Bridge Vibration Research Articles

Effect of deterioration overtime on the power spectral density of the bridge vibration responses under real traffic

Working in an environment with many influencing factors can lead to the deterioration of construction. For bridges, the harshness and unpredictability of the environment can come from temperature, air humidity, wind, soil, and vehicle loads. Over time, these factors cause the quality of the bridge to degrade. Because there are too many factors acting simultaneously with varying degrees of influence, this paper only focuses on the parameter that represents the degradation over time, regardless of which factor the degradation is due to. The proposed parameter has a one-way variation with time, and its change is a sensitive indicator to operation process of the bridge. This parameter is calculated using measurement data of the bridge’s vibration over time and in response to actual traffic loads. This demonstrates the viability of this idea in the experiment.

The footbridge Jesípek – application of radar interferometry for dynamic response evaluation

Recent advances in radar systems have led to the development of radar interferometry (RI) methods for contactless vibration monitoring of large-scale structures, i.e. bridges, water tower reservoirs, and factory chimneys. Interferometric radars are devices capable to measure with 200 Hz sampling frequency and relative movement precision of 0.1 mm up to 0.01 mm. The major part of this paper describes an in-situ footbridge experiment near Hradec Králové. Radar interferometry devices were deployed along with ordinary techniques compounded by accelerometers, wiring, and acquisition station. Experiment was focused on the evaluation of basic dynamic structural properties such as natural frequencies and mode shapes. A lot of attention was also given to the result comparison of these measurement methods. Test results have confirmed the applicability of RI for bridge vibration monitoring.

Research on coupled vibrations between the low-to-medium speed maglev train and a long-span continuous beam bridge

This study investigates the strong coupling vibration between low-to-medium speed maglev trains and the track beam, which results from unique transmission principle of the trains. The research focuses on the impact of train parameters on the dynamic response of the car-bridge system, using a long-span continuous beam bridge as the background. Initially, a multi-body dynamics model of maglev trains was established based on the theory of maglev force equivalence as stiffness and damping. Subsequently, the solid element available in ANSYS was employed to construct a finite element model of the large-span bridge. In SIMPACK, the train-bridge coupled system was established to evaluate the dynamic response of the coupling system under various working conditions. The results indicate that the equivalent models of maglev train demonstrates excellent control performance. The vehicle parameters of weight and speed do not significantly affect the bridge vibration characteristics. However, the lateral dynamic behavior of the bridge increases significantly when the train velocity reaches 160 km/h. The operation of double-line trains in opposing directions can result in more complex bridge vibrations, with a greater dynamic response observed. Therefore, the analysis of the coupled vibration of the car-bridge system under complex operating conditions is required in the design phase. Analyzing the coupled vibration of train-bridge systems during the design phase is crucial for ensuring the safe and efficient of maglev trains.

H∞ Optimization of Three-Element-Type Dynamic Vibration Absorber with Inerter and Negative Stiffness Based on the Particle Swarm Algorithm.

Dynamic vibration absorbers (DVAs) are extensively used in the prevention of building and bridge vibrations, as well as in vehicle suspension and other fields, due to their excellent damping performance. The reliable optimization of DVA parameters is key to improve their performance. In this paper, an H∞ optimization problem of a novel three-element-type DVA model including an inerter device and a grounded negative stiffness spring is studied by combining a traditional theory and an intelligent algorithm. Firstly, to ensure the system's stability, the specific analytical expressions of the optimal tuning frequency ratio, stiffness ratio, and approximate damping ratio with regard to the mass ratio and inerter-mass ratio are determined through fixed-point theory, which provides an iterative range for algorithm optimization. Secondly, the particle swarm optimization (PSO) algorithm is used to further optimize the four parameters of DVA simultaneously. The effects of the traditional fixed-point theory and the intelligent PSO algorithm are comprehensively compared and analyzed. The results verify that the effect of the coupling of the traditional theory and the intelligent algorithm is better than that of fixed-point theory alone and can make the two resonance peaks on the amplitude-frequency response curves almost equal, which is difficult to achieve using fixed-point theory alone. Finally, we compare the proposed model with other DVA models under harmonic and random excitation. By comparing the amplitude-frequency curves, stroke lengths, mean square responses, time history diagrams, variances and decrease ratios, it is clear that the established DVA has a good vibration absorption effect. The research results provide theoretical and algorithm support for designing more effective DVA models of the same type in engineering applications.

