Rotation of an elastically mounted unbalanced shaft may be in general
affected by its lateral vibration, due to a ''vibrational torque''. Th
is interaction is nonlinear, and can be neglected only in case of an u
nlimited power supply. Whenever the available power of the drive is co
mparable with power consumption due to vibration, various nonlinear ph
enomena may be observed, the most well-known of these being the so cal
led Sommerfeld effect - slowing down or complete capture of the shaft
at resonance. The corresponding steady-state motions and their stabili
ty can be studied by asymptotic methods, as applied to the governing n
onlinear set of two second-order equations. However, study of transien
t motions in general requires numerical solution. This numerical solut
ion is obtained here, and extensive parametric studies are performed o
f the Sommerfeld effect. In particular, the influence is evaluated of
damping ratio and slope of the torque-speed curve of the drive on a pa
ssage/capture threshold. The results of numerical simulation, as well
as experiments with a physical model, also demonstrate the effect of s
mooth passage through resonance with a limited power supply, based on
using a ''switch'' of suspension stiffness from a certain artificially
increased value to the design one. A brief description is presented a
lso of time-variant components of the resonant amplitude and rotationa
l frequency responses in the case of capture, as observed both in nume
rical simulation studies and in experiments. Whilst these components a
re small compared with the corresponding constant ones, i.e. steady-st
ate vibration amplitude and rotational frequency, the above observatio
ns indicate the possibility for periodic or chaotic nonstationarity in
the system's response.