Parametric Excitation with an Asymmetric Characteristic in a Self-exciting System

Behaviors of a self-exciting system of van der Pol type subjected to a parametric excitation are investigated. In the present paper the parametric excitation is expressed by the product of a nonlinear function of deflection with an asymmetric characteristic and a periodic function of time. A resonance of order 1/2 and the solution in the neighborhood of the resonance are obtained by the averaging method and the effects of nonlinearity are investigated. since a squared nonlinearity merely makes the resonance have a constant component, it is found that a cubic nonlinearity plays a more important part in the occurrence of the resonance.