On the Wave Solution for Beams on a Viscoelastic Foundation Subjected to a Travelling and Oscillating Force

Abstract

The motion of continuous systems under travelling loads is an interesting problem from the theoretical and practical point of view. Applications of the results in many fields of engineering cause that the problem is still the object of intensive investigations. The problem discussed in the present paper can be treated as a generalization of that formulated and partially solved by Mathews /1/ for the Bernoulli-Euler beam on an elastic foundation under a moving harmonically oscillating force. To solve the problem, Mathews introduced a moving coordinate system connected with the force and expressed the response of the beam in the form of standing waves, which allows to obtain the solution in a region of small velocities and frequencies bounded by the curve of a “critical” solution, cf. /1/. In the present analysis an alternative formulation of the problem is given which yields a solution in the form of travelling waves.