Non-stationary random ground vibration due to loads moving along a railway track

The pseudo-excitation method (PEM) and the precise integration algorithm are combined to compute the non-stationary random ground vibration caused by loads moving along a railway track at constant speed. The rails are modeled as a single infinite Euler beam connected to sleepers and hence to ballast. This ballast rests on the ground, which is assumed to consist of layered transversely isotropic soil. The equations of motion of the system are established in a Cartesian coordinate system which moves with the loads. The non-stationary power spectral density and the time-dependent standard deviation can be derived conveniently by means of PEM, while the precise integration algorithm for two-point boundary value problems is applied to the solution of the equations of motion in the frequency/wavenumber domain. By virtue of the transverse isotropic property of the layered soils, the threefold iteration process in the frequency/wavenumber domain is reduced into a twofold iteration process. Hence the computational efficiency is improved considerably.