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.

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.

Dynamic Response of a Cantilevered Beam Under Combined Moving Moment, Torque and Force

2020 ◽  
Vol 20 (05) ◽  
pp. 2050065
Author(s):  
Denil Chawda ◽  
Senthil Murugan
Keyword(s):  
Dynamic Response ◽  
High Speed ◽  
Moving Load ◽  
Numerical Results ◽  
Moving Loads ◽  
Element Analysis ◽  
Dirac Delta ◽  
Rayleigh Beam ◽  
Moving Force ◽  
Cantilevered Beam

This paper studies the dynamic response of a cantilevered beam subjected to a moving moment and torque, and combination of them with a moving force. The moving loads are considered to traverse along the length of the beam either from fixed-to-free end or free-to-fixed end. The beam is considered to have constant material and geometric properties. The beam is modeled using the Rayleigh beam theory considering the rotary inertia effects. The Dirac-delta function used to model the moving loads in the governing partial differential equations (PDEs) has complicated the solution of the problem. The Eigenfunction expansions coupled with the Laplace transformation method is used to find the semi-analytical solution for the resulting governing PDEs. The effects of moving loads on the dynamic response are studied. The dynamic effects are quantified based on the number of oscillations per unit travel time of the moving load and the Dynamic Amplification Factor (DAF) of the beam’s tip response. Numerical results are also analyzed for the two-speed regimes, namely high-speed and low-speed regimes, defined with respect to the critical speed of the moving loads. The accuracy of the analytical solutions are verified by the finite element analysis. The numerical results show that the loads moving with low speeds have significant impact on the dynamic response compared to high speeds. Also, the moving moment has significant impact on the amplitude of dynamic response compared with the moving force case.

scholarly journals Dynamic Response Analysis of a Simply Supported Double-Beam System under Successive Moving Loads

2019 ◽  
Vol 9 (10) ◽  
pp. 2162 ◽  
Author(s):  
Lizhong Jiang ◽  
Yuntai Zhang ◽  
Yulin Feng ◽  
Wangbao Zhou ◽  
Zhihua Tan
Keyword(s):  
Dynamic Response ◽  
Analytical Method ◽  
Amplitude Spectrum ◽  
Analytical Calculation ◽  
Response Analysis ◽  
Moving Loads ◽  
Analytical Expression ◽  
Simply Supported ◽  
Beam System ◽  
Double Beam

The dynamic response of a simply supported double-beam system under moving loads was studied. First, in order to reduce the difficulty of solving the equation, a finite sin-Fourier transform was used to transform the infinite-degree-of-freedom double-beam system into a superimposed two-degrees-of-freedom system. Second, Duhamel’s integral was used to obtain the analytical expression of Fourier amplitude spectrum function considering the initial conditions. Finally, based on finite sin-Fourier inverse transform, the analytical expression of dynamic response of a simply supported double-beam system under moving loads was deduced. The dynamic response under successive moving loads was calculated by the analytical method and the general FEM software ANSYS. The analysis results show that the analytical method calculation results are consistent with ANSYS’ calculation, thus validating the analytical calculation method. The simply supported double-beam system had multiple critical speeds, and the flexural rigidity significantly affected both peak vertical displacement and critical speed.

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.

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>

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