Vibrations Of Footbridges Research Articles

Analysis of Harmonic Vibration of Cable-Stayed Footbridge under the Influence of Changes of the Cables Tension

Abstract The paper presents numerical analysis of harmonically excited vibration of a cable-stayed footbridge caused by a load function simulating crouching (squats) while changing the static tension in chosen cables. The intentional synchronized motion (e.g., squats) of a single person or group of persons on the footbridge with a frequency close to the natural frequency of the structure may lead to the resonant vibrations with large amplitudes. The appropriate tension changes in some cables cause detuning of resonance on account of stiffness changes of structures and hence detuning in the natural frequency that is close to the excitation frequency. The research was carried out on a 3D computer model of a real structure - a cable-stayed steel footbridge in Leśnica, a quarter of Wrocław, Poland, with the help of standard computer software based on FEM COSMOS/M System.

Evaluation of human-induced vibration of continuous footbridges

With the development of construction materials and the introduction of high strength steel and concrete, the human-induced vibration became a dominant criterion for the design of pedestrian bridges. Currently, longer spans and lightweight bridges have been comprised in most of design trends. This leads to lower the natural frequencies of the system which have a great effect on the dynamic performance of bridges subjected to human activities. Although the design of steel footbridges could reach the optimum level of design in terms of strength criterion, it might not reach the acceptance level for vibration condition. This will enforce the designer to choose section profiles with higher inertia to enhance stiffness of the whole system. This paper presents an overall assessment for floor vibration problem due to pedestrian induced vertical forces on continuous composite footbridges. The footfall method presented by concrete centre CCIP-016 is adopted in this study to evaluate the response factor and acceleration of pedestrian bridges using a FEA software package Robot Structural Analysis.

Field Investigations On the Lateral Vibration Features Of Prestressed Concrete Stress Ribbon Footbridges

The prestressed concrete (PC) stress ribbon footbridge is a type of suspension bridge without towers, which has been applied in Japan and all over the world for years in light of its low construction cost and aesthetic merit. It generally consists of the precast concrete slabs with embedded cables. However, the walking-induced lateral vibration trouble of the Millennium Bridge in London in 2000 gave a lesson to the engineers that the lateral vibration feature must be taken into consideration for the footbridge vibration evaluation. In this sense, the field investigations on the lateral vibration features of 14 pre-stressed concrete stress ribbon footbridge in Japan was carried out by artificial impact and damping free vibration tests. According to the investigations, the larger the bridge span, the lower the frequencies of lateral-related vibration modes. In addition, based on the damping-free vibration field tests, there was a tendency toward the damping constant degradation when bridge span became larger.

A firefly algorithm for the design of force and placement of friction dampers for control of man-induced vibrations in footbridges

It is known that the use of passive energy dissipation devices, as friction dampers, reduces significantly the dynamic response of structures subjected to dynamic actions. However, the parameters of each damper as well as the best placement of these devices remain difficult to determine. Although some studies on optimization of tuned mass damper and viscous/viscoelastic dampers are being developed, works on optimum use of friction dampers is still lacking. Thus, in this paper, the simultaneous optimization of force and placement of friction dampers is proposed. To solve this optimization problem, the recently developed firefly algorithm is employed, which is able to deal with non-convex optimization problems, involving mixed discrete and continuous variables. For illustration purposes, two common footbridges are analyzed, in which the cost function is to minimize the maximum acceleration of the structures, whereas forces and positions of friction dampers are the design variables. The results showed that the proposed method was able to determine the optimum friction forces of each damper as well as their best positions in the structures. The maximum acceleration was reduced in more than 95 % for the Warren truss footbridge, with three friction dampers, and in more than 92 % for the Pratt truss footbridge, with only two friction dampers. In addition, the proposed methodology is quite general and it is believed that it can be recommended as an effective tool for optimum design of friction dampers for structural response control. Thus, this paper shows that the design of friction dampers can be done in a safe and economic way.

