On the Response of a Beam Subjected to a Cyclic Moving Load

1969 ◽  
Vol 91 (4) ◽  
pp. 925-930 ◽  
Author(s):  
P. G. Kessel ◽  
A. L. Schlack
Keyword(s):  
Natural Frequency ◽  
Elastic Foundation ◽  
Infinite Number ◽  
Circular Cylindrical Shell ◽  
Moving Load ◽  
Relative Importance ◽  
Steady State Response ◽  
Rotatory Inertia ◽  
State Response ◽  
Load Movement

A theoretical analysis is presented on the damped steady state response of a simply supported beam on an elastic foundation subjected to a cyclic moving load that oscillates longitudinally along the beam about a fixed point. Loadings of this type have been recently shown to yield an infinite number of load movement frequencies that will excite resonance of a given natural frequency of an elastic member or system of members. It is the purpose of this investigation to introduce damping into the problem in order to determine both the absolute and relative importance of this infinite number of load movement frequencies that will excite a given natural frequency of a beam. The mathematical analogy between the problem of a beam resting on an elastic foundation and that of a long circular cylindrical shell with axial and rotatory inertia neglected is noted. Hence the results obtained are applicable to either problem. Numerical results are presented to illustrate the effects of damping, frequency of oscillation of load movement and amplitude of load movement on the dynamic deflection of the beam.

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.

DLSFEM–PML formulation for the steady-state response of a taut string on visco-elastic support under moving load

Meccanica ◽  
2019 ◽  
Vol 55 (4) ◽  
pp. 765-790 ◽  
Author(s):  
Diego Froio ◽  
Egidio Rizzi ◽  
Fernando M. F. Simões ◽  
António Pinto da Costa
Keyword(s):  
Steady State ◽  
Moving Load ◽  
Elastic Support ◽  
Steady State Response ◽  
State Response ◽  
Taut String

Moving Load on a Fluid-Solid Interface: Subsonic and Intersonic Regimes

1973 ◽  
Vol 40 (4) ◽  
pp. 885-890 ◽  
Author(s):  
T. C. Kennedy ◽  
G. Herrmann
Keyword(s):  
Steady State ◽  
Moving Load ◽  
Point Load ◽  
Numerical Results ◽  
Plane Interface ◽  
Steady State Response ◽  
State Response ◽  
Solid Interface

The steady-state response of a semi-infinite solid, with an overlying semi-infinite fluid, subjected at the plane interface to a moving point load is determined for subsonic and intersonic load velocities. Some numerical results for the displacements at the interface are presented and compared to the results obtained in the absence of the fluid.

Forced Lateral Vibration of a Uniform Cantilever Beam With Internal and External Damping

1960 ◽  
Vol 27 (3) ◽  
pp. 551-556 ◽  
Author(s):  
Ho Chong Lee
Keyword(s):  
Steady State Response ◽  
Lateral Vibration ◽  
Rotatory Inertia ◽  
Stress Strain ◽  
Inertia Effects ◽  
State Response ◽  
Spring Element ◽  
Stress Strain Relation ◽  
Tabular Method ◽  
Strain Relationship

The steady-state response problem of a uniform beam with a sinusoidal shaking force at the base is studied for the case where the beam material is the general linear substance represented by a model having an additional spring element in parallel with the Maxwell elements. In the analysis, the stress-strain relationship is applied only to the longitudinal strain of the beam, leaving the shear stress-strain relation to be that of a perfectly elastic material. The exact solution with a numerical example is given for one case where the shear and rotatory inertia effects are neglected. This result is compared with the solution obtained by a tabular method. The results of both methods are in excellent agreement.

Moving Load on a Fluid-Solid Interface: Supersonic Regime

1973 ◽  
Vol 40 (1) ◽  
pp. 137-142 ◽  
Author(s):  
T. C. Kennedy ◽  
G. Herrmann
Keyword(s):  
Steady State ◽  
Closed Form ◽  
Moving Load ◽  
Closed Form Solution ◽  
Point Load ◽  
Form Solution ◽  
Steady State Response ◽  
Entire Space ◽  
State Response ◽  
Supersonic Regime

The steady-state response of a semi-infinite solid with an overlying semi-infinite fluid subjected at the plane interface to a moving point load is determined for supersonic load velocities. The exact, closed-form solution valid for the entire space is presented. Some numerical results for the displacements at the interface are calculated and compared to the results obtained when no fluid is present.

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