Journal of the Korean Society of Manufacturing Process Engineers (한국기계가공학회지)

The Korean Society of Manufacturing Process Engineers (한국기계가공학회)
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Coupled Bending and Torsional Vibrations Analysis of Cracked L-shaped Beam

크랙을 가진 L형 단면 보의 횡-비틀림 연성진동 해석

  • 손인수 (동의대학교 기계공학과) ;
  • 김창호 (동의대학교 기계공학과) ;
  • 조정래 (한국폴리텍VI대학 달성캠퍼스 자동차과)
  • Received : 2011.02.07
  • Accepted : 2011.08.08
  • Published : 2011.08.31
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Abstract

In this paper, the influence of a crack on the natural frequency of cracked cantilever L-shaped beam with coupled bending and torsional vibrations by analytically and experimentally is analyzed. The L-shaped beam with a crack is modeled by Hamilton's principle with consideration of bending and torsional energy. The two coupled governing differential equations are reduced to one sixth-order ordinary differential equation in terms of the flexural displacement. The crack is assumed to be in the first, second and third mode of fracture and to be always opened during the vibrations. The theoretical results are validated by a comparison with experimental measurements. The maximal difference between the theoretical results and experimental measurements of the natural frequency is less than 7.5% in the second vibration mode.

Keywords

References

  1. Datta, P. K. and Lal, M. K., "Parametric Instability of a Non-prismatic Bar with Localized Damage Subjected to an Intermediate Periodic Axial Load", Computer and Structures, Vol. 4, No. 6, pp. 1199-1202, 1992.
  2. 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
  3. Chondros, T. G., Dimarogonas, A. D. and Yao, J., "A Continuous Cracked Beam Vibration Theory", Journal of Sound and Vibration, Vol. 215, No. 1, pp. 17-34, 1998. https://doi.org/10.1006/jsvi.1998.1640
  4. Tsai, T. C. and Wang, Y. Z., "The Vibration of a Multi-crack Rotor", International Journal of Mechanical Science, Vol. 39, No. 9, pp. 1037-1053, 1997. https://doi.org/10.1016/S0020-7403(97)00005-2
  5. Chondros, T. G., Dimarogonas A. D. and Yao, J., "Vibration of a Beam with a Breathing Crack", Journal of Sound and Vibration, Vol. 229, No. 1, pp. 57-67, 2001.
  6. Owolabi, G. M., Swamidas, A. S. J. and Seshadri, R., "Crack Detection in Beams Using Changes in Frequencies and Amplitudes of Frequency Response Functions", Journal of Sound and Vibration, Vol. 265, No. 1, pp. 1-22, 2003. https://doi.org/10.1016/S0022-460X(02)01264-6
  7. 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
  8. Lee, Y. S. and Sheu, J. J., "Free Vibration of an Extensible Rotating Inclined Timoshenko Beam", Journal of Sound and Vibration, Vol. 304, pp. 606-624, 2007. https://doi.org/10.1016/j.jsv.2007.03.005
  9. Loya. J. A., Rubio., L. and Fernandez-Saez, L., "Natural Frequency for Bending Vibration of Timoshenko Cracked Beam", Journal of Sound and Vibration, Vol. 290, No 3-5, pp. 640-653, 2006. https://doi.org/10.1016/j.jsv.2005.04.005
  10. Lele, S. P. and Maiti, S. K., "Modelling of Transverse Vibration of Short Beams for Crack Detection and Measurement of Crack Extension", Journal of Sound and Vibration, Vol. 257, No. 3, pp. 559-583, 2002. https://doi.org/10.1006/jsvi.2002.5059
  11. Li, J., Shen, R., Hua, H. and Jin, X., "Response of Monosymmetric Thin-walled Timoshenko Beams to Random Excitations", International Journal of Solids and Structures, Vol. 41, pp. 6023-6040, 2004. https://doi.org/10.1016/j.ijsolstr.2004.05.030
  12. Viola, E., Ricci, P. and Aliabadi, M. N., "Free Vibration Analysis of Axially Loaded Cracked Timoshenko Beam Structures Using the Dynamic Stiffness Method", Journal of Sound and Vibration, Vol. 304, pp. 124-153, 2007. https://doi.org/10.1016/j.jsv.2007.02.013
  13. Ricci, P. and Viola, E., "Stress Intensity Factors for Cracked T-sections and Dynamic Behaviour of T-beams", Engineering Fracture Mechanics, Vol. 73, pp. 91-111, 2006. https://doi.org/10.1016/j.engfracmech.2005.06.003
  14. Son, I. S. and Jo. J. R., "Stability Analysis of Cracked Cantilever T-beams Subjected to Subtangential Follower Force", Journal of KSMPE, Vol. 9, No. 3, pp. 49-55, 2010.
  15. Li, J., Li, W., Shen, R. and Hua, H., "Coupled Bending and Torsional Vibration of Nonsymmetrical Axially Loaded Thin-walled Bernoulli-Euler Beams", Mechanics Research Communications, Vol. 31, pp. 697-711, 2004. https://doi.org/10.1016/j.mechrescom.2004.04.005