STOCHASTIC FINITE-ELEMENTS FOR A BEAM ON A RANDOM FOUNDATION WITH UNCERTAIN DAMPING UNDER A MOVING FORCE

An infinitely long beam on an elastic foundation is subjected to a constant force which is moving with a constant speed along it. The beam rests on a random foundation the stiffness of which is a random function of the length co-ordinate. The coefficient of viscous damping is also a random variable. The steady state vibration is analyzed. It appears that a stochastic stationary process occurs, viewed by an observer moving together with the moving force. A stochastic finite element analysis by means of the first order perturbation and first order second-moment method provides an evaluation of the variance of the deflection and of the bending moment of the beam. The effects of several parameters and of various types of correlation functions are investigated. It is shown that the randomness of the foundation is of greater importance than the uncertainty in the damping. The dynamic and stochastic effects increase with increasing speed of the movement of the force in the subcritical domain, but decrease in the supercritical domain. The coefficient of variation of the deflection of the beam is larger than that of the bending moment at the point of application of the moving force. © 1993 Academic Press Limited.