Influence of pier-water interaction on natural vibration characteristics of bridge with complex piers in water

In order to clarify the influence of water on the natural vibration of bridge with complex piers, based on a continuous beam with 4-column pier, the numerical analysis model is established. Single column circular pier is taken to discuss the range of waters. Then the influences of water on the natural vibration are analyzed. The research shows that waters reduce the natural frequency. When waters area width is less than 10 m, the natural frequency of the pier decreases. And the first-order longitudinal bending frequency is reduced by 3.36%. When waters area width is more than 10 m, the vibration frequencies tend to be stable gradually. Therefore, the waters 10 m can be regarded as an infinite boundary. The natural frequencies of single column pier and 4-column pier decrease with the increase of water depth. When the water depth is less than 10 m, the changes of natural frequency of the first four orders of single column pier are relatively small, and the changes of 5–10 order natural frequency are large. The maximum effect of the first ten orders is 14.84%. The natural vibration frequency of the bridge decreases gradually with the increase of water depth. The maximum effect of the first five orders is 3.33%.

Periodic-Filtering Method for Low-SNR Vibration Radar Signal

Radar is a non-contact, high-precision vibration measurement device and an important tool for bridge vibration monitoring. Vibration information needs to be extracted from the radar phase, but the radar phase information is sensitive to noise. Under low signal-to-noise ratio (SNR) data acquisition conditions, such as low radar transmission power or a long observation distance, differential phase jump errors occur and clutter estimation becomes difficult, which leads to inaccurate inversion of vibration deformation. Traditional low-pass filtering methods can filter out noise to improve SNR, but they require oversampling. The sampling rate needs to be several times higher than the Doppler bandwidth, which is several times higher than the vibration frequency. This puts high data acquisition requirements on radar systems and causes large data volumes. Therefore, this paper proposes a novel vibration signal filtering method called the periodic filtering method. The method uses the periodicity feature of vibration signals for filtering without oversampling. This paper derives the time-domain and frequency-domain expressions for the periodic filter and presents a deformation inversion process based on them. The process involves extracting the vibration frequency in the Doppler domain, suppressing noise through periodic filtering, estimating clutter using circle fitting on the data complex plane, and inverting final deformation with differential phase. The method is verified through simulation experiments, calibration experiments, and bridge vibration experiments. The results show that the new periodic filtering method can improve the SNR by five times, resolve differential phase jumps, and accurately estimate clutter, thus getting submillimeter-level vibration deformation at low SNR.

Vibration detection of stay-cable from low-quality CCTV images using deep-learning-based dehazing and semantic segmentation algorithms

This study aims to monitor excessive vibrations in the stay-cables of long-span bridges, which can cause structural defects or discomfort to the public. Traditional methods like structural health monitoring (SHM) systems and computer vision techniques are impractical and costly for monitoring all stay-cables. Therefore, this study proposes a cost-effective solution using surveillance cameras (CCTV) commonly used for monitoring traffic conditions. Deep learning and computer vision techniques were used for semantic segmentation, dehazing, and tracking to address technical challenges in selecting feature points and image quality. Synthetic image generation was employed to obtain sufficient training images with pixel-wise annotations. The proposed framework was first validated using laboratory-scale experiments and applied to actual CCTV images collected under various environmental conditions. Parametric studies confirmed the efficiency of image synthesis and additional loss functions. The proposed method provides a viable alternative to monitor cable vibrations in long-span bridges using existing CCTV systems.

