Parametric Excitation in a Self-exciting System : 2nd Report, Behaviors in the Regions of Resonances of Orders 1/3 and 2
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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, self-excitation and parametric excitation induce resonances of higher orders than orders 1 and 1/2. In the present paper firstly, behaviors in the region of subharmonic resonance of order 1/3 are investigated in the phase plane by using the averaging method. Next an approximate solution and the stability of a parametric resonance of order 2 is determined. In the neighborhood of this resonance a vibration with beat character occurs and then its amplitude is easily obtained. It is ascertained from the results of numerical calculation that the approximate solutions have high accuracy.
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関連論文
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