A wave number based approach for the evaluation of the Green's function of a one-dimensional railway track model

A new wave number based approach is proposed for the evaluation of the time-domain Green's function for the railway track idealized as an infinite Euler-Bernoulli beam overlying a Pasternak-type viscoelastic foundation. In the proposed approach, the rail beam response is first computed in the time wave number domain by solving a generalized single-degree-of-freedom system problem using the classical Duhamel integral technique. The Green's function is subsequently evaluated by inverting the so-obtained time wave number solution to the time-space domain. In contrast with the conventional approach, the computational time for evaluating the Green's function using the proposed approach is much smaller. Further, the proposed solution of the Green's function is shown to be convenient for directly evaluating the time-domain response of a rail beam subjected to various types of time-dependent loads. As an illustration, the Green's function is applied to obtain the time-domain response of the rail beam (overlying a viscoelastic layer) subjected to a uniformly moving oscillator by using a novel and simple two-step iterative scheme. The time-domain deflection analysis reveals that the introduction of damping into the oscillator system brings the rail beam response much closer to that associated with the constant moving load idealization. However, if the moving oscillator system is acted upon by an arbitrarily time-varying external vertical load, significantly higher values of rail beam deflections are observed.