Ambient modal identification using multi-rank parallel factor decomposition

Summary In this paper, the problem of underdetermined modal identification where the number of modes to be identified is larger than the available sensor measurements is addressed using parallel factor decomposition and blind source separation. Underdetermined situations not only arise when the number of sensors are limited but also when narrowband excitations are present in the measurements, for example, in pedestrian-induced vibration of footbridges. The basic premise of the proposed algorithm is based on multiple-rank parallel factor decomposition of covariance tensors constituted from vibration response measurements. Unlike conventional parallel factor decomposition using a single rank order, the proposed method utilizes multiple rank order decompositions. A stability chart constructed from identified sources through such multiple rank orders allows for the robust estimation of active modes. The statistical characteristics of the resulting modes are evaluated in order to delineate the sources corresponding to external disturbances versus inherent modes of the system. The proposed framework enables an automated selection of rank order, detection of external harmonics and an estimation of modal parameters that are relatively insensitive to the sensor configuration. The performance of the algorithm is illustrated using both numerical studies and an experimental study using pedestrian-induced vibration measurements of a stress-ribbon bridge located at the Technical University—Berlin, Germany. Copyright © 2014 John Wiley & Sons, Ltd.

Tuned Mass Damper optimization for the mitigation of human-induced vibrations of pedestrian bridges

The design of Tuned Mass Dampers (TMD) to satisfy serviceability requirements is becoming more and more usual in the current design of footbridges. This paper analyzes the TMD design for the mitigation of pedestrian-induced vibrations with three main objectives: the introduction of a specific TMD optimization criterion for pedestrian-induced vibrations of footbridges, a critical analysis of the applicability to this specific loading scenario of classic literature optimization criteria, and a quantification of the TMD efficiency in the reduction of the footbridge acceleration. A numerical optimization criterion is proposed, based on the maximization of an efficiency factor, defined as the ratio between the uncontrolled acceleration standard deviation and the controlled one. Optimum TMD parameters are compared with classic criteria given by the literature. A possible modification of TMD parameters that permits to keep the TMD relative displacement within prescribed limits (aspect that is often a technical requirement in the TMD design) is also discussed. Monte Carlo simulations are carried out in order to confirm the validity of the standard deviation-based optimization for the reduction of the maximum dynamic response of the bridge. An application to a real footbridge is finally presented.

Lateral Pedestrian-Induced Vibrations of Footbridges: Characteristics of Walking Forces

The forces a walker exerts to an oscillating floor differ significantly from those exerted to a fixed floor. This is because of a natural and unconscious gait modification, deriving from the necessity of minimizing energy consumption while maintaining balance. Among other factors, these forces depend on the frequency and amplitude of oscillation of the floor, and this dependency is claimed to be responsible for most of the large amplitude vibrations observed on flexible footbridges. This paper reports the results of an extensive experimental campaign carried out using an instrumented treadmill, and aimed at evaluating the characteristics of the lateral force exerted by pedestrians when walking on a floor driven into a harmonic lateral motion with varying frequency and amplitude. The total measured force is separated into motion-dependent or self-excited components proportional to the floor velocity and acceleration, respectively, and an external excitation, which is independent of the floor motion. The variation of the acceleration- and velocity-proportional forces together with the characteristics of the spectra of the external excitation is discussed.

Vibration Control of a Cable-stayed Footbridge Using the Tension Changes of Cable

The paper presents the theoretical analysis for active reducing resonant vibration in cable-stayed footbridges. The method relies on changing the static tension in chosen cables. The tension changes cause a change in those natural frequencies that are close to the excitation frequency. The paper also seeks to establish which combinations of tensions in cables lead to the fastest change in the values of a chosen natural frequency. For this purpose eigenproblem sensitivity analysis, formulated for the structure according to the second order theory were used. The effectiveness of the method was tested using an FEM model of a footbridge.

Motor Vehicle Traffic-Induced Vibration Characteristics of the Ground and Urban Pedestrian Overpass

Since the 21st century, Beijing accelerate the process of internationalization. The level of the construction of Beijing city also faced a new challenge. The city traffic problems in Beijing is badly in need of improving. The stiffness of pedestrian bridge is so low that produce large vibration in the influence of ground traffic, which has a psychological effect on the pedestrian, even may cause psychological panic, anxiety and other adverse reactions. This study by monitoring the footbridge vibration at Beijing City Garden Road ,establishing finite element model to know about its severity under Motor vehicle traffic loads to get Vibration mechanics parameters. Use ISO, UK, Japan bridge design specifications and standard to check to make a scientific and reasonable evaluation on the vibration comfort about it.

