%0 Generic
%D 2010
%T CODIMENSION-THREE BIFURCATIONS OF NONLINEAR VIBRATION-CONTROLLED SYSTEMS
%A 蔡循恒
%A 曾全佑
%P 21
%X The nonlinear dynamics of a vibration-controlled magnetic system are studied via a three-mode discretization of the governing partial differential equations. The analysis focuses specifically on the effects of modal coupling through the nonlinear terms in the system equation. A bifurcation analysis of the system is performed using sophisticated nonlinear theories, including the center manifold theory and the normal form theorem. The results show that when the first mode and the higher modes are excited simultaneously by the control forces, the three-mode approximation method predicts the existence of a triple zero degeneracy accompanied by complicated bifurcation phenomena. Comparing the dynamics structure predicted by the three-mode approximation model with that obtained from a single-mode approach, it is found that if the higher modes are excited by the control forces, the effects of modal coupling should be taken into consideration since a complicated dynamics structure may exist as a result.
%7 02
%8 2010 / 1