Bifurcation and Chaos of Rotating Inextensional Ring

Abstract

Abstract In this paper, the nonlinear dynamics of the inextensional ring structure is investigated. Based on the elasticity theory and the assumption of the inextension of ring, a dynamical model of the ring is established considering the elastic support, the external load and the damping. Then, according to the Galerkin method, the nonlinear mode functions of inextensional ring are used to obtain the order differential equations of ring. Finally, the numerical simulation is carried out and the nonlinear behavior, such as double-period bifurcation, quasi-periodic motion and chaos, is discussed. And the effect of the disturbance of the rotating velocity on the nonlinear behavior of ring is investigated.