Dynamic Model of a Discrete-Pontoon Floating Bridge Subjected by Moving Loads

2010 ◽  
Vol 29-32 ◽  
pp. 732-737 ◽  
Author(s):  
Zhang Jun ◽  
Jun Liu ◽  
Xiao Lu Ni ◽  
Wei Li ◽  
Rong Mu
Keyword(s):  
Moving Load ◽  
Elastic Beam ◽  
Beam Model ◽  
Moving Loads ◽  
Concentrated Force ◽  
Vehicle Load ◽  
Comparison Results ◽  
Floating Bridge ◽  
Mass Spring ◽  
Damping Systems

A discrete-pontoon floating bridge is studied based on the beam model with assumption of the bridge deck as a elastic beam with uniform section, live load such as vehicle as moving concentrate forces, and pontoons as independent mass-spring-damping systems with singular degree of freedom. The comparison results of between vehicles and moving concentrated force show that a vehicle load can be simplified as one moving concentrated force. The present model can study not only a single moving load but also multiple moving loads.

Linear Dynamics of an Elastic Beam Under Moving Loads

2000 ◽  
Vol 122 (3) ◽  
pp. 281-289 ◽  
Author(s):  
G. Visweswara Rao
Keyword(s):  
Internal Resonance ◽  
Multiple Scales ◽  
Moving Load ◽  
Mass Parameter ◽  
Equations Of Motion ◽  
Elastic Beam ◽  
Mass Effect ◽  
Moving Loads ◽  
Parameter Ratio ◽  
Load Mass

The dynamic response of an Euler-Bernoulli beam under moving loads is studied by mode superposition. The inertial effects of the moving load are included in the analysis. The time-dependent equations of motion in modal space are solved by the method of multiple scales. Instability regions of parametric resonance are identified and the moving mass effect is shown to significantly affect the transient response of the beam. Importance of modal interaction arising out of the possible internal resonance is highlighted. While the external resonance is due to the gravity effects of the moving load, the parametric and internal resonance solely depends on the load mass parameter—ratio of the moving load mass to the beam mass. Numerical results show the influence of the load inertia terms on the beam response under either a single moving load or a series of moving loads. [S0739-3717(00)01703-7]

scholarly journals On the Dynamic Response of a Beam to a Randomly Moving Load

1968 ◽  
Vol 35 (1) ◽  
pp. 1-6 ◽  
Author(s):  
J. K. Knowles
Keyword(s):  
Dynamic Response ◽  
Wiener Process ◽  
Stationary Process ◽  
Moving Load ◽  
Elastic Beam ◽  
Bending Moment ◽  
Concentrated Force ◽  
Stochastic Function

The problem considered is that of an infinitely long elastic beam subject to a moving concentrated force whose position is a stochastic function of time, X(t). The expected deflection and expected bending moment are analyzed, with special attention being given to the case of a stationary process X(t) and to the case in which X(t) is a Wiener process.

scholarly journals Response Analysis of Ladder Beams Under Inertial Moving Load

2018 ◽  
Vol 23 (No 3, September 2018) ◽  
Author(s):  
Hongliang Li ◽  
Bo Zhang ◽  
Yunxuan Gong ◽  
Donghua Wang
Keyword(s):  
High Speed ◽  
Moving Load ◽  
Vibration Characteristics ◽  
Vibration Response ◽  
Response Analysis ◽  
Beam Model ◽  
Inertia Effect ◽  
Moving Loads ◽  
Model Free ◽  
Variable Section

With the continuous development of industry, variable-section beams and high speed moving loads with large mass are widely used. Thus, it is of great significance to study the vibration response of variable-section beam with the consideration of inertia effect. Most past research focuses on the vibration response on uniform beams considering inertial effects, but there is little research on the vibration response of moving loads on variable section beam considering the inertia effect. In this paper, a variable section beam is simplified as a multi-stage ladder beam. Using the Euler-Bernoulli beam model, free-vibration characteristics and forced vibration characteristics of cantilever ladder beam are analysed. Following this step the vibration response considering the influence of the inertia effect is studied and compared with the situation that does not consider the influence of inertia effect. The results show that the mass, velocity, and acceleration of moving loads influence the effect of inertia on the response. Mass is the main factor affecting the results. The inertia effect caused by the acceleration and velocity can be ignored when the mass of moving load is small. The results have good engineering applicability.

