Vibrations of a track caused by variation of the foundation stiffness

The paper deals with the stochastic analysis of a single-degree-of-freedom vehicle moving at constant velocity along a simple track structure with randomly varying support stiffness. The track is modelled as an infinite Bernoulli-Euler beam resting on a Kelvin foundation, which has been modified by the introduction of a shear layer. The vertical spring stiffness in the support is assumed to be a stochastic homogeneous field consisting of a small random variation around a deterministic mean value. First, the equations of motion for the vehicle and beam are formulated in a moving frame of reference following the vehicle. Next, a first-order perturbation method is proposed to establish the relationship between the variation of the spring stiffness and the responses of the vehicle mass and the beam. Numerical examples are given for various parameters of the track. The response spectra obtained from the perturbation analysis are compared with the a numerical solution, in which finite elements with transparent boundary conditions are used. The circumstances, under which the first-order perturbation approach provides satisfactory results, are discussed.