Silesian University of Technology
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year
Keywords:
Cable-stayed bridge,
In-situ measurement,
Dynamic characteristics,
Random traffic flow,
Modal analysis techniques
Related subjects:
Architecture and design,
Architecture,
Architects, buildings

© 2025 Monika NAPIERAJ, Piotr GÓRSKI, published by Silesian University of Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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