Analysis of Elastic Beam Subjected to Moving Dynamic Loads

2011 ◽  
Vol 250-253 ◽  
pp. 1187-1191 ◽  
Author(s):  
Ren Zuo Wang ◽  
Shi Kai Chen ◽  
Chung Yue Wang ◽  
Bin Chin Lin
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Large Deformation ◽  
Moving Load ◽  
Elastic Beam ◽  
Dynamic Loads ◽  
Frame Structures ◽  
Moving Loads ◽  
Vector Form ◽  
Rigid Frame

The main object of this paper is to apply the vector form intrinsic finite element (VFIFE, or V-5) techniques in nonlinear large deformation dynamic analysis for the responses of moving loads on rigid frame structures. In this study, the simulation of moving loading is brought into the vector form intrinsic finite element method. It can effectively simulate the moving load. Comparing the results of the numerical simulations by VFIFE with the results obtained from other literatures, they are very close. It proved that VFIFE can effectively simulate the nonlinear large deformation dynamic problem.

scholarly journals Analysis of the Vibration of the Ground Surface by Using the Layered Soil: Viscoelastic Euler Beam Model due to the Moving Load

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Hong-Yuan Huang ◽  
Ming-Jie Zhao ◽  
Yao Rong ◽  
Yang Sun ◽  
Xiao Xiao
Keyword(s):  
Moving Load ◽  
Ground Surface ◽  
Surface Displacement ◽  
Layered Soil ◽  
Beam Model ◽  
Moving Loads ◽  
Subway Tunnel ◽  
Euler Beam ◽  
Maximum Value ◽  
Viscoelastic Characteristics

Moving loads will have a certain impact on the safety of the structures. Since concrete is a viscoelastic material, the elastic concrete model cannot describe its viscoelastic characteristics under moving loads. It is necessary to establish a model that can describe the viscoelastic characteristics of concrete materials. In addition, the layered of the soil is also an important factor affecting the propagation of subway vibration waves. Considering the effects of the properties of the concrete material of the subway tunnel structure and the layered soil foundation as well as the load velocity on the vibration of the ground surface caused by the moving load, the standard linear elastic solid Euler beam model is described for the subway tunnel structure in this paper. The equivalent stiffness of the layered soil-viscoelastic beam coupling system subjected to a moving load is formed by using the transmission and reflection matrix (TRM) method. The numerical solution of ground surface displacement caused by subway tunnel in time-space domain is obtained by IFFT algorithm. The correctness of the algorithm is verified by comparing with the reference results. Numerical results show that, with the increase of the viscous coefficient of the viscoelastic Euler beam, the vibration amplitude of the ground surface will decrease. Up to a certain value of the increasing the viscous coefficient of the Euler beam, it will have little effect on the vibration amplitude of the ground surface. Therefore, the standard solid model of viscoelastic Euler beam can well describe the creep and relaxation of materials. The model of viscoelastic beam is reasonable for the working condition of subway tunnel concrete structure. At high speed of moving load, the maximum value of ground surface displacement spectrum will appear at the smaller frequency domain and the maximum value of displacement spectrum will also increase for the soft layer soil, while it is opposite to that of the stiffer layer soil.

A Steadily Moving Load on an Elastic Beam Resting on a Tensionless Winkler Foundation

1979 ◽  
Vol 46 (1) ◽  
pp. 175-180 ◽  
Author(s):  
J. Choros ◽  
G. G. Adams
Keyword(s):  
Moving Load ◽  
Elastic Beam ◽  
Energy Criterion ◽  
Winkler Foundation ◽  
Coordinate Systems ◽  
Bernoulli Beam ◽  
Concentrated Force ◽  
Closed Form Solutions ◽  
Euler Bernoulli Beam ◽  
Steady State Solutions

An infinitely long Euler-Bernoulli beam resting on a tensionless Winkler foundation is considered. Steady-state solutions are obtained for a downward directed concentrated force moving with constant speed. First, the critical load necessary to initiate separation of the beam from the foundation is determined for a range of speed. For loads greater than critical, one or more regions of noncontact can be expected to occur. Closed-form solutions of the differential equations are obtained in terms of local coordinate systems which significantly reduces the coupling among the various regions. The extent and location of the noncontact regions, as well as the corresponding beam deflections, are then determined for a range of force and speed. The results show that many solutions are possible and the final determination is based on an energy criterion.

Asymptotic derivation of a refined equation for an elastic beam resting on a Winkler foundation

2021 ◽  
pp. 108128652110238
Author(s):  
Barış Erbaş ◽  
Julius Kaplunov ◽  
Isaac Elishakoff
Keyword(s):  
Ad Hoc ◽  
Moving Load ◽  
Low Frequency ◽  
Elastic Beam ◽  
Winkler Foundation ◽  
One Dimensional ◽  
Beam Equations ◽  
Dimensional Equation ◽  
Phase And Group Velocities ◽  
Group Velocities

A two-dimensional mixed problem for a thin elastic strip resting on a Winkler foundation is considered within the framework of plane stress setup. The relative stiffness of the foundation is supposed to be small to ensure low-frequency vibrations. Asymptotic analysis at a higher order results in a one-dimensional equation of bending motion refining numerous ad hoc developments starting from Timoshenko-type beam equations. Two-term expansions through the foundation stiffness are presented for phase and group velocities, as well as for the critical velocity of a moving load. In addition, the formula for the longitudinal displacements of the beam due to its transverse compression is derived.

