Transactions of the Korean Society for Noise and Vibration Engineering (한국소음진동공학회논문집)

The Korean Society for Noise and Vibration Engineering (한국소음진동공학회)
권호 표지
DOI QR코드

DOI QR Code

Natural Vibration Analysis of Thick Rings

두꺼운 링의 고유진동 해석

  • 박정우 (인하대학교 대학원 기계공학과) ;
  • 김세희 (인하대학교 대학원 기계공학과) ;
  • 김창부 (인하대학교 기계공학부)
  • Published : 2005.10.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we have systematically formulated the equations concerned to the in-plane and out-of-plane motions and deformations of a thick circular beam by using the kinetic and strain energies in order to analyse natural frequencies of a thick ring. The effects of variation of radius of curvature across the cross-section and also the effects of bending shear, extension and twist are considered. The equations of motion for natural vibration analysis of a ring are obtained utilizing the cyclic symmetry of vibration modes of the ring. The frequencies calculated using thick ring model and thin ring model are compared and discussed with the ones obtained from finite element analysis using the method of cyclic symmetry with 20-node hexahedral solid elements for rings with the different ratio of radial thickness to mean radius.

Keywords

References

  1. Rao, S. S. and Sundararajan, V., 1969, 'In -plane Flexural Vibrations of Circular Rings,' Transactions of ASME, Journal of Applied Mechanics, Vol. 91, pp. 620-625
  2. Rao, S. S., 1971, 'Effects of Transverse Shear and Rotary Inertia on the Coupled Twist-bending Vibrations of Circular Rings,' Journal of Sound and Vibration, Vol. 16, No. 4, pp. 551-566 https://doi.org/10.1016/0022-460X(71)90662-6
  3. Davis, R., Henshell, R. D. and Warburton, G. B., 1972 'Curved Beam Finite Elements for Coupled Bending and Torsional Vibration,' Earthquake Engineering and Structural Dynamics, Vol. 1, pp. 165-175 https://doi.org/10.1002/eqe.4290010205
  4. Kirkhope, J., 1976. 'Out-of-plane Vibration of Thick Circular Ring,' Journal of the Engineering Mechanics Division, ASCE, Vol. 102, No. EM2, pp. 239-247
  5. Lebeck, A. O. and Knowlton, J. S, 1985, 'A Finite Element for the Three-dimensional Deformation of a Circular Ring,' International Journal for Numerical Methods in Engineering, Vol. 21, pp. 421-435 https://doi.org/10.1002/nme.1620210304
  6. Davis, R., Henshell, R. D., and Warburton, G. B., 1972 'Constant Curvature Beam Finite Elements for In-plane Vibration,' Journal of Sound and Vibration, Vol. 25, No. 4, pp. 561-576 https://doi.org/10.1016/0022-460X(72)90478-6
  7. Kirkhope, J., 1977. 'In-plane Vibration of a Thick Circular Ring,' Journal of Sound and Vibration, Vol. 50, No. 2, pp. 219-227 https://doi.org/10.1016/0022-460X(77)90356-X
  8. Bickford, W. B. and Maganty, S. P., 1986, 'On the Out-of-plane Vibrations of Thick Rings,' Journal of Sound and Vibration, Vol. 108, No. 3, pp. 503-507 https://doi.org/10.1016/S0022-460X(86)80043-8
  9. Cowper, G. R., 1966, 'The Shear Coefficient in Timoshenko's Beam Theory,' Journal of Applied Mechanics, Vol. 33, pp. 335-340 https://doi.org/10.1115/1.3625046
  10. Sokolnikoff, I. S., 1956, Mathematical Theory of Elasticity, McGraw-Hill, New York
  11. 김창부, 안영철, 2000, '송풍기 임펠러의 순환대칭성을 이용한 고유치해석,' 한국소음진동공학회논문집, 제 10 권, 제 3 호, pp. 523-530
  12. 김창부, 최상현, 2002, '마이크로 3축 링 자이로스코프의 동역학,' 한국소음진동공학회논문집, 제 12 권, 제 12 호, pp. 1001-1009
  13. Kuhl, W., 1942, 'Messungen zu den Theorien der Eigenschingungen von Kreisringen Beliebiger Wandstarke,' Akustiche Zeitschrift, Vol. 7, pp, 125-152