Narrow Results

The variation of the instantaneous frequencies of bridges under moving vehicles is a problem not well studied in the literature. A theoretical framework is presented for the problem, considering the variation in frequencies for both the bridge and moving vehicle. First, the equations of motion are written for the two sub-systems. By solving the eigenvalue problem, analytical solutions in closed-form are derived from the frequencies of the vehicle and bridge that are coupled with each other. Based on this, the variation pattern, range, and dominating factors involved are studied, along with the special cases of moving mass and moving load. The results reveal that, if a moving vehicle is to be used as a tool for measuring the bridge frequencies or for detecting the bridge damages, the frequency variation caused by moving vehicles should be taken into account. Such an effect will be crucial when the vehicle mass is not negligible compared with the bridge mass or when the resonance condition is approached.

The response of the contact point of the vehicle with the bridge, rather than the vehicle itself, is proposed for modal identification of bridges by a moving test vehicle. To begin, approximate closed-form solutions were derived for the vehicle and contact-point responses, and they were verified by finite element solutions. The contact-point acceleration is born to be free of the vehicle frequency, an annoying effect that may overshadow the bridge frequencies in case of rough surface. From the frequency response function (FRF) of the vehicle with respect to the contact point, it was shown that the contact-point response generally outperforms the vehicle response in extracting the bridge frequencies because it could identify more frequencies. In the numerical simulations, the contact-point response was compared with the vehicle response for various scenarios. It is concluded that in each case, say, for varying vehicle speeds or frequencies, for smooth or rough road surfaces, with or without existing traffic, the contact-point response outperforms the vehicle response in extracting either the frequencies or mode shapes of the bridge.

The instantaneous amplitude squared (IAS) of the driving component of the contact-point response of a moving test vehicle was proposed for the damage detection of the sustaining bridge. As a supplement to the properties previously presented for the IAS, this paper is aimed at unveiling the key feature of the discontinuity amplification inherent in the IAS through the double guarantee of a “square operation” in the definition and a “second derivative” in computing the contact-point response. The capability of the IAS was demonstrated with regard to the effects of the environmental noise, vehicle damping and bridge damping in the numerical simulation. It is confirmed that the IAS can be reliably used in the damage detection of bridges by a moving test vehicle.

Mode shapes estimated from the vehicle responses are normally used to detect bridge damage efficiently for their high spatial resolution. However, an updated baseline finite element model (FEM) is normally required to quantify damages for such an approach. A two-stage damage detection procedure is presented for bridges by utilizing the mode shape estimated from a moving vehicle. Damage locations are first determined through a damage localization index (DLI) defined by regional mode shape curvature (RMSC). Then the relationship between the damage extents and the RMSC changes is investigated by FEM simulation. Finally, an equation set to quantify the single and multiple damages is deduced by combining the RMSCs and the relationship between the damage extents and the RMSC changes established by an un-updated FEM. Numerical and experimental examples are carried out to verify the validity and efficiency of the two-stage method. The results revealed that it can localize and quantify damages with satisfactory precision by using the response measured from one sensor only.

An effective procedure is proposed for extracting bridge frequencies including the higher modes using the vehicle collected data. This is enabled by the use of the contact-point response, rather than the vehicle response, for processing by the extreme-point symmetric mode decomposition (ESMD). The intrinsic mode functions (IMFs) so decomposed are then processed by the FFT to yield the bridge frequencies. A systematic study is conducted to compare the proposed procedure with existing ones, while assessing the effects of various parameters involved. The proposed procedure was verified in the field for a two-span bridge located at the Chongqing University campus. It was confirmed to perform better than the existing ones in extracting bridge frequencies inclusive of the higher modes. The following are the reasons: (1) the ESMD is more efficient than the EMD in that remarkably less IMFs are generated; (2) the modal aliasing problem is largely alleviated, which helps enhancing the visibility of bridge frequencies in general; and (3) the contact-point response adopted is free of the vehicle frequency, which makes the higher frequencies more outstanding and detectable.

The indirect method for bridge modal identification based on the response of moving vehicles has attracted widespread attention in recent years. However, most existing studies only focus on the simply supported bridge, while continuous girder bridges are widely used in practical engineering. Therefore, this study proposes an indirect frequency identification method for continuous girder bridges. First, the mode shape formula of the equal-span continuous beam is deduced using the three-moment equations, and the analytical solution of the vehicle vibration response is deduced via the vehicle–bridge coupled vibration theory. Second, the derived analytical solution is verified through numerical analysis results and field test results. Finally, the effects of bridge and vehicle parameters on the frequency identification accuracy are analyzed. The results show that a reasonable frequency of the trailer should be selected to avoid the resonance between the vehicle and the bridge for better performance. The research findings can provide a reference for the indirect identification of continuous girder bridges based on the response of moving vehicles.

The critical signal component extracted from the bridge response caused by a moving vehicle is normally used to construct damage index for damage detection. The dynamic response of bridges subjected to moving vehicle includes several components, among which the quasi-static component reflects the inherent characteristics of the bridge. In view of this, this paper presents a bridge damage detection method based on quasi-static component of the moving vehicle-induced dynamic response. First, damage-induced changes of the natural-frequency component, moving-frequency component and quasi-static component responses are investigated via a simply-supported beam bridge. The quasi-static component response is proved to be less sensitive to the moving velocity of the load and more suitable for damage detection. Subsequently, a quasi-static component response extraction method is proposed based on analytical mode decomposition (AMD) and moving average filter (MAF). The extracted quasi-static component response is further employed to localize and quantify damages. Finally, numerical simulations are conducted to examine the feasibility, accuracy and advantages of the proposed damage detection method. The results indicated that the proposed method performs well in different damage scenarios and is insensitive to the moving velocity of the load and road roughness.