The Calculation of the Supporting Stress of Track Plate in Ballastless High-Speed Rail Structure

2011 ◽  
Vol 97-98 ◽  
pp. 3-9
Author(s):  
Yang Wang ◽  
Quan Mei Gong ◽  
Mei Fang Li
Keyword(s):  
Stress Distribution ◽  
High Speed ◽  
Design Theory ◽  
Moving Load ◽  
Structure Design ◽  
Track Structure ◽  
Beam Model ◽  
High Speed Rail ◽  
Slab Track ◽  
Ballastless Track

The slab track is a new sort of track structure, which has been widely used in high-speed rail and special line for passenger. However, the ballastless track structure design theory is still not perfect and can not meet the requirements of current high-speed rail and passenger line ballastless track. In this paper, composite beam method is used to calculate the deflection of the track plate and in this way the vertical supporting stress distribution of the track plate can be gotten which set a basis for the follow-up study of the dynamic stress distribution in the subgrade. Slab track plate’s bearing stress under moving load is analyzed through Matlab program. By calculation and analysis, it is found that the deflection of track plate and the rail in the double-point-supported finite beam model refers to the rate of spring coefficient of the fastener and the mortar.The supporting stress of the rail plate is inversely proportional to the supporting stress of the rail. The two boundary conditions of that model ,namely, setting the end of the model in the seams of the track plate or not , have little effect on the results. We can use the supporting stress of the track plates on state 1to get the distribution of the supporting stress in the track plate when bogies pass. Also, when the dynamic load magnification factor is 1.2, the track plate supporting stress of CRST I & CRST II-plate non-ballasted structure is around 40kPa.

Moving-load-induced vibrations of a moored floating bridge

1998 ◽  
Vol 66 (4) ◽  
pp. 435-461 ◽  
Author(s):  
Jong-Shyong Wu ◽  
Po-Yun Shih
Keyword(s):  
Moving Load ◽  
Floating Bridge

Analytical evaluation of track response in the vertical direction due to a moving load

2016 ◽  
Vol 23 (18) ◽  
pp. 2989-3006 ◽  
Author(s):  
Wlodzimierz Czyczula ◽  
Piotr Koziol ◽  
Dariusz Kudla ◽  
Sergiusz Lisowski
Keyword(s):  
Steady State ◽  
Moving Load ◽  
Vertical Direction ◽  
Vertical Displacement ◽  
Steady State Response ◽  
Concentrated Force ◽  
State Response ◽  
Weakly Coupled ◽  
Wide Range ◽  
Rail Deflection

In the literature, typical analytical track response models are composed of beams (which represent the rail) on viscoelastic or elastic foundations. The load is usually considered as a single concentrated force (constant or varying in time) moving with constant speed. Concentrated or distributed loads or multilayer track models have rarely been considered. One can find some interesting results concerning analysis of distributed loads and multilayer track structures that include both analytical and numerical approaches. However, there is a noticeable lack of sufficient comparison between track responses under concentrated or distributed load and between one and multilayer track models. One of the unique features of the present paper is a comparison of data obtained for a series of concentrated and distributed loads, which takes into account a wide range of track parameters and train speeds. One of the fundamental questions associated with the multilayer track model is the level of coupling between the rail and the vibrations of the sleepers. In this paper, it is proved that sleepers are weakly coupled with the rail if the track is without significant imperfections, and the steady-state response is analyzed for this case. In other words, sleeper vibrations do not influence the rail vibrations significantly. Therefore the track is analyzed by means of a two-stage model. The first step of this model determines rail vibration under a moving load, and then the sleeper vibration is calculated from previously obtained kinematic excitation. The model is verified by comparison of the obtained results with experimental data. Techniques based on Fourier series are applied to the solution of the steady-state track response. Another important problem associated with track response under moving loads arises from the analysis of the effect of longitudinal forces in rails on vertical displacement. It is shown that, in the case of the steady-state response, longitudinal forces do not influence rail displacements significantly and this observation remains correct for a wide range of track parameters and train speeds. The paper also analyzes the legitimacy of the statement that additional rail deflection between sleepers, compared to the continuous rail support, can be considered as a track imperfection.

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