Dynamics of a beam on a bilinear elastic foundation under harmonic moving load

The paper is dedicated to the dynamical analysis of an isolated concrete slab on an elastic foundation to moving load effect of one axle load. The computational models of one axle load and a slab are mathematically described by the system of ordinary differential equations. The equations of motion are solved numerically in the environment of program system MATLAB. The plate response and dynamic load are monitored at a certain speed and certain initial conditions, depending on the properties of the elastic subgrade.

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

Journal of Applied Mechanics ◽

10.1115/1.3423122 ◽

1973 ◽

Vol 40 (4) ◽

pp. 1040-1044 ◽

Cited By ~ 8

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.

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

Journal of Engineering for Industry ◽

10.1115/1.3591775 ◽

1969 ◽

Vol 91 (4) ◽

pp. 925-930 ◽

Cited By ~ 2

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.

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