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

The steady state response of an elastic ring subjected to a uniformly movin g load is considered. It is assumed that the ring is attached by visco-elas tic 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 "metho d of images". The ring patterns are analyzed. It is shown that for small ve locities of the load the ring pattern is almost perfectly symmetric with re spect to the lending point. If the load velocity is smaller, but comparable with the minimum-phase velocity T-ph(min) of waves in the ring, the patter n becomes slightly asymmetric V-ph(min) the pattern becomes due to viscosit y of the springs. When the load moves faster than V-ph(min) wave-like and s ubstantially asymmetric. The condition of resonance is found. It is shown t hat resonance occurs when either the ring length is divisible to the wavele ngth of a wave radiated by the load or the velocity of the load is close to V-ph(min). (C) 2000 Academic Press.