Browse > Article
http://dx.doi.org/10.5050/KSNVN.2006.16.1.057

Modeling for the Natural Vibration Analysis of a Rotating Thin Ring  

Kim, Chang-Boo (인하대학교 기계공학부)
Kim, Sehee (인하대학교 대학원 기계공학과)
Publication Information
Transactions of the Korean Society for Noise and Vibration Engineering / v.16, no.1, 2006 , pp. 57-65 More about this Journal
Abstract
In this paper, we present the principle of virtual work, from which the exact non-linear equations of motion of a rotating ring can be derived, by using the theory of finite deformation. For a thin ring of which the effect of variation in curvature across the cross-section is neglected, the radial displacement and the extensional stress are determined from the principle of virtual work at the steady state where the ring is rotating with a constant angular velocity. And also we formulate systematically the governing equations concerned to the in-plane vibrations and the out-of-plane vibrations at the disturbed state by using the principle of virtual work which is expressed with the disturbed displacements about the steady state. The formulated governing equations are classified by four models along the cases of considering or neglecting all or partly the secondary effects of flexural shear, rotary inertia, circumferential extension, and twist inertia. The natural vibrations of thin rings are analyzed, and its results are compared and discussed.
Keywords
Rotating Ring; Virtual Work; Finite Deformation; Thin Ring; In-plane Vibration; Out-of-plane Vibration; Secondary Effects;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Chidamparam, P. and Leissa. A. W., 1993, 'Vibrations of Planar Curved Beams, Rings, and Arches,' Appl. Mech. Rev., ASME, Vol. 46, No.9, pp. 467-483   DOI
2 Carrier, G. F., 1945, 'On the Vibration of the Rotating Ring,' Quarterly of Applied Mechanics, Vol.3, pp.235-245
3 Meirovitch, L., 1970, Methods of Analytical Dynamics, McGraw-Hill, New York
4 Bickford, W. B. and Reddy, E. S., 1985, 'On the In-plane Vibrations of Rotating Ring,' Journal of Sound and Vibration, Vol. 101, No. 1, pp. 13-22   DOI   ScienceOn
5 Bert, C. W. and Chen, T. L. C, 1978, 'On Vibration of a Thick Flexible Ring Rotating at High Speed,' Journal of Sound and Vibration, Vol. 61, No. 4, pp. 517-570   DOI   ScienceOn
6 Washizu, K., 1982, Variational Methods in Elasticity and Plasticity, Pergamon Press, Oxford
7 Endo, M., Hatamura, K., Sakata, M. and Taniguchi, O., 1984, 'Flexural Vibration of a Thin Rotating Ring,' Journal of Sound and Vibration, Vol.92, No. 2, pp. 261-272   DOI   ScienceOn
8 Bickford, W. B. and Maganty, S. P., 1986, 'Out-of-plane Vibrations of Thick Rotating Rings,' Journal of Sound and Vibration, Vol. 110, No. 1, pp. 121-127   DOI   ScienceOn
9 Kim, W. and Chung, J., 2002, 'Free Nonlinear Vibration of a Rotating Thin Ring with In-plane and Out-of-plane Motions,' Journal of Sound and Vibration, Vol. 258, No. 1, pp. 167-178   DOI   ScienceOn
10 Love, A. E. H., 1944, A Treatise on the Mathematical Theory of Elasticity, Dover, New York