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.

scholarly journals The edge waves on a Kirchhoff plate bilaterally supported by a two-parameter elastic foundation

2015 ◽  
Vol 23 (12) ◽  
pp. 2014-2022 ◽  
Author(s):  
J Kaplunov ◽  
A Nobili
Keyword(s):  
Phase Velocity ◽  
Elastic Foundation ◽  
Moving Load ◽  
Kirchhoff Plate ◽  
Winkler Foundation ◽  
Edge Waves ◽  
Bending Waves ◽  
Pasternak Elastic Foundation ◽  
Two Parameter ◽  
Limiting Value

In this paper, the bending waves propagating along the edge of a semi-infinite Kirchhoff plate resting on a two-parameter Pasternak elastic foundation are studied. Two geometries of the foundation are considered: either it is infinite or it is semi-infinite with the edges of the plate and of the foundation coinciding. Dispersion relations along with phase and group velocity expressions are obtained. It is shown that the semi-infinite foundation setup exhibits a cut-off frequency which is the same as for a Winkler foundation. The phase velocity possesses a minimum which corresponds to the critical velocity of a moving load. The infinite foundation exhibits a cut-off frequency which depends on its relative stiffness and occurs at a nonzero wavenumber, which is in fact hardly observed in elastodynamics. As a result, the associated phase velocity minimum is admissible only up to a limiting value of the stiffness. In the case of a foundation with small stiffness, asymptotic expansions are derived and beam-like one-dimensional equivalent models are deduced accordingly. It is demonstrated that for the infinite foundation the related nonclassical beam-like model comprises a pseudo-differential operator.

scholarly journals Dynamics of a beam on elastic foundation - impact of the bilinear characteristic of the foundation upon the propagation of the bending wave

2018 ◽  
Vol 178 ◽  
pp. 06008
Author(s):  
Traian Mazilu ◽  
Cristian Ioan Cruceanu
Keyword(s):  
Elastic Foundation ◽  
Piecewise Linear ◽  
Acoustic Power ◽  
Piecewise Linear Function ◽  
Railway Traffic ◽  
Beam On Elastic Foundation ◽  
Bending Waves ◽  
Rate Of Decay ◽  
Rail Deflection ◽  
The Impact

Rail is an important source of noise in the railway traffic and its acoustic power is depending on the rate of decay of vibration. The main characteristic of the track in terms of the vertical elasticity is the so-called track modulus which results from the load-rail deflection curve. In general, this curve is nonlinear and it can be approximated using piecewise linear function with bilinear characteristic. In this paper, the response of a beam on elastic foundation with bilinear characteristic due to constant and harmonic loads is investigated, pointing out the impact of the foundation characteristic on the rail response and the propagation of the bending waves along the track.

Steady-State Vibrations of a Beam on a Pasternak Foundation for Moving Loads

1980 ◽  
Vol 47 (4) ◽  
pp. 879-883 ◽  
Author(s):  
H. Saito ◽  
T. Terasawa
Keyword(s):  
Steady State ◽  
Constant Velocity ◽  
Moving Load ◽  
Equations Of Motion ◽  
Pasternak Foundation ◽  
Moving Loads ◽  
Euler Beam ◽  
Exponential Fourier Transform ◽  
Steady State Solutions ◽  
Beam Theories

The response of an infinite beam supported by a Pasternak-type foundation and subjected to a moving load is investigated. It is assumed that the load is uniformly distributed over the finite length on a beam and moves with constant velocity. The equations of motion based on the two-dimensional elastic theory are applied to a beam. Steady-state solutions are determined by applying the exponential Fourier transform with respect to the coordinate system attached to the moving load. The results are compared with those obtained from the Timoshenko and the Bernoulli-Euler beam theories, and the differences between the displacement and stress curves obtained from the three theories are clarified.

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