Nonlinear Dynamic Behavior Of The Inextensional Thick Ring Investigated

The research in ring oscillate has sustained for hundreds years.The stability and safety of ring is close related to the health operation of the whole mechanical system.Recently,some research notices the linear vibration characteristic of the inextensional ring considering the pre-stress and gyroscopic effect.However,those effects are neglected when the nonlinear behavior of the ring is analyzed.In this paper,we focus on the inextensional ring structure,whose in-plane dynamical model considering the rotational pre-stress and gyroscopic effect is set up.By the numerical solution of the motion equations of the model,the nonlinear behavior of ring is investigated.Our works are introduced as following:Firstly,using the energy principle,the kinetic energy of the rotational ring is derived,and the potential energy is obtained by the stress function considering pre-stress and flexible support spring.Then,by the variation principle,the motion equations of ring are set up.Next,the nth nonlinear mode functions of ring which meet the continuous and periodic conditions are employed to reduce the partial differential equations of model to nonlinear ordinary differential equations by applying the Galerkin's procedure.Finally,the response is obtained from the numerical solution,and the response history,phase diagram and Poincare map are used to analyze the nonlinear behavior of the inextensional ring.The result shows there are lots of quasi-periodic motions in the response.