Abstract
Motivated by observations of low-frequency “snaking” motions of circular sawblades encountered during cutting operations, we study the large amplitude transverse vibrations of an imperfect, flexible, lightly damped, circular plate spinning near a critical speed resonance. Of particular interest are the effects of imperfection and the conditions under which low-frequency, amplitude and phase modulated traveling waves, that is snaking motions, can arise in this system. This is accomplished through a local bifurcation analysis of the first-order averaged equations governing the nonlinear interaction, under conditions of a 1 : 1 internal resonance, of a pair of backward and forward traveling waves. Experiments are performed at reduced ambient pressure on a rotating steel disk with imperfection induced through attached point masses, to confirm qualtitatively the analytical predictions. The experiments also indicate an unexplained, additional superposed slow motion on all solution branches.