Dynamic Analysis of Coupled Train and Cracked Bridge Systems Using Multiscale Finite Element Modeling

Cracking frequently encountered in railway bridges can lead to significant changes in bridge dynamic characteristics and further dynamic performance of train–bridge interaction (TBI) system. It is desirable to develop an effective method to understand the dynamic behavior of coupled train and cracked bridge systems. This paper proposes a framework for coupled vibration analysis of train and cracked bridge systems using multiscale finite element modeling. A multiscale bridge model adopting frictional surface–surface contact to characterize nonlinear breathing phenomenon of the crack is incorporated into the three-dimensional coupled TBI model. Subsequently, a multiloop numerical solution strategy is formulated to solve the established dynamic equation of coupled train and cracked bridge systems. The proposed framework is used to analyze the cracked beams presented in the literature, and the obtained and literature data are compared. Moreover, an actual heavy-haul railway bridge is taken as an illustrative example, in which vehicle dynamic response, bridge vibration, and train running safety index are calculated considering various crack types, train speeds, and track conditions. The results show that apart from the bridge displacement and acceleration, the presence of crack can have a large influence on the vehicle acceleration response, derailment factor, and offload factor. Differences larger than ±10% in the maximum dynamic indices associated with the intact and cracked bridges are observed, indicating the necessity of considering the crack damage in train–bridge coupled dynamic analysis.

Dynamic Amplification Factors of an Arch Bridge Under Random Traffic Flows

Among large-span bridges, arch bridges have relatively high stiffness, which may lead to large dynamic amplification factors (DAFs). The DAFs suggested by current codes mostly originate from common simply supported beam bridges. Previous DAF studies on dynamic vehicle–bridge solutions for arch bridges have mainly focused on one or two side-by-side vehicles. However, complex traffic flows with randomness rather than one or two vehicles act on bridges. DAFs that consider the effects of random traffic flows have not previously been reported. In this study, a random traffic–bridge vibration solution was established to explore the DAFs of arch bridge components. The randomness of the traffic parameters and road roughness was explored. The randomness of the external excitation, including traffic flow and road roughness, resulted in random dynamic responses and DAFs of the arch bridge components. Normal distributions could be used to fit the DAF distributions of each arch bridge component under random vehicle spacing, weight, speed, and road roughness. Under random traffic parameters, the coefficients of variation of the DAFs exceeded the 5% accepted level. The shortest suspenders were more sensitive to the randomness of the traffic flow parameters. Both the mean and coefficient of variation of the DAFs increased with worsening of the road conditions. The influence of the randomness of the road roughness on the DAFs of arch bridges must be considered, particularly for the shortest suspender. The 95% upper confidence limits of the DAFs for all components may be greater than the suggested values in the code.

Prediction of Vortex-Induced Vibration Response of Open Bridge Girder Based on Machine Learning Method

The [Formula: see text]-shaped open section girder is a very common section, which has been widely used in the construction of modern bridges. However, compared with a streamlined box girder, it is easy to cause vortex-induced vibration (VIV) in bridges due to its bluff section shape and poor aerodynamic stability. In this paper, a typical open section with a height–width ratio of 10:1 is taken as the research object. Through wind tunnel tests and numerical simulation technology, the time-history data of VIV of the [Formula: see text]-shaped section are obtained. By selecting three different neural network models to establish the relationship between external parameters (wind attack angle, wind speed, turbulence) and structural response parameters (the onset wind speed of VIV, the length of the lock-in interval). After comparing different machine learning methods, the most suitable machine learning model is selected to predict the VIV response characteristics of the main girder. The research results show that the typical open section has a serious VIV phenomenon. The BP neural network model has the best performance in predicting the VIV performance of the open section in terms of calculation speed, prediction accuracy and solving nonlinear adaptability. At the same time, it is found that different characteristic parameters of the incoming wind field have different influences on the prediction results of the VIV response. Among them, the wind attack angle is the key parameter that affects the onset wind speed of VIV, but the turbulence intensity has a greater impact on the maximum amplitude of VIV. At the same time, the optimized BP model can predict the characteristic parameters of VIV response under unknown wind fields. This paper provides a new idea to study the effect of different incoming flow parameters on the performance of section VIV and further improves people’s understanding of VIV system.