Application of the pseudo-excitation method to assessment of walking variability on footbridge vibration

The pseudo-excitation method is applied to determine the non-stationary vibration response of footbridges to variable pedestrian excitation. Excitation forces are described by their spectral densities, the models of which are taken from the literature. In addition a simple spectral model is proposed to encompass both intra- and inter-pedestrian variability. Comparison is made to Monte Carlo simulations of random pedestrian events and a means of estimating extreme statistics of random walking is given. The method is shown to be accurate and efficient. Consequently, this work should find value in explaining differences between observed and modelled responses.

Modeling of crowd load in vertical direction using biodynamic model for pedestrians crossing footbridges

In the analysis of vibration of footbridges in vertical direction, for crowd situations, there is evidence in the literature that the whole effect of pedestrian action is not well modeled when applying current force-only models to represent such an action. In these models, the action of each pedestrian is represented by a pulsating force applied on the structure. In this paper, a crowd load model is proposed for sparse and dense crowds (with densities up to around 1.0 pedestrian/m2) in which biodynamic models are added to represent the whole action of pedestrians. The focus of the investigation is on vibration effects in vertical direction. Comparisons with measurements on a prototype footbridge were carried out and made it possible to identify differences in the structural response when applying force-only and force-biodynamic models to represent the pedestrian action. The latter (proposed) model resulted in a better agreement with the measurements.

A modal precise integration method for the calculation of footbridge vibration response

This paper presents a computationally efficient methodology for determining footbridge vibration response when subject to pedestrian excitation suitable for use in a Monte Carlo framework. A general modal precise integration method is developed for moving force problems. A closed-form solution for the transition matrix for the important case of a simply-supported beam subject to harmonic moving loads is given. The proposed method is efficient and accurately estimates important statistics of response in pedestrian excitation problems. This method should therefore find value in assessing new or existing footbridges when subject to random pedestrian excitation.

Calculation for the Critical Number of Pedestrians on a Footbridge by Using the Modified Nakamura’s Model

The problem of the critical number of pedestrians is significant in the study of lateral vibrations of footbridges since it can cause serviceability for the footbridges. By considering the pedestrians mass on the footbridge increases slowly, the modified Nakamuras model can be regarded as a fast-slow system which can be used to calculate the critical number of pedestrians. The influence of the time delay of interaction between pedestrians and the footbridge on the critical number of pedestrians is analyzed. Comparison with other results indicates the correctness of our formula predicting the critical number of pedestrians. Furthermore, our research suggests that the existence of the time delay can make the critical number of pedestrians less, which means that the time delay helps to improve the safety of the footbridge.

Analysis on Natural Vibration and Dynamic Response of Footbridge

According to vibration problem of the footbridge, the dynamic characteristics and dynamic responses of the footbridge were analyzed under pedestrian load. Based on one 22m×10 straight line footbridge, this paper established the spatial finite element model to analyze its natural vibration characteristics and discuss the effects on the natural vibration characteristics induced by both connection factors of beam ends and pedestrians weight. And then the dynamic responses of the footbridge caused by pedestrian dynamic load were calculated to analyze the structure stress. In addition, to analyze the calculation result of displacement responses so as to evaluate the comfort of pedestrians. The results show that the natural frequency is lower, and it will probably induce the resonance and larger dynamic response value under pedestrian load although the footbridge structure is safe. Moreover, reducing vibration methods and treatment measures to the footbridge were introduced, and the effective measure was suggested to reduce vibration amplitude at last.

Evaluating the vertical vibration response of footbridges using a response spectrum approach

In this paper, the vertical vibration response of footbridges subjected to dynamic loads induced by walking humans is assessed via a response spectrum approach. The dynamic walking load in the vertical direction is applied on the bridges using two different loading schemes: (1) a stationary load at the mid-span and (2) a moving load across the bridge. The response spectrum analysis is carried out using a Generalized Single Degree of Freedom procedure which has been verified by comparing its predictions with the results of a Multi-Degrees of Freedom modeling.The results obtained indicated that the response spectrum approach is capable of accurately predicting the footbridge vibration response. The results obtained also indicated that the main parameters that affect the induced accelerations in footbridges due to the human walking loads in the vertical direction are the footbridge mass and damping ratio.

