Parametric excitation with an asymmetric characteristic in a self-exciting system. (1st report, Behaviors of region of resonance of order 1/2)

Abstract

Behaviors of a self-exciting system 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 of 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. Since a squared nonlinearity merely makes the resonance have a constant component, it is found that a cubic nonlinearity plays more important parts in the occurrence of the resonance.