Multifrequency resonances of flexible linkages

摘要

In this paper, considering the geometric non-linearity due to the large elastic deformations of flexible links, the non-linear dynamic equation of elastic linkages is set up. Both the quadratic and cubic non-linearities are included in thenon-dimensional dynamic equation of the system. The multi-frequency resonances of motive mechanisms and static mechanisms, such as super-harmonic resonances and combination resonances, are investigated with the Method of Multiple Scales. The paper hasrevealed that the superharmonic resonances caused by the quadratic and cubic non-linearities as well as the multifrequency nature of inertial forces of motive mechanisms coincide with the critical speeds. and that the combination resonance caused by theinternal resonance and the cubic non-linearity as well as the multifrequency nature of inertial forces is the reason to produce the non-synchronism phenomenon of the critical speeds of the rocker and the coupler.