Comparative Study on the Vertical Dynamic Responses of Simply Supported Beam Subjected to Two Typical Vehicle Models

2012 ◽  
Vol 178-181 ◽  
pp. 2424-2428
Author(s):  
Chun Sheng Shan ◽  
Wei Ye ◽  
Heng Li ◽  
Xiao Zhen Li
Keyword(s):  
High Speed ◽  
Damping Ratio ◽  
Dynamic Responses ◽  
Vehicle Speed ◽  
Vehicle Model ◽  
Euler Beam ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Systems Model ◽  
Mass Spring

A novel simplified vehicle model i.e. arbitrary moving mass-spring systems model, which can be simplified into moving loads model, is put forward and proved to be capable of analyzing the vertical dynamic responses of bernoulli-euler beam. Based on the matlab platform, a simply supported beam with a span of 40 m serviced in Beijing-Shanghai High-speed Railway is selected as the case study. The similarities and differences of vertical dynamic responses of the bridge based on this two vehicle models are compared. On this basis, the effects of vehicle speed and bridge damping ratio on the bridge’s dynamic magnification factor is studied. The computation results show that this new vehicle model is effective and reliable in its practical application.

Analysis of Dynamic Response of Simply-Supported Girder Bridge in High-Speed Railway Based on the Moving Rows Mass-Spring Model

2012 ◽  
Vol 193-194 ◽  
pp. 919-924
Author(s):  
Jin Feng Wu ◽  
Zhi Jun Zhang ◽  
Xiao Zhen Li
Keyword(s):  
High Speed ◽  
Damping Ratio ◽  
Spring Model ◽  
Simply Supported ◽  
Mass Spring Model ◽  
Girder Bridge ◽  
Set Up ◽  
Mass Spring ◽  
The Impact ◽  
Bridge System

The vibration theory of beam and D’Alembert principle are used to set up vehicle-bridge system for a simply-supported girder bridge under the moving rows mass-spring model. The kinematic equations of vehicle and bridge are derived separately. And with the force balanced relationship and the displacement compatibility conditions between wheels and rail, the equations of vehicle-bridge system are established. A calculating program is complicated with MATLAB language and solved by Newmark-β method. Results show that the effect of the damping ratio on the impact factor is significant and running speed of the vehicle is one of the main actors resulting in vibration of the system.

Analysis of Vertical Dynamic Response of Simply Supported Beam Traversed by Successive Moving Loads

2014 ◽  
Vol 556-562 ◽  
pp. 751-754 ◽  
Author(s):  
Xiao Ping Wang ◽  
Ming Shui Li
Keyword(s):  
Dynamic Response ◽  
Damping Ratio ◽  
Amplification Coefficient ◽  
Vehicle Speed ◽  
Moving Loads ◽  
Maximum Displacement ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Calculation Results ◽  
Dynamic Amplification

In this paper, The vertical vibration’s analytical expression of Euler-Bernoulli beam traveled by moving loads is used to analyze the effect factors such as vehicle speed and damping ratio. The calculating program is made with MATLAB to analyze the dynamic response of a bridge as an illustrative example. A 32 meters simply supported beam traversed by moving loads of 8 ICE3 motor cars is analyzed. The calculation results show that the maximum displacement of the bridge appears at or near the mid-span and it has nothing to do with the position of the loads. The dynamic amplification coefficient of displacement at mid-span is not linearly increased with the vehicle speed improving. The damping ratio can decrease the dynamic response of the bridge dramatically, especially at the resonance speed.

Vertical track irregularity analysis of high-speed railways on simply-supported beam bridges based on the virtual track inspection method

2020 ◽  
pp. 095440972092457
Author(s):  
Tianci Gao ◽  
Jianli Cong ◽  
Ping Wang ◽  
Jianxing Liu ◽  
Yuan Wang ◽  
...  
Keyword(s):  
High Speed ◽  
Three Dimensional ◽  
Vertical Direction ◽  
Vehicle Speed ◽  
Simply Supported Beam ◽  
Inspection Method ◽  
Track Geometry ◽  
Simply Supported ◽  
The Relationship ◽  
Track Irregularities

Understanding the relationship between the static and dynamic track geometry irregularities is crucial for the proper maintenance of rail infrastructures and the reduction of on-site workload. This paper focuses on the analysis of the dynamic and static track irregularities on simply-supported beam bridges for high-speed railways. Based on the simulation of three-dimensional vehicle–track–bridge dynamics, a virtual track inspection method is proposed according to the measurement principle with the inertial reference. With the static irregularity provided as the initial input to the simulation model, the virtual track inspection of dynamic track irregularities is carried out considering different supporting structures, i.e. subgrade and bridges. Furthermore, the characteristics and advantages of the proposed model are investigated in the “rigid track structure”. Then, using the virtual track inspection method, this paper analyzes the relationship between the dynamic and static track irregularities (in the vertical direction) on the simply-supported beam bridge in both the time and frequency domains with respect to different train speeds, and the simulation results are validated by real-world measurements. Numerical results show that the stiffness irregularity in the vertical direction is periodical, with the cycle length equal to the span of the bridge. Furthermore, there is an obvious linear relationship between the dynamic and static irregularities. Also, the regression coefficient increases with increasing vehicle speed.

