scholarly journals Closure to “Discussion of ‘Steady-State Vibrations of Beam on Elastic Foundation for Moving Load’” (1955, ASME J. Appl. Mech., 22, p. 436)

1955 ◽  
Vol 22 (3) ◽  
pp. 436
Author(s):  
J. T. Kenney
Keyword(s):  
Steady State ◽  
Elastic Foundation ◽  
Moving Load ◽  
Beam On Elastic Foundation

Steady-State Vibrations of Beam on Elastic Foundation for Moving Load

1954 ◽  
Vol 21 (4) ◽  
pp. 359-364
Author(s):  
J. T. Kenney
Keyword(s):  
Steady State ◽  
Elastic Foundation ◽  
Critical Velocity ◽  
Constant Velocity ◽  
Analytic Solution ◽  
Moving Load ◽  
Viscous Damping ◽  
Beam On Elastic Foundation ◽  
Bending Waves ◽  
Free Bending

Abstract This paper presents an analytic solution and resonance diagrams for a constant-velocity moving load on a beam on an elastic foundation including the effect of viscous damping. The limiting cases of no damping and critical damping are investigated. The possible velocities for the propagation of free bending waves are found and their relation to the critical velocity of the beam is studied.

Steady-State Responses of a Beam on Idealized Strain-Hardening Foundations for a Moving Load

1973 ◽  
Vol 40 (4) ◽  
pp. 1040-1044 ◽  
Author(s):  
T. M. Mulcahy
Keyword(s):  
Steady State ◽  
Strain Hardening ◽  
Elastic Foundation ◽  
Moving Load ◽  
Elastic Beam ◽  
Point Load ◽  
One Dimensional ◽  
Wide Range ◽  
Steady State Responses ◽  
State Responses

The steady-state responses to a point load moving with constant velocity on an elastic beam which rests on two types of idealized strain-hardening foundations are considered. The one-dimensional elastic-rigid foundation problem is shown to be equivalent to an elastic foundation with two traveling point loads. The opposing loads produce deflections which remain bounded for all load velocities and less than the corresponding elastic foundation results. The deflections of a one-dimensional elastic-perfectly plastic foundation are shown to be bounded for all load velocities. However, deflections significantly larger than the corresponding elastic foundation results occur over a wide range of velocities which are less than the elastic foundation critical velocity.

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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