Bridge Frequency Scanning Using the Contact-Point Response of an Instrumented 3D Vehicle: Theory and Numerical Simulation

Scanning the bridge’s frequencies from the passing vehicle’s vibration data has been frequently investigated recently. However, in previous studies, vehicles were typically simplified to quarter- or half-car models, and apparent disparity could be observed between the models and real vehicles. To make the vehicle model more practical, in this study, a 3D vehicle model is built to extract the bridge’s frequencies from vehicle vibrations. For the first time, equations for calculating the contact-point (CP) response of the 3D vehicle model are derived with tire damping. Furthermore, residual CP responses between front and rear wheels are utilized to eliminate the inverse effects of road roughness, making the bridge frequencies outstanding in the frequency domain. The robustness of the proposed method is tested under different influence factors, and two possible measurement errors are as follows: the sensor position and axle distance when applying the proposed method in engineering. Results show that the proposed method performs stably under the influence of different road roughness classes and tire damping. Bridge frequencies can be identified when the vehicle is travelling at a highway speed (108 km/h in this study). Environmental noises can submerge the bridge’s high-order frequencies but have little influence on the low-frequency range. High bridge damping will restrain the transmission of bridge vibration to the vehicle, making high-order bridge frequencies less visible. In addition, the errors introduced by a vehicle body sensor position can be eliminated when calculating the CP responses for tires, thus will not influence bridge frequency identification. To avoid possible errors induced by manual measurement of the axle distance, a novel cross-correlation function-based method is employed, which is verified effective and practical for calculating residual CP responses.

Bridge vibration energy harvesting for wireless IoT-based structural health monitoring systems: A review

Vibration energy has the advantage of abundant availability in the environment of the bridge structure due to consistent traffic flow and high-speed wind blowing. The vibration energy present at the bridge site can be harvested for powering the wireless sensors mounted on the bridge for health monitoring and making the system self-powered. The bridge vibrations are usually low frequency and low acceleration excitations, therefore, its transduction to useful electrical energy is a challenge. However, several techniques are being utilized to harvest the bridge vibration and a variety of bridge energy harvesters are being developed for this purpose. This work has reviewed energy harvesters claimed to be designed for bridge vibrations. The study is split into two categories, first section discusses the energy harvesters developed for bridge vibrations tested only in-lab environments. The second section is about the harvesters that have been characterized on real bridge structures to verify their effectiveness. The study reveals that the bridge energy harvesters can extract enough power to operate the wireless sensors for the health monitoring of bridge structures. Moreover, the architecture, fabrication, input excitation, and output performance of the reported harvesters with modeling techniques are discussed.

Extracting Bridge Frequencies from The Dynamic Responses of Moving and Non-moving Vehicles

Bridges can continuously suffer from structural deterioration due to inclement environmental and operational effects, making a timely inspection necessary to ensure the reliability and functionality of bridges. Recent progress in vehicle-bridge interactions has promoted the vehicle scanning method (VSM) for bridge frequency extraction, whereby the bridge frequency is typically identified from the dynamic response of a passing vehicle to reflect the bridge's health condition. Despite numerous endeavors, the low-speed limitation of the moving test vehicle and the adverse influence of road roughness still hinder the general application of VSM. In this regard, this paper presents a novel VSM for bridge frequency extraction by integrating moving and non-moving vehicles. By introducing the novel non-moving vehicle, the bridge vibration content becomes more obvious in the dynamic response of the moving vehicle, which is beneficial to the associated indirect bridge frequency extraction. Moreover, the non-moving vehicle is nearly free from the influence of road roughness, such that the performance of VSM for bridge frequency extraction can be enhanced against noisy real-world environments. To understand the inherent mechanism of the proposed method, a vehicle-bridge coupling system with moving and non-moving vehicles is theoretically formulated, and the analytical solutions of the coupled system are derived and numerically validated. Furthermore, several case studies are presented to comprehensively investigate key factors affecting the performance of bridge frequency extraction through the proposed method. The results indicate that incorporating a non-moving vehicle can significantly increase the extractability of bridge frequencies in vehicle responses. It becomes possible to accurately identify the first four-order bridge frequencies of a simply supported bridge (rather than the first two-order bridge frequencies using a moving vehicle exclusively) from the vehicle response after introducing a non-moving vehicle. More importantly, the adverse effect of the high-speed moving test vehicle and road roughness can be significantly alleviated by the non-moving vehicle, and therefore the proposed method becomes more robust in actual applications. Besides, further insights are provided in terms of the implementation strategies of the proposed method.