Modal Coordinate Formulation for a Simply Supported Bridge Subjected to a Moving Train Modelled as Two-Stage Suspension Vehicles

2005 ◽  
Vol 219 (10) ◽  
pp. 1027-1040 ◽  
Author(s):  
P Lou ◽  
G-L Dai ◽  
Q-Y Zeng
Keyword(s):  
Degrees Of Freedom ◽  
Virtual Work ◽  
Time Integration ◽  
Computer Time ◽  
Dynamic Responses ◽  
Euler Beam ◽  
Two Stage ◽  
Simply Supported ◽  
Mass Spring ◽  
Moving Train

Modal coordinate formulation for analysing the dynamic interaction between a moving train and a simply supported bridge is presented in this article. The train is composed of a series of identical vehicles, and each vehicle is modelled as a four-wheelset mass-spring-damper multi-rigid body system with two-stage suspension having ten degrees of freedom (DOFs). A simply supported bridge, together with the track, is modelled as a Bernoulli-Euler beam. The deflection of the beam is described by superimposing modes. The train and the beam are regarded as an entire dynamic system, and then the modal coordinate formulation with time-dependent coefficients for this system is directly derived from the principle of virtual work. The formulation is solved by direct time integration method, to obtain the dynamic responses of this system. The correctness of the proposed formulations is illustrated by a comparison with the existing literature. The formulation helps save computer time using a few beam modes for analysing the dynamic responses of an entire train-bridge interaction system. The proposed formulation can also be applied to analyse the dynamic responses of a simply supported bridge subjected to a moving train modelled as two-wheelset four DOFs vehicles. Two numerical examples are given for illustrating the applications of the proposed formulation.

Analytical Solution to Vertical Dynamic Response of Simply Supported Beam Bridge Traversed by Successive Moving Loads

2012 ◽  
Vol 178-181 ◽  
pp. 2345-2352 ◽  
Author(s):  
Zhi Jun Zhang ◽  
Jin Feng Wu ◽  
Li Zhong Song ◽  
Song Hua Ma ◽  
Xiao Zhen Li
Keyword(s):  
Analytical Solution ◽  
Dynamic Response ◽  
High Speed ◽  
Damping Ratio ◽  
Moving Loads ◽  
Simply Supported Beam ◽  
Railway Bridges ◽  
Simply Supported ◽  
High Speed Trains ◽  
Analytical Expressions

In this paper, vibration theory is used to deduce vertical vibration’s analytical expressions of Euler- Bernoulli beam traveled by moving loads. In the analytical expression, the influences of the train’s travelling speed ,the mode of vibration ,the mass and rigidity of beam itself and the damping ratio of the system are considered comprehensively. Then the calculating program is made with MATLAB to analyze the dynamic response of a bridge as an illustrative example, so as to check the correctness of the analytical solution. Then a 32 meters simply supported beam traversed by moving loads of 8 ICE3 motor cars is analyzed. The calculation results show that the analysis method in this paper can really give accurate results to the beam subjected to arbitrarily spacing loads . The analytical expressions can be applied to preliminary design of railway bridges and assessment of the expected maximum vibration levels under high-speed trains.

Analytical Solution for Vertical Dynamic Response of Railway Simply Supported Beam Bridge under Bidirectional Moving Loads

2012 ◽  
Vol 594-597 ◽  
pp. 1552-1556
Author(s):  
Wei Ye ◽  
Xiao Zhen Li ◽  
Hong Duan ◽  
Chun Sheng Shan ◽  
Xiao Han Liu
Keyword(s):  
High Speed ◽  
Vertical Vibration ◽  
Simulation Software ◽  
Dynamic Responses ◽  
Moving Loads ◽  
Simply Supported Beam ◽  
Double Line ◽  
Simply Supported ◽  
Numerical Result ◽  
Beam Bridge

In this thesis, the dynamic responses of simply supported beam bridge in a double-line railway under bidirectional moving loads are mainly studied. To study the characteristics of Euler- Bernoulli beam, a train is simplified as a series of concentrated forces with fixed wheelbase.Structural dynamics is used to deduce the analytical expressions of vertical vibration of simply supported beam under bidirectional moving loads. By simulation software MATLAB, the numerical result of the dynamic responses of simply supported beam bridge could be obtained. Then the 48 meters simply supported beam bridge in a high-speed railway is analyzed, the dynamic responses of simply supported beam of bidirectional moving loads with different interarrival times are discussed.Finally, some general laws for the design of double-line railway bridge are gained.

