Random vibration of an elastic half-space subjected to a moving stochastic load

• An novel method is proposed to study ground vibration due to a moving random load.
• A closed-form solution of random vibration responses is derived in an integral form.
• The random responses in all subsonic, transonic and supersonic cases are analysed.

In this paper, a non-stationary random vibration problem of an elastic half-space under a moving stochastic load modelling the dynamic characteristic of the train load is studied. An analytical method combining the pseudo-excitation method (PEM) and Fourier transformation method (FTM) is proposed. Because the load is moving and random, the responses at fixed locations in the half-space have characteristics of evolutionary non-stationary randomness. By means of the FEM, the non-stationary random vibration analysis is transformed into a conventional moving pseudo harmonic load problem. A closed-form solution of random vibration responses is derived in an integral form, which avoids step-by-step integration in time domain and thus leads to great saving in computational time. An adaptive quadrature method is adopted in order to obtain the desired numerical results of the singular integrand with non-stationary power spectral density. Through numerical examples, the proposed method is first validated, and then the dynamics characteristics of the non-stationary random responses of the half-space in all subsonic, transonic and supersonic cases are analysed.