Abstract
In a self-exciting system of Van der Pol type with the restoring force expressed as the product of a non-linear function of deflection and a periodic function of time. parametric resonances and moreover subharmonic vibrations can occur. Steady state solutions in the regions of parametric resonance of first order and of subharmonic resonance of order l/2 and the stability are determined by a transformation to the rotating coordinate system and the averaging method. In the neighborhood of these resonances a beat phenomenon occurs and its amplitude is estimated by an approximate limit cycle. By numerical calculations it is ascertained that approximate solutions have high accuracy.
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