Damped test vehicle for scanning bridge frequencies: Theory, simulation and experiment

Highlights

• A realistic theory for damped vehicle moving over simple bridge.

• Derive a new procedure for calculating the contact point (CP) response.

• Being free of vehicle frequency, CP response is good for obtaining higher bridge frequencies.

• CP response is less affected by vehicle damping compared with the vehicle response.

• Ongoing traffic is positive to deal with the negative effect of road roughness.

Abstract

By the vehicle scanning method, an instrumented test vehicle is used to scan the frequencies of vibration of the underlying bridge. In this paper, a realistic theory is proposed considering the damping effect of the test vehicle, which was not well studied previously. Bridge damping is ignored since the bridge vibration sensed by the moving vehicle is transient in nature. The vehicle response was criticized for the presence of vehicle frequency, which renders "scanning" less effective. In contrast, the response of the vehicle's contact point (CP) with the bridge is free of the vehicle frequency and enables us to extract more bridge frequencies. For the model adopted, closed-form solutions are firstly derived for both the vehicle and CP responses, with their transmissibility discussed. Through the numerical simulations and field test, the following are concluded: (1) The improved procedure for the CP response is reliable for scanning the first few bridge frequencies; (2) the effect of vehicle damping on the CP response can be ignored; (3) the performance of the CP response is always better than the vehicle response for each scenario studied; and (4) ongoing traffic is a positive effect that can outbalance the negative effect of surface roughness.

Introduction

As a critical component of infrastructure for transportation, bridges play an important role in maintaining the normal function of the lifeline system. However, due to aging, overloading in traffic, and natural disasters, such as earthquakes, typhoons, and flooding, etc., the health condition of a bridge may decline in various forms in its service life, e.g., the deterioration in materials, cracking in cross sections, loosening or breaking connection, support settlements, scouring in column foundations, etc. In order to access the health condition of a bridge, vibration-based monitoring methods have been widely adopted to diagnose the variation in modal properties, particularly the frequencies of vibration, of the bridge.

For a long time, the modal properties of a bridge have been identified by the direct method, i.e., through the direct deployment of vibration sensors and data loggers on the bridge of concern. Along these lines, a huge amount of researches has been carried out, for which various sources have been used to excite the bridge, such as ambient vibration [1], truck impact loads [2], [3], [4], traffic flows [5], [6], etc. From time to time, reviews of the works conducted up-to-date along the lines of vibration-based damage identification methods have been published [7], [8], [9], [10]. The direct method allows the bridge vibration to be continuously monitored, but it also results in a tremendously large amount of data, the so-called sealike data, that cannot be effectively utilized. In addition, the one-system-per-bridge basis is too expensive to be popularly applied, in terms of the installation or maintenance cost. Moreover, the lifespan of the equipment and sensors deployed on a bridge is not going to have a lifespan longer than the bridge to be protected, due to the relative short cycle of electronic devices.

To circumvent the above drawbacks, the indirect method or lately known as the vehicle scanning method (VSM) was proposed by Yang and co-workers in 2004 for detecting the bridge modal properties using an instrumented vehicle [11], [12]. The feasibility of this technique was experimentally verified by field investigations [13], [14], [15] and laboratory test [16]. Since no sensors are required on the bridge, this method has the advantage of mobility, efficiency and economy. Using the instrumented test vehicle, it was demonstrated that in addition to natural frequencies [11], [17], [18], [19], other properties of the bridge can also be detected, such as mode shapes [20], [21], [22], damping ratios [23], [24] and damages [25,26]. Over the years, various processing techniques have been employed to enhance the VSM aimed at modal and damage detection, e.g., the EMD-based method [27,28], wavelet-based algorithm [26,29], mode shape squares (MOSS) method [30], global filtering method (GFM) [31], genetic algorithm-based method [32], wave number-based technique [33], among others. For advances in applications of the VSM to bridges, readers are referred to the review papers in Refs. [34], [35], [36].

In principle, a test vehicle is designed to have higher transmissibility from the bridge, i.e., to receive as much as possible the vibrations transmitted from the bridge, such that the bridge modal properties can be well contained. As such, the test vehicle should be designed to have has as less damping as possible. In reality, however, damping is a factor that cannot be totally ignored. For this reason, the effect of vehicle damping has to be studied, especially on how it affects the VSM in extracting the bridge properties. Previously, it was demonstrated that vehicle damping can affect the vehicle frequency and pavement roughness in the measurement [37], as well as the dynamic response of bridges [38].

As a side note, the design of test vehicles is very different from the design of passenger cars, in that the latter is focused on the riding comfort or lower transmissibility of vibrations from the bridge. This can be achieved via the use of a certain amount of damping for the vehicles [39].

In using the test vehicle to scan the bridge dynamic properties, the vehicle response is often obtained by vibration sensors fixed on the car body or axle of the test vehicle. One problem in this regard is that the presence of vehicle frequency in the vehicle response may render the extraction of bridge frequencies difficult in spectral analysis, especially when coupled by surface roughness [40]. To resolve this problem, the response of the vehicle's contact point (CP) with the bridge was proposed as a better parameter for scanning the bridge properties [41]. Since the CP moves on the bridge along with the test vehicle, it cannot be directly measured, but can be calculated by a backward procedure. One advantage with the CP response is that it is born to be free of the vehicle frequency and thus allows more bridge frequencies to be detected. Recently, it was demonstrated that the CP response can be used to identify bridge frequencies and mode shapes [41], damping ratios [24], and damages [42]. This study can be regarded as a refinement of the above approaches using the CP response in that the effect of vehicle damping is duly taken into account.

The organization of the paper is as follows: In Section 2, a more realistic theory is presented for the vehicle-bridge interaction (VBI) system considering the vehicle damping, by which both the vehicle and CP responses are obtained. In Section 3, an improved backward calculation procedure is presented for the CP response, while the transmissibility between the CP and vehicle responses is discussed. In Section 4, the analytical results obtained in Sections 2 and 3 are verified by comparison with the finite element simulation using the VBI element [12]. In Section 5, a parametric study is conducted for the effects of vehicle damping ratio, vehicle speed, environmental noise, pavement roughness, and ongoing traffic. In Section 6, a field test is conducted to verify the theory presented in this paper. Finally, conclusions are given in Section 7.