Study On Vibration Characteristics Of Wound Ring

As a common part of mechanical structure,the vibration characteristics and stability of ring have been studied from the last century to the present,but there are little reports on the nonlinear vibration characteristics and stability of the inextensional ring.In this thesis,a constant torque flexure hinge on a spacecraft antenna based on annular structure is studied.The dynamic characteristics of a ring system are considered when the ring is subjected to winding force.For this kind of rotating ring affected by winding force,it is more suitable to use the inextensional ring model to model the moving system,and the influence of gyro effect is considered in the modeling.The specific work of this paper is as follows:Firstly,a thin ring rotating at a constant speed is used as the object of study.In this thesis,by using Hamiltonian principle and variational method,the equation of motion of the winding ring is established.The influences of external load,elastic support and structural damping on the vibration characteristics of the ring system are considered when establishing the potential energy function and kinetic energy function of the ring system.The expression of winding force is derived according to the balance of force on the ring system.Secondly,the steady-state analysis is performed on the resulted equations of motion.The equations of motion are simplified by Lagrange multiplier method and inextensional condition of rings.According to the simplified equations of motion,the natural frequencies of four different cases are obtained respectively.It is concluded that the damping has little effect on the natural frequency,while the gyroscopic moment plays a great role on the natural frequency.Then,the equations of motion are obtained by using the Galerkin method to separate variables.The nonlinear partial differential equation is transformed into a system of nonlinear ordinary differential equations with variable coefficients.The approximate analytical solution of the motion equation is obtained by using the multiscale method applicable to the gyro system.The nonlinear algebraic equations are obtained according to the steady-state conditions.Then,Lyapunov stability theory is used to analyze the stability of the ring system.Finally,the Julia combined with Newton-Raphson method is used to perform numerical experiments on the approximate analytical solution,and the amplitude-frequency characteristic curves are drawn,and the global nonlinear dynamic characteristics of the system are analyzed.Runge-kutta method is used to solve nonlinear ordinary differential equations,and the time history diagrams,phase diagrams and Poincare maps of different excitation amplitudes and friction factors at bifurcation points are drawn.Based on this,the local nonlinear dynamic characteristics of the system are analyzed,and the nonlinear behaviors such as period-double and chaotic motion are revealed in the vibration response of the ring.The conclusions obtained in this thesis provide theoretical support for the stability and safety of spacecraft flexure hinge structure,and have a deeper understanding of nonlinear vibration characteristics of the ring system under the action of winding force,so as to provide some help for the design and vibration analysis of such torus system.