Topology and Sizing Optimization of Truss-Like Pedestrian Bridges with Viscous Dampers and Inerters

The design of footbridges has begun to receive more attention in recent years due to cases in which undesirable vibrations occurred. The utilization of passive energy dissipation systems to control bridge responses has become popular as a remedy for this matter. This paper proposes the use of inerters to mitigate pedestrian bridge vibrations, and explores their potential. This is done by presenting a topology and sizing optimization methodology for pedestrian bridges equipped with fluid viscous dampers and inerters. Planar truss-like bridges are examined, loaded under dynamic and static loads. All constructive elements’ sizes (including dampers) serve as continuous design variables. The objective is to minimize a cost function of the bridge. The optimization process is constrained by demanding responses of interest not to exceed allowable values, along with global and local buckling. A first-order gradient-based optimization algorithm is adopted to lessen the computational effort. Lastly, a discretization postprocess is offered to lead to discrete designs of relevant design variables, such as steel cross sections. The results shed light on the advantages of combining inerters in pedestrian bridges.

Dynamic modeling and analysis on planar free vibration of long-span arch bridges during construction

The cantilever construction model, which consists of the arch, towers and cables, can be regarded as a cable-stayed system and is widely applied in constructing long-span arch bridges. The vibration induced by this temporary structure's unstable property has a safety risk and deserves to be concerned. Thus, a fully analytical beam-spring-arch model is presented for the cantilever and closure construction states of long-span arch bridges. Subsequently, based on the boundary and continuity conditions, the governing differential equations for in-plane free vibration are derived according to the Hamilton principle and solved using the transfer matrix method to determine frequencies and mode shapes of the system. Meanwhile, the results calculated by the proposed method are verified with the finite element method. Finally, the effects of structural parameter variations during construction on in-plane vibration properties are investigated. The results show that as the length of the erected arch rib gets longer, the system's first six-order frequencies and mode shapes are significantly affected. Moreover, the veering phenomenon is observed. The cables can increase the frequencies of the system to a certain extent. The model that neglects the tower's vibration would overestimate the stiffness of the erection system unless the tower's stiffness is much bigger than the arch.

Investigation of Vortex-Induced Vibration of Double-Deck Truss Girder with Aerodynamic Mitigation Measures

The long-span double-deck truss girder bridge has become a recommend structural form because of its good performance on traffic capacity. However, the vortex-induced vibration (VIV) characteristics for double-deck truss girders are more complicated and there is a lack of related research. In this research, wind tunnel tests were utilized to investigate the VIV characteristics of a large-span double-deck truss girder bridge. Meanwhile, the VIV suppression effect of the aerodynamic mitigation measures was measured. Furthermore, the VIV suppression mechanism was studied from the perspective of vortex shedding characteristics. The results indicated that the double-deck truss girder had a significant VIV when the wind attack angles were +3° and +5°. The aerodynamic mitigation measures had an influence on the VIV response of the double-deck truss girder. The upper chord fairing and lower chord inverted L-shaped deflector plate played a crucial role in suppressing VIV. Numerical analysis indicated that vortex shedding above the upper deck or in the wake region may dominate vertical VIV, while vortex shedding in the wake region of the lower deck may dominate torsional VIV. The upper chord fairing and lower chord inverted L-shaped deflector plate disrupted the original vortex shedding pattern in both regions, thereby suppressing VIV. This research can provide a foundation for bridge design and vibration suppression measures for large-span double-deck truss girder bridges.

