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.

The Stress State in Inhomogeneous Elastic Beam at Combined Strength

2014 ◽  
Vol 501-504 ◽  
pp. 645-648 ◽  
Author(s):  
Vladimir I. Andreev ◽  
Elena V. Barmenkova ◽  
Alena V. Matveeva
Keyword(s):  
Inverse Problem ◽  
Stress State ◽  
Modulus Of Elasticity ◽  
Elastic Beam ◽  
Bending Moment ◽  
Optimization Method ◽  
Theory Of Elasticity ◽  
Simultaneous Action ◽  
Concentrated Force ◽  
Inhomogeneous Bodies

In paper describes a method of optimization the stress state of an elastic beam, subjected to the simultaneous action of the central application of concentrated force and bending moment. Optimization method based on solving the inverse problem of the theory of elasticity of inhomogeneous bodies, the essence of which is to determine the law of changing the modulus of elasticity on the beams height for which stress state will be given.

scholarly journals Dynamic Response of a Beam Subjected to Moving Load and Moving Mass Supported by Pasternak Foundation

2012 ◽  
Vol 19 (2) ◽  
pp. 205-220 ◽  
Author(s):  
Rajib Ul Alam Uzzal ◽  
Rama B. Bhat ◽  
Waiz Ahmed
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Dynamic Response ◽  
Moving Load ◽  
Bending Moment ◽  
Dynamic Responses ◽  
Moving Mass ◽  
Pasternak Foundation ◽  
Partial Differential ◽  
Foundation Parameters

This paper presents the dynamic response of an Euler- Bernoulli beam supported on two-parameter Pasternak foundation subjected to moving load as well as moving mass. Modal analysis along with Fourier transform technique is employed to find the analytical solution of the governing partial differential equation. Shape functions are assumed to convert the partial differential equation into a series of ordinary differential equations. The dynamic responses of the beam in terms of normalized deflection and bending moment have been investigated for different velocity ratios under moving load and moving mass conditions. The effect of moving load velocity on dynamic deflection and bending moment responses of the beam have been investigated. The effect of foundation parameters such as, stiffness and shear modulus on dynamic deflection and bending moment responses have also been investigated for both moving load and moving mass at constant speeds. Numerical results obtained from the study are presented and discussed.

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.

scholarly journals Analytical Solution for the Boundary Value Problem of Euler-Bernoulli Beam Subjected to Accelerated Distributed Load

2021 ◽  
Vol 17 (1) ◽  
pp. 17-38
Author(s):  
Mustapha Adewale Usman ◽  
Fatai Akangbe Hammed ◽  
Debora Oluwatobi Daniel
Keyword(s):  
Analytical Solution ◽  
Dynamic Response ◽  
Boundary Value Problem ◽  
Moving Load ◽  
Boundary Value ◽  
Elastic Beam ◽  
Transportation Industry ◽  
Distributed Load ◽  
Wide Range ◽  
Order Four

The study of dynamic response of beam-like structures to moving or static loads has attracted and still attracting a lot of attention due to its wide range of applications in the construction and transportation industry especially when transverse by travelling masses. Hence, analytical solution for the boundary value problem (BVP) of elastic beams subjected to distributed load was investigated. The partial differential equation of order four were analysed to determine the dynamic response of the elastic beam under consideration and solved analytically. Effects of different parameters such as the mass of the load, the length of the moving load, the distance covered by the moving load, the speed of the moving and the axial force were considered. Result revealed that the values of the deflection with acceleration being considered increases than the system where acceleration of the moving load is negligible.

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.

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.

Effects of Moving Speeds of Dynamic Loads on the Deflections of Gear Teeth

1981 ◽  
Vol 103 (2) ◽  
pp. 357-363 ◽  
Author(s):  
K. Nagaya ◽  
S. Uematsu
Keyword(s):  
Dynamic Response ◽  
Timoshenko Beam ◽  
Gear Tooth ◽  
Bending Moment ◽  
Dynamic Loads ◽  
Gear Teeth ◽  
Moving Speed

For the dynamic response problems of gear teeth, the dynamic loads which act upon the gear teeth should be considered as a function of both the position and the moving speed. In previous studies, the effects of the moving speed have not been considered. In this paper the effects of the moving speed of dynamic loads on the deflection and the bending moment of the gear tooth are investigated. The results are obtained from the elastodynamic analysis of the tapered Timoshenko beam.

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