종동력을 받는 티모센코 보의 안정성에 미치는 크랙과 끝질량의 영향

Effects of Crack and Tip Mass on Stability of Timoshenko Beam Subjected to Follower Force

  • 손인수 (동의대학교 기계공학과) ;
  • 윤한익 (동의대학교 기계공학과) ;
  • 안태수 (동의대학교 대학원 기계공학과)
  • 발행 : 2008.06.01

초록

In this paper, the stability of a cracked cantilever Timoshenko beam with a tip mass subjected to follower force is investigated. In addition, an analysis of the flutter instability(flutter critical follower force) and a critical natural frequency of a cracked cantilever Euler / Timoshenko beam with a tip mass subjected to a follower force is presented. The vibration analysis on such cracked beam is conducted to identify the critical follower force for flutter instability based on the variation of the first two resonant frequencies of the beam. Therefore, the effect of the crack's intensity, location and a tip mass on the flutter follower force is studied. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments. The crack is assumed to be in the first mode of fracture and to be always opened during the vibrations.

키워드

참고문헌

  1. Beck, M., "The Buckling Load of a Tangentially Loaded Beam Clamped on One Side," Z. Angew. Math. Phys., Vol. 3, pp. 225-228, 1952 https://doi.org/10.1007/BF02008828
  2. Leipholz, H., "Stability Theory," Academic Press, 1970
  3. Ruotolo, R., Surace, C., Crespo, P. and Storer, D., "Harmonic Analysis of the Vibrations of a Cantilevered Beam with a Closing Crack," Computers and Structures, Vol. 61, No. 6, pp. 1057-1074, 1996 https://doi.org/10.1016/0045-7949(96)00184-8
  4. Takahashi, I., "Vibration and Stability of a Cracked Shaft Simultaneously Subjected to a Follower Force with an Axial Force," Int. Journal of Solids and Structures, Vol. 35, No. 23, pp. 3071-3080, 1997 https://doi.org/10.1016/S0020-7683(97)00364-8
  5. Kim, K. H. and Kim, J. H., "Effect of a Crack on the Dynamic Stability of a Free-Free Beam Subjected to a Follower Force," Journal of Sound and Vibration, Vol. 233, No. 1, pp. 119-135, 2000 https://doi.org/10.1006/jsvi.1999.2793
  6. Wang, Q., "A Comprehensive Stability Analysis of a Cracked Beam Subjected to Follower Compression," Int. Journal of Solids and Structures, Vol. 41, No. 18-19, pp. 4875-4888, 2004 https://doi.org/10.1016/j.ijsolstr.2004.04.037
  7. Dado, M. H. F. and Abuzeid, O., "Coupled Transverse and Axial Vibration Behaviour of Cracked Beam with End Mass and Rotary Inertia," Journal of Sound and Vibration, Vol. 261, No. 4, pp. 675-696, 2003 https://doi.org/10.1016/S0022-460X(02)01004-0
  8. Son, I. S., Yoon, H. I. and Ahn, T. S., "Stability Analysis of Cracked Beam with Tip Mass and Follower Force," Transactions of KSNVE, Vol. 17, No. 7, pp. 605-610, 2007 https://doi.org/10.5050/KSNVN.2007.17.7.605
  9. Ryu, B. J., Shin, K. B. and Kim, H. J., "Influence of Partial Elastic Foundations on Dynamic Stability of a Cantilevered Timoshenko Beam with a Tip Mass under a Follower Force," Journal of KSPE, Vol. 22, No. 10, pp. 65-71, 2005
  10. Zhu, X., Li, T. Y., Zhao, Y. and Liu, J. X., "Structural Power Flow Analysis of Timoshenko Beam with an Open Crack," Journal of Sound and Vibration, Vol. 297, No. 1-2, pp. 215-226, 2006 https://doi.org/10.1016/j.jsv.2006.03.034
  11. Viola, E., Ricci, P. and Aliabadi, M. H., "Free Vibration Analysis of Axially Loaded Cracked Timoshenko Beam Structures Using the Dynamic Stiffness Method," Journal of Sound and Vibration, Vol. 304, No. 1-2, pp. 124-153, 2007 https://doi.org/10.1016/j.jsv.2007.02.013
  12. Harris, C. M., "Shock and Vibration Handbook (Fourth Edition)," McGraw-Hill, Chapter 7, 1961