Optimization and Validation of Piezoelectric Cantilever Designs for Energy Harvesting from Bridge Vibrations

This study proposes an optimization strategy for bridge applications with a vibration-based energy harvester design. Piezoelectric cantilevers with multiple degrees of freedom (DOF) are designed and optimized to match resonant frequencies with the vibration frequencies of a full-scale bridge structure under different loading conditions and measurement locations. The specific optimization procedures include bridge vibration acceleration measurement, simulation model development for estimating the resonant frequencies, a regression model for optimization of mass combinations, and final installation on the full-scale bridge for validation. The results show that the simulation model predicted the resonant frequencies of cantilevers with less than 1 Hz difference compared with laboratory measurements. Following the entire optimization procedures proposed in this study, the optimized 2-DOF and 3-DOF cantilevers were capable of generating 18.9 [Formula: see text] J and 23.4 [Formula: see text] J energy under one loading pass, respectively, which were significantly higher than those from the baseline designs. The feasibility of the proposed optimization strategy was demonstrated and validated for vibration-based energy harvesting from bridge structures.

A High-Reliability Piezoelectric Tile Transducer for Converting Bridge Vibration to Electrical Energy for Smart Transportation.

Piezoelectric energy transducers offer great potential for converting the vibrations of pedestrian footsteps or cars moving on a bridge or road into electricity. However, existing piezoelectric energy-harvesting transducers are limited by their poor durability. In this paper, to enhance this durability, a piezoelectric energy transducer with a flexible piezoelectric sensor is fabricated in a tile protype with indirect touch points and a protective spring. The electrical output of the proposed transducer is examined as a function of pressure, frequency, displacement, and load resistance. The maximum output voltage and maximum output power obtained were 6.8 V and 4.5 mW, respectively, at a pressure of 70 kPa, a displacement of 2.5 mm, and a load resistance of 15 kΩ. The designed structure limits the risk of destroying the piezoelectric sensor during operation. The harvesting tile transducer can work properly even after 1000 cycles. Furthermore, to demonstrate its practical applications, the tile was placed on the floor of an overpass and a walking tunnel. Consequently, it was observed that the electrical energy harvested from the pedestrian footsteps could power an LED light fixture. The findings suggest that the proposed tile offers promise with respect to harvesting energy produced during transportation.

온도에 따른 도개교량의 구성 부품별 진동 민감도 분석

선박의 이동을 돕는 역할을 하는 bascule bridge는 해외에서 수십 년 이상 주의 깊게 정비하며 연구되고 있다. 도개교는 매일 혹은 자주 도개가 일어나기 때문에 유지보수가 매우 중요하며 특히 도개시 도개 부품별 진동 민감도에 대한 연구가 필요하다. 최근 교량의 유지보수 및 안전에 대한 요구가 높아져 안전점검이 이루어지고 있으나, 도개교에 대한 측정 및 분석은 부족한 실정이다. 국내 유일의 도교인 영도대교는 부식과 노후화로 철거되었다가 2013년 재건되어 현재 하루에 한 번 운영되고 있다. 본 연구에서는 도개교인 영도대교의 도개과정 및 상시거동을 계측하고, 진동 및 소음 민감도를 측정, 분석하여 도개교의 실제 거동을 파악하였다.

Field Evaluation of Piezoelectric Energy Harvesters on Bridge Structure

This study aims to develop and evaluate vibration-based piezoelectric energy harvesters for generating power from a bridge structure. New designs of multiple-degree-of-freedom (DOF) cantilevers were proposed and evaluated in a laboratory and on a full-scale bridge. It was found that all cantilever designs showed potential of generating 35 V voltage outputs under a simple sinusoidal vibration scenario in the laboratory. Field testing results showed that the match between the vibration frequencies of bridge structure and the resonant frequencies of cantilevers significantly affected the voltage output from the piezoelectric energy harvester under moving tire loads. Through adding more DOF on the same cantilever, the voltage attenuation from peaks generated by the cantilever turned to be less significant after each load passing, leading to greater energy outputs in some cases. With adjusting the mass combination in the 3-DOF cantilever design, the voltage output and energy production reached 11.1 V and 58.2 μJ under one single loading pulse, respectively, which was higher than 9.2 V and 14.9 μJ obtained from the best scenario of 1-DOF cantilevers. The study findings indicate the potential of developing multi-band piezoelectric energy harvesters for harvesting energy from bridge vibrations.