Metrikine A.V., Tochilin M.V.


Steady-state vibrations of an elastic ring under a moving load


Journal of Sound and Vibration 232(3), 511-524, 2000



Summary. The steady-state response of an elastic ring to a uniformly moving load is considered. It is assumed that the ring is attached by visco-elastic springs to an immovable axis and the load is radial and point like. An exact analytical solution of the problem is obtained by applying the “method of images”. The ring patterns are analyzed. It is shown that for small velocities of the load the ring pattern is almost perfectly symmetric with respect to the loading point. If the load velocity is smaller, but comparable with the minimum phase velocity  of waves in the ring, the pattern becomes slightly asymmetric due to viscosity of the springs. When the load moves faster than , the pattern becomes wave-like and substantially asymmetric. The condition of resonance is found. It is shown that resonance occurs when either the ring length is divisible to the wavelength of a wave radiated by the load or the velocity of the load is close to .