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
_{}. |