Dynamic Response of the Spectral Element Model by Using the FFT

2007 ◽  
Vol 345-346 ◽  
pp. 845-848
Author(s):  
Joo Yong Cho ◽  
Han Suk Go ◽  
Usik Lee
Keyword(s):  
Fourier Transforms ◽  
Initial Conditions ◽  
Element Model ◽  
Spectral Element ◽  
Dynamic Responses ◽  
Analysis Method ◽  
Euler Beam ◽  
Exact Analytical Solutions ◽  
Simply Supported ◽  
Spectral Analysis Method

In this paper, a fast Fourier transforms (FFT)-based spectral analysis method (SAM) is proposed for the dynamic analysis of spectral element models subjected to the non-zero initial conditions. To evaluate the proposed SAM, the spectral element model for the simply supported Bernoulli-Euler beam is considered as an example problem. The accuracy of the proposed SAM is evaluated by comparing the dynamic responses obtained by SAM with the exact analytical solutions.

Experimental Study on the Dynamic Deformation of Simply Supported Beam in Chinese High-speed Railway

2018 ◽  
Author(s):  
Gonglian Dai ◽  
Meng Wang ◽  
Tianliang Zhao ◽  
Wenshuo Liu
Keyword(s):  
High Speed ◽  
Structure Design ◽  
Dynamic Coefficient ◽  
Bridge Structure ◽  
High Speed Railway ◽  
Simply Supported Beam ◽  
Vertical Stiffness ◽  
Simply Supported ◽  
Speed Up ◽  
Design Speed

<p>At present, Chinese high-speed railway operating mileage has exceeded 20 thousand km, and the proportion of the bridge is nearly 50%. Moreover, high-speed railway design speed is constantly improving. Therefore, controlling the deformation of the bridge structure strictly is particularly important to train speed-up as well as to ensure the smoothness of the line. This paper, based on the field test, shows the vertical and transverse absolute displacements of bridge structure by field collection. What’s more, resonance speed and dynamic coefficient of bridge were studied. The results show that: the horizontal and vertical stiffness of the bridge can meet the requirements of <b>Chinese “high-speed railway design specification” (HRDS)</b>, and the structure design can be optimized. However, the dynamic coefficient may be greater than the specification suggested value. And the simply supported beam with CRTSII ballastless track has second-order vertical resonance velocity 306km/h and third-order transverse resonance velocity 312km/h by test results, which are all coincide with the theoretical resonance velocity.</p>

Dynamic Response of an Elastic-Supported Bridge Beam Subjected to Velocity-Varied Moving Loads

2012 ◽  
Vol 594-597 ◽  
pp. 2802-2807
Author(s):  
Fu Liang Mei ◽  
Gui Ling Li
Keyword(s):  
Dynamic Response ◽  
Beam Theory ◽  
Dynamic Responses ◽  
Force Model ◽  
Superposition Method ◽  
Moving Loads ◽  
Coupled Vibration ◽  
Vehicle Model ◽  
Vibration Model ◽  
Mass Spring

Dynamic response of an elastic-supported bridge under speed-varied moving loads was investigated. A mathematical model of vehicle-bridge coupled oscillation for an elastic-supported bridge was built up by means of 1/4 vehicle model (Mass-Spring-Mass) and Euler-Bernoulli beam theory. And then dynamic equations of vehicle-bridge coupled oscillation in matrix form were established using two former orders general coordinates of an elastic-supported beam and model superposition method. The influences of vehicle-bridge coupled vibration model, elastic-supported stiffness, entrance speeds and acceleration /deceleration of moving loads on the dynamic responses of bridges were studied. Vehicle-bridge coupled vibration model based on 1/4 vehicle model can more accurately describe the dynamic characters of bridges than that based on constant moving force model. Elastic-supported stiffness only has an impact on the fluctuation amplitudes of dynamic responses. The vehicle-induced impact factor is dependent on the entrance speeds, acceleration/deceleration of moving loads and elastic-supported stiffness.

Research on the Natural Frequency Solving Method of the Simply Supported Beam Bridge with Cracks

2013 ◽  
Vol 437 ◽  
pp. 51-55
Author(s):  
Ping Yi Sun ◽  
Yan Hua Wang ◽  
Han Bing Liu ◽  
Guo Jin Tan
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Beam Model ◽  
Euler Beam ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Solution Methods ◽  
Element Approach ◽  
Experimental Values ◽  
Beam Bridge

Two kinds of natural frequency solution methods for the simply supported beam bridge with cracks are presented respectively based on the Bernoulli-Euler beam model and the finite element approach. Multiple groups of crack damages are supposed on the experimental simply supported steel I-beam, and the natural frequencies of the experimental beam are measured in all the crack cases. By comparing the calculated natural frequencies respectively obtained by the above two methods with the experimental values, the characteristics of the two kinds of natural frequency solving methods are evaluated.

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