Parametric Excitation in a Self-excited Vibration System : 3rd Report, The Influence of Cubic Non-linearity

抄録

In a self-excited vibration system with the restoring force expressed as the product of a non-linear function of deflection and a periodically variable coefficient, parametric resonances and subharmonic vibrations occur. In the present paper the influence of cubic non-linearity which is considered to induce subharmonic vibrations on such a system is investigated in detail. Approximate solutions of a system with the non-linear restoring force expressed as a cubic function are determined by the previously reported method. Consideration of that system without a self-excitation suggests the occurrence regions of a subharmonic resonance of order 1/2 and parametric resonances of first and second orders. In some numerical examples conforming to the suggestion, the system dealt with in the previous report is also considered in detail.