Dynamic finite element analysis of a nonlinear beam subjected to a moving load

In this paper, the deterministic and random vibration analysis of a nonlinear beam on an elastic foundation subjected to a moving load, which may simulate railway track, runway, etc. has been performed. The effects of longitudinal deflection and inertia have been considered so that the coupled equations of longitudinal and transverse deflections can be derived based on Bernoulli-Euler hypothesis. The randomness of the beam profile has been considered in such a way that the mean line of the beam is variable with respect to position in the vertical plane and is superimposed by stochastic uncertainty, and the moving load travels along the beam with constant velocity or acceleration. The deterministic and statistical dynamic responses of the beam have been calculated by using the Galerkin's method in conjunction with the finite element method, and the derived nonlinear system differential equation has been solved by using the implicit direct integration method. In particular, the standard deviation of the transverse deflection of the nonlinear beam has been calculated and presented by using the Monte Carlo simulation technique. Also, the distribution of the midpoint deflection of the beam has been investigated by using the probability paper plot.