DOI QR코드

DOI QR Code

Study on the Stability of Cantilevered Pipe Conveying Fluid Subjected to Distributed Follower Force

분포종동력을 받는 외팔 송수관의 안정성에 관한 연구

  • 공창덕 (조선대학교 항공우주공학과) ;
  • 박요창 (충남대학교 대학원 기계공학과)
  • Published : 2005.04.01

Abstract

The paper discussed on the stability of cantilevered pipe conveying fluid subjected to distributed follower force. Governing equations of motion are derived by extended Hamilton's principle, and the numerical scheme using finite element method is applied to obtain the discretized equations. The critical flow velocity as a function of the distributed follower force for the various mass ratio is determined. The flutter configurations of the pipes at the critical flow velocities are drawn graphically at every twelfth period to define the order of quasi-mode of flutter configuration The critical mass ratios, at which the transference of the eigenvalue branches related to flutter take place, are definitely determined. Also, the effect of damping on the stability of the system is considered.

본 연구에서는 분포 종동력을 받는 외팔 송수관의 안정성에 대하여 연구하였다. 지배 운동 방정식은 확장 해밀턴의 원리에 의해 유도 되었으며, 유한 요소법에 의해 수치해석이 이루어 졌다. 다양한 질량비에 대하여 분포 종동력 값에 따른 임계 유속 값을 결정하였다. 임계 유속에서의 플러터 모드 형상의 차수를 결정하기 위하여 1/12의 주기로 그려, 질량비에 따른 임계 유속의 그래프에 있어서 플러터가 발생하는 고유치 분기의 차수와 함께 명기하였다. 또한 내부감쇠가 시스템의 안정성에 미치는 영향을 조사하였다.

Keywords

References

  1. Beck, M., 'Die Knicklast des einseitig eingespannten, tangential gedrckten Stabes', ZAMP, VoI.3(3), 1952, pp.225-228 https://doi.org/10.1007/BF02008828
  2. Park, Y. and Mote, C. D., 'The Maximum Controlled Follower Force on a Free-Free Beam Carrying a Concentrated Mass', Journal of Sound and Vibration, Vol. 98(3), 1985, pp.247-256 https://doi.org/10.1016/0022-460X(85)90388-8
  3. Langthjem, M. A. and Sugiyama, Y. 'Dynamic stability of columns subjected to follower loads: A survey', Journal of Sound and Vibration, Vol. 238(5), 2000, pp.809-851 https://doi.org/10.1006/jsvi.2000.3137
  4. Bourrieres, F. J., 'Sur un phenomene d'oscillation auto-entretenue en mecanique des fluides reels', Publications Scientifiques et Techniques du Ministere de l' Air, 1939, No.147
  5. Benjamin, T. B., 'Dynamics of a System of Articulated Pipes Conveying Fluid (I. Theory)', Proceedings of the Royal Society, Series A, Vol.261, 1961, pp.457-486
  6. Benjamin, T. B., 'Dynamics of a System of Articulated Pipes Conveying Fluid (II.Experiment)', Proceedings of the Royal Society, Series A, Vol.261, 1961, pp.487-499
  7. Gregory, R. W. and Paidoussis, M. P., 'Unstable Oscillation of Tubular Cantilevers Conveying Fluid(I. Theory)', Proceedings of the Royal Society (London), Series A, Vo1.293, 1961, pp.512-527
  8. Gregory, R. W. and Paidoussis, M. P., 'Unstable Oscillation of Tubular Cantilevers Conveying Fluid(II. Experiment)', Proceedings of the Royal Society (London), Series A, Vol.293, 1961, pp.528-542.
  9. Paidoussis, M. P. 'Dynamics of vertical tubular cantilevers conveying fluid', Mechanical Engineering Research Laboratories Erport MERL 69-3, Department of Mechanical Engineering, McGill University, Montreal, Quebec, Canada, 1969
  10. Hill, J, L. and Swanson, C. P. 'Effects of lumped masses on the stability of fouid cinveying tubes', Journal of Applied Mechanics 37, 1970, pp.494-497 https://doi.org/10.1115/1.3408533
  11. Paidoussis, M. P. 'Dynamics of tubular cantilevers conveying fluid', Journal of Mechanical Engineering Science 12, 1970, pp.85-103 https://doi.org/10.1243/JMES_JOUR_1970_012_017_02
  12. Sugiyama, Y., Tanaka, T., Kishi T. and Kawagoe, H. 'Effect of a Spring Support on the Stability of Pipes Conveying Fluid', Journal of Sound and Vibration, Vol. 100, 1985, pp.257-270. https://doi.org/10.1016/0022-460X(85)90419-5
  13. Sugiyama, Y., Matsumoto, S. and Iwatsubo, T, 'Studies on Stability of Two-Degree-of-Freedom Artculated Pipes Conveying Fluid (The Effect of a Damper), Jour. Jpn. Soc. Mech. Eng., (in Japanese) Vol.52, No. 85, 1986, pp.264-270
  14. Leipholz, H., 'Stability of Elastic Systems', Sijthoff & Noordhoff, Alphen aan den Rijn, 1962
  15. Ryu, S. U, Sugiyama, Y. and Ryu, B. J., 'Eigenvalue Branches and Modes for Flutter of Cantilevered Pipes Conveying Fluid', Computers and Structures, Vol. 80, 2002, pp.1231-1241 https://doi.org/10.1016/S0045-7949(02)00083-4
  16. Becker, O., 'Zum Stabilitatsverhalten des dur- chstromten garaden Rohres mit elasticher Ouerstutyung', Maschinenbautechnik, Vol.28, 1979, pp.325-327