Response of an infinite beam on a locally inhomogeneous viscoelastic foundation interacting with a moving oscillator – The Green’s Function Approach

Transition zones in railway tracks require a high maintenance frequency which leads to high costs and delays. To better understand the underlying mechanisms, a one-dimensional model is used, consisting of an infinite Euler-Bernoulli beam resting on locally inhomogeneous viscoelastic Winkler foundation subjected to a moving oscillator. The governing equation is solved by means of the time-domain Green’s function method using convolution integrals in terms of the unknown contact force. To this end, the Green’s functions of the beam-foundation sub-system and of the oscillator are computed independently. They are combined through the nonlinear contact relation. The sources of nonlinearity are: the Hertzian contact relation and the possibility of contact loss between the oscillator and the beam. Results show that the contact force in the transition zone can reach 3-6 times the steady-state one. In some cases, the contact loss occurs at the oscillator velocity of around 75% of the critical velocity in the structure. The model can be used for preliminary design of transition zones in railway tracks, for preliminary predictions of a structure’s remaining life time and for fatigue predictions of a train’s wheelset.