Abstract
The vertical oscillations of an infinite Bernoulli-Euler beam resting on a viscous inertial base with two elastic characteristics under the action of a deforming carriage which is continuously moving at a constant velocity is considered. The carriage, consisting of a system of rigid bodies with viscoelastic couplings between them, makes contact with the beam via viscoelastic springs at a finite number of points which allows the small vertical oscillations of the elements of the carriage to be described by a system of ordinary differential equations with constant coefficients. A technique is proposed for obtaining the asymptotic forms of the solution at long times. The asymptotic forms of the solutions are presented and they are analysed for certain types of loads.
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