Field Testing on Natural Frequencies of a Cable-Stayed Footbridge Based on Ambient Excitation

Many footbridges may suffer from the intensive vibration induced by human activities. To be a direct and effective approach, field measurement is widely utilized to assess the vibration serviceability of footbridge. The field measurement and modal identification of a cable-stayed footbridge is conducted in this study. The dynamic responses of the example footbridge subjected to ambient excitations are collected through field measurement and utilized to identify the structural dynamic properties by using two approaches. The made observation indicate that the peak acceleration responses at different testing points are different to great extent but the spectrum properties of all the points are quite similar. The fundamental frequency for the vertical vibration of the concerned footbridge is close to the lower frequency of the pedestrian loading and a relatively large vibration and discomfort of pedestrians can be observed

Effectiveness of “Detuned” TMD's for Beam-Like Footbridges

The dynamic properties of Tuned Mass Dampers (TMD's) used to reduce the vibrations of footbridges are generally based on the optimization criterion of Den Hartog. However the spring, mass and damper of a TMD may possess slight fabrication tolerances or change its damping element properties due to temperature, which can result in a detuning of a TMD. The study presented deals with the influence of a detuning on the performance of a TMD. A simplified model for beam-like footbridges under pedestrian loading is proposed. It is shown that a 2-DOF-system in harmonic stationary motion represents a good approximation of the beam structure under transient time-dependent load. Graphs are given to assess the increase of acceleration and the decrease of effectiveness due to detuning. A case study on a footbridge with a span of 45 m demonstrates its accuracy.

Application of Nakamura’s Model to Describe the Delayed Increase in Lateral Vibration of Footbridges

AbstractNakamura’s model is proposed to describe lateral vibrations of a footbridge induced by pedestrians. The model is found to be a slow-fast system if the number of pedestrians on a footbridge increases slowly. Then, based on the delayed bifurcation theory, Nakamura’s model can be used to describe the delayed increase in the lateral vibration of the footbridge. The critical number of pedestrians on the footbridge is calculated by using the delayed bifurcation theory to quantitatively demonstrate our analysis. By comparison with a previously obtained formula, the rationality of the authors’ formula for predicting the critical number of pedestrians is illustrated. Based on the authors’ formula, the experimental parameter k=300 used in the previously obtained formula does not seem to be always applicable to other bridges. Based on Nakamura’s model, the value of the parameter k seems to be affected mainly by the properties of the pedestrians on the bridge rather than those of the bridge.

Calculation of the Periodic Solution in Nakamura’s Model

Nakamura’s model is one of the most practical models describing the lateral vibrations of footbridges induced by pedestrians. This paper presents a calculation of the periodic solution in Nakamura’s model. After a Hopf bifurcation analysis of Nakamura’s model, the amplitude of the lateral vibration is computed by using the energy method. The correctness and accuracy of the calculation is demonstrated by numerical simulations. Then, how the factors and variables in Nakamura’s model effect the amplitude is investigated based on the analytic solution. Our analysis results may be used to explain why the most of the predict results of Nakamura’s model are larger than the measure data.

A model of pedestrian-induced bridge vibration based on full-scale measurement

It is now well-known that, under pedestrian excitation, flexible footbridges can exhibit large-amplitude vibrations that impact their serviceability. In particular, some footbridges of suspended spans have exhibited significant lateral oscillation due to pedestrian–bridge interaction. This paper presents the characteristics of pedestrian-induced vibration of a prestressed concrete beam bridge observed using full-scale measurement. The effect of the pedestrian loading on the oscillation frequency of the bridge, as well as its implication on the mechanism of pedestrian–bridge interaction, is investigated. Based on the understanding of the prototype vibration, a model is developed to enable assessment of the amplitude of footbridge vibration induced by pedestrian excitation.