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.

scholarly journals An Analytical Study on Dynamic Response of Multiple Simply Supported Beam System Subjected to Moving Loads

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Zhipeng Lai ◽  
Lizhong Jiang ◽  
Wangbao Zhou
Keyword(s):  
Partial Differential Equations ◽  
Analytical Solution ◽  
Dynamic Response ◽  
High Speed ◽  
Moving Load ◽  
Moving Loads ◽  
Spatial Displacement ◽  
High Speed Railway ◽  
Simply Supported ◽  
Beam System

Based on Euler–Bernoulli beam theory, first, partial differential equations were established for the vibration of multiple simply supported beams subjected to moving loads. Then, integral transforms were conducted on the spatial displacement coordinate and time in the partial differential equations, and the frequency-domain response of multiple simply supported beams subjected to moving loads was obtained. Next, by conducting the corresponding inverse transforms on the displacement frequency-domain responses of multiple simply supported beams, the spatial displacement time-domain responses were obtained. Finally, to validate the analytical method reported in this paper, the dynamic response of a typical double simply supported rail-bridge beam system of high-speed railway in China subjected to a moving load was carried out. The results show that the analytical solution proposed in this paper is consistent with the results obtained from a finite element analysis, validating and rationalizing the analytical solution. Moreover, the system parameters were analyzed for the dynamic response of double simply supported rail-bridge beam system in high-speed railway subjected to a moving load with different speeds; the conclusions can be beneficial for engineering practice.

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.

Analysis on Vertical Dynamic Response of Simply-Supported Bridge Subjected to a Series of Moving Harmonic Loads

2013 ◽  
Vol 361-363 ◽  
pp. 1329-1334
Author(s):  
Jing Feng Zhang ◽  
Xiao Zhen Li ◽  
Li Zhong Song ◽  
Chun Sheng Shan
Keyword(s):  
Analytical Solution ◽  
Dynamic Response ◽  
Resonance Phenomenon ◽  
Superposition Method ◽  
Analysis Model ◽  
Harmonic Frequency ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Mode Superposition Method ◽  
Calculation Results

In this thesis, a dynamic analysis model is established that subjected to a series of moving harmonic loads, and the analytical solution of the dynamic response is deduced based on the mode superposition method. Based on this analytical solution, a program is made to calculate the vertical dynamic response of simply-supported beam. The calculation results show that the analytical solution is reasonable and correct. When the harmonic frequency is near to the fundamental frequency of the simply-supported beam, the resonance phenomenon will occur. The dynamic response of the beam will decrease as the speed increases, and the presence of damp can suppress the vibration of the bridge.

Finite Element Analysis on Dynamic Response of Bridge Structures under Moving Loads with Uniform Speed

2011 ◽  
Vol 90-93 ◽  
pp. 1015-1018
Author(s):  
Wen Zhang ◽  
De Can Yang
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Dynamic Response ◽  
Moving Load ◽  
Moving Loads ◽  
Element Analysis ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
The Finite Element Analysis ◽  
Bridge Structures

The dynamic response of simple supported beam under the moving load is analyzed. The finite element analysis software MIDAS is used to simulate the process of when the uniform constant force moving through the simply supported beam. The first 5 natural frequencies of simply supported beam are obtained with the modal analysis and compared with the analytical solution. The feasibility of the finite element method is verified.

scholarly journals Three-Dimensional Dynamic Analyses of Track-Embankment-Ground System Subjected to High Speed Train Loads

2014 ◽  
Vol 2014 ◽  
pp. 1-19 ◽  
Author(s):  
Qiang Fu ◽  
Changjie Zheng
Keyword(s):  
Dynamic Response ◽  
High Speed ◽  
Concrete Slab ◽  
Three Dimensional ◽  
Element Model ◽  
Moving Loads ◽  
Infinite Elements ◽  
Ground System ◽  
High Speed Trains ◽  
Train Speed

A three-dimensional finite element model was developed to investigate dynamic response of track-embankment-ground system subjected to moving loads caused by high speed trains. The track-embankment-ground systems such as the sleepers, the ballast, the embankment, and the ground are represented by 8-noded solid elements. The infinite elements are used to represent the infinite boundary condition to absorb vibration waves induced by the passing of train load at the boundary. The loads were applied on the rails directly to simulate the real moving loads of trains. The effects of train speed on dynamic response of the system are considered. The effect of material parameters, especially the modulus changes of ballast and embankment, is taken into account to demonstrate the effectiveness of strengthening the ballast, embankment, and ground for mitigating system vibration in detail. The numerical results show that the model is reliable for predicting the amplitude of vibrations produced in the track-embankment-ground system by high-speed trains. Stiffening of fill under the embankment can reduce the vibration level, on the other hand, it can be realized by installing a concrete slab under the embankment. The influence of axle load on the vibration of the system is obviously lower than that of train speed.

scholarly journals Dynamic analysis of railway bridges exposed to high-speed trains considering the vehicle–track–bridge–soil interaction

2021 ◽  
Author(s):  
Paul König ◽  
Patrick Salcher ◽  
Christoph Adam ◽  
Benjamin Hirzinger
Keyword(s):  
Dynamic Response ◽  
High Speed ◽  
Element Model ◽  
Bernoulli Beam ◽  
Railway Bridges ◽  
Modal Expansion ◽  
High Speed Trains ◽  
Mass Spring ◽  
Track Bridge ◽  
Euler Bernoulli Beam

AbstractA new semi-analytical approach to analyze the dynamic response of railway bridges subjected to high-speed trains is presented. The bridge is modeled as an Euler–Bernoulli beam on viscoelastic supports that account for the flexibility and damping of the underlying soil. The track is represented by an Euler–Bernoulli beam on viscoelastic bedding. Complex modal expansion of the bridge and track models is performed considering non-classical damping, and coupling of the two subsystems is achieved by component mode synthesis (CMS). The resulting system of equations is coupled with a moving mass–spring–damper (MSD) system of the passing train using a discrete substructuring technique (DST). To validate the presented modeling approach, its results are compared with those of a finite element model. In an application, the influence of the soil–structure interaction, the track subsystem, and geometric imperfections due to track irregularities on the dynamic response of an example bridge is demonstrated.

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.

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