Browse > Article
http://dx.doi.org/10.3795/KSME-A.2003.27.1.042

Nonlinear Modelling for the Vibration Analysis of a Rotating Ring with the In-Plane/Out-of-Plane Deformations  

Kim, Won-Suk (한양대학교 BK21 기계분야 사업단)
Chung, Jin-Tai (한양대학교 공과대학 기계공학과)
Publication Information
Transactions of the Korean Society of Mechanical Engineers A / v.27, no.1, 2003 , pp. 42-47 More about this Journal
Abstract
Nonlinear models for a thin ring rotating at a constant speed are developed. The geometric nonlinearity of displacements is considered by adopting the Lagrange strain theory for the circumferential strain. By using Hamilton’s principle, the coupled nonlinear partial differential equations are derived, which describe the out-of-plane and in-plane bending, extensional and torsional motions. The natural frequencies are calculated from the linearized equations at various rotational speeds. Finally, the computation results from the nonlinear models are compared with those from a linear model. Based on the comparison, this study recommends which model is appropriate to describe the behavior of the rotating ring.
Keywords
Rotating Ring; Geometric Nonlinearity; In-Plane Flexural Vibration; Out-of-Plane Flexural Vibration; Stiffening Effect;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 Huang, S. C., and Soedel, W., 1987, 'Effects of Coriolis Acceleration on the Free and Forced In-plane Vibrations of Rotating Rings on Elastic Foundation,' Journal of Sound and Vibration, Vol. 115, pp. 253-274   DOI   ScienceOn
2 Evensen, D. A., 1966, 'Nonlinear Flexural Vibrations of Circular Rings,' ASME Journal of Applied Mechanics, Vol. 33, pp. 553-560   DOI
3 Carrier, G. F., 1945, 'On the Vibrations of the Rotating Ring,' Quarterly of Applied Mathematics, Vol. 3, pp. 235-245   DOI
4 Chung, J., Oh, J.-E., and Yoo, H. H., 2000, 'Nonlinear Vibration of a Flexible Spinning Disc with Angular Acceleration,' Journal of Sound and Vibration, Vol. 231, pp. 375-391   DOI   ScienceOn
5 Chung, J., Kang, N.-C., and Lee, J. M., 1996, 'A Study on Free Vibration of a Spinning Disk,' KSME International Journal, Vol. 10, pp. 138-145   DOI
6 Rao, S. S., and Sundararajan, V., 1969, 'In-plane Flexural Vibrations of Circular Rings,' ASME Journal of Applied Mechanics, Vol. 36, pp. 620-625   DOI
7 Natsiavas, S., 1994, 'Dynamics and Stability of Non-linear Free Vibration of Thin Rotating Rings,' International Journal of Non-Linear Mechanics, Vol. 29, pp. 31-48   DOI   ScienceOn
8 Bickford, W. B., and Reddy, E. S., 1985, 'On the In-plane Vibrations of Rotating Rings,' Journal of Sound and Vibration, Vol. 101, pp. 13-22   DOI   ScienceOn
9 Lee, S. Y., and Chao, J. C., 2000, 'Out-of-plane Vibrations of Curved Non-uniform Beams of Constant Radius,' Journal of Sound and Vibration, Vol. 238, pp. 443-458   DOI   ScienceOn
10 Kirkhope, J., 1976, 'Out-of-plane Vibration of Thick Circular Ring,' Proceedings of the American Society of Civil Engineers, Vol. 102, pp. 239-247
11 Maganty, S. P., and Bickford, W. B., 1987, 'Large Amplitude Oscillations of Thin Circular Rings,' ASME Journal of Applied Mechanics, Vol. 54, pp. 315-322   DOI
12 Eley, R., Fox, C. H. J., and McWilliam, S., 2000, 'Conolis Coupling Effects on the Vibration of Rotating Rings,' Journal of Sound and Vibration, Vol. 238, pp. 459-480   DOI   ScienceOn
13 Kim, S. K., Chung, J. and Lee, S. I., 2001, 'Nonlinear Vibration Analysis of a Rotating Ring,' Transactions of the KSME, A, Vol. 25, pp. 1119-1124   과학기술학회마을
14 Blevins, R. D., 1979, Formulas for Natural Frequency and Mode Shape, New York: Van Nostrand Reinhold Co., Chapter 9