Modeling for the Natural Vibration Analysis of a Rotating Thick Ring

회전하는 두꺼운 링의 고유진동 해석을 위한 모델링

In this paper, the equations of motion by which the natural vibration of rotating thick ring can be analyzed accurately are presented. These equations are derived from the theory of finite deformation and the principle of virtual work. The effects of variation in curvature across the ring cross-section can be considered in these equations. The ring models are called as thick ring model and thin ring model respectively as the effects of variation in curvature are considered or neglected. The radial displacement of ring which is rotating at constant angular velocity is determined by a non-linear equation derived from the principle of virtual work. The equations of the in-plane and out-of-plane vibrations at disturbed state are also formulated from the principle of virtual work. They can be expressed as the combination of the radial displacement at the steady state and the disturbed displacements about the steady state. The natural vibrations of rings with different thickness are analyzed by using the presented ring models and 3-dimensional finite element method to verify accuracy of the presented equations of motion. Its results are compared and discussed.