On the Oscillations of the Euler-Bernoulli Beam on an Elastic Base

Abstract

The oscillations of the Euler-Bernoulli beam on an elastic base under the influence of a moving normal load is considered. The Rayleigh and Timoshenko beam model in the calculations was used. To determine the beam displacements from an instantaneous point impact, which is represented as a product of Dirac delta functions, Fourier transforms in coordinate and time are used. The methodology and algorithm for solving the problem have been developed. In a general analytical form, the solution of the frequency equation is not possible, in a particular case, calculations in the MATLAB software package are performed. The analysis of the results shows that the deflections of the beam increase slightly when the speed of the train increases to a speed close to critical.