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Free Vibration of a Rotating Ring on an Elastic Foundation

Research paper by Hu Ding, Minghui Zhu, Zhen Zhang, Ye-Wei Zhang, Li-Qun Chen

Indexed on: 31 Jul '17Published on: 17 May '17Published in: International journal of applied mechanics



Abstract

International Journal of Applied Mechanics, Ahead of Print. In the present paper, free vibration of a rotating ring supported by an elastic foundation is studied by analytical method, finite element (FE) simulation and experiment. By adopting the ring analogy of Timoshenko beam theory, the nonlinear vibration of the rotating ring on an elastic foundation is modeled based on Hamilton’s principle. Radial and tangential deformation are considered. By solving the generalized eigenvalue problem, natural frequencies and flexural modes are obtained. Furthermore, the Euler–Bernoulli (E–B) theory is also employed to investigate the free vibration. For determining the necessity of the Timoshenko theory, the flexural vibration frequencies from two theories are compared. Specifically, the effects of the radius and the radial height (the thickness) of the ring on the difference between the two models are studied. In order to confirm the analytical results, finite element analysis and experiments on three test specimens are used to verify the natural frequency and flexural mode predictions. Overall, this work shows the necessity of the Timoshenko theory for studying free vibration of an elastic ring.