Vibration of a periodically supported beam on an elastic half-space (Q1976212)

The authors consider the actual problem of steady-state vibrations of a periodically supported beam on an elastic half-space under a uniformly moving harmonically varying load. Such models are common for the description of railroad track. The rail is simulated as a beam, while supports reflect the properties of pads, sleepers, and track subsoil. Three-dimensional subsoil is replaced by a set of springs with a frequency-dependent stiffness. The stiffness has an imaginary part and is derived using Fourier transform. The existence of zeros of the equivalent stiffness means that there exists a critical regime of motion. For example, if the beam is subjected to a moving constant load and the velocity of motion tends to the velocity of Rayleigh waves, the steady-state beam displacements become infinite. This effect is of practical importance for high-speed trains, especially if the track subsoil is soft and the velocity of Rayleigh waves is about 200 km/h.