Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

New formulation for vibration analysis of Timoshenko beam with double-sided cracks

  • Ayatollahi, M.R. (Fatigue and Fracture Laboratory, Department of Mechanical Engineering, Iran University of Science and Technology) ;
  • Hashemi, R. (Fatigue and Fracture Laboratory, Department of Mechanical Engineering, Iran University of Science and Technology) ;
  • Rokhi, H. (Fatigue and Fracture Laboratory, Department of Mechanical Engineering, Iran University of Science and Technology)
  • Received : 2008.04.28
  • Accepted : 2009.11.27
  • Published : 2010.03.10
⟨ Previous Next ⟩

Abstract

It is the intention of this study to synthesize the effects of double-edge cracks on the dynamic characteristics of a beam. The stiffness matrix is first determined for a Timoshenko beam containing two same-line edge cracks. The presented model is then developed for elements with two parallel double-sided cracks, considering the interaction between the stress fields of adjacent cracks. Finally, a finite element code is implemented, to examine the influence of depth and location of double cracks, on the natural frequencies of the damaged system.

Keywords

References

  1. Abraham, O. and Brandon, J.A. (1995), "The modeling of the opening and closure of a crack", J. Vib. Acoustic., 117, 370-377. https://doi.org/10.1115/1.2874463
  2. Anifantis, N. and Dimarogonas, A.D. (1980), "Stability of columns with single crack subjected to follower and vertical loads", Int. J. Solids Struct., 19, 281-291.
  3. Boltezar, M., Strancar, B. and Kuhelj, A. (1998), "Identification of transverse crack location in flexural vibration of free-free beams", J. Sound Vib., 211, 729-734. https://doi.org/10.1006/jsvi.1997.1410
  4. Chen, L.W. and Chen, C.L. (1988), "Vibration and stability of cracked thick rotating blades", Comput. Struct., 28, 67-74. https://doi.org/10.1016/0045-7949(88)90093-4
  5. Chen, L.W. and Jeng, C.J. (1993), "Vibration analysis of cracked pre-twisted blades", Comput. Struct., 46, 133- 140. https://doi.org/10.1016/0045-7949(93)90173-B
  6. Chondors, T.G. and Dimarogonas, A.D. (1980), "Identification of cracks in welded joints of complex structures", J. Sound Vib., 69, 531-538. https://doi.org/10.1016/0022-460X(80)90623-9
  7. Christides, S. and Barr, A.D. (1984), "On-Dimensional theory of cracked Bernoulli-Euler beams", Int. J. Mech. Sci., 26, 639-648. https://doi.org/10.1016/0020-7403(84)90017-1
  8. Dansheng, W., Hongping, Z., Chuanyao, C. and Yong, X. (2007), "An impedance analysis for crack detection in the Timoshenko beam based on the anti- resonance technique", Acta Mech. Solida Sin., 20, 228-235. https://doi.org/10.1007/s10338-007-0727-8
  9. Dentsoras, A.J. and Dimarogonas, A.D. (1983), "Resonanse controlled fatigue crack propagation", Eng. Fract. Mech., 17, 381-386. https://doi.org/10.1016/0013-7944(83)90088-7
  10. Dimarogonas, A.D. (1976), Vibration Engineering, St. Paul (Minnesota), West publisher.
  11. Dimarogonas, A.D. and Massouros, G. (1980), "Torsional vibration of a shaft with a shaft with a circumferential crack", Eng. Fract. Mech., 15, 439-444.
  12. Douka, E. and Hadjileontaidis, L.J. (2005), "Time-frequency analysis of the free vibration response of a beam with a breathing crack", NDT&E Int., 38, 3-10. https://doi.org/10.1016/j.ndteint.2004.05.004
  13. Ghondros, T.G. and Dimarogonas, A.D. (1979), "Identification of cracks in circular plates welded at the contour", Proceedings of ASME Design Eng. Tech. Conf., Et. Louis, U.S.A., 79-DET-106.
  14. Gounaris, G. and Dimarogonas, A.D. (1988), "A finite element of a cracked prismatic beam for structural analysis", Comput. Struct., 28, 309-313. https://doi.org/10.1016/0045-7949(88)90070-3
  15. Gounaris, G., Anifantis, N. and Dimarogonas, A.D. (1991), "Dynamics of cracked hollow beams", Eng. Fract. Mech., 39, 931-940. https://doi.org/10.1016/0013-7944(91)90101-6
  16. Haisty, B. and Springer, W. (1988), "A general beam element for use in damage assessment of complex structures", J. Vib. Acoust. Stress Reliab., 251, 13-38.
  17. Khaji, N., Shafiei, M. and Jalalpour, M. (2009), "Closed-form solutions for crack detection problem of Timoshenko beams with various boundary conditions", Int. J. Mech. Sci., 51, 667-681. https://doi.org/10.1016/j.ijmecsci.2009.07.004
  18. Kisa, M. and Brandon, J. (2000), "The effects of closure of cracked on the dynamics of a cracked cantilever beam", J. Sound Vib., 238, 1-18. https://doi.org/10.1006/jsvi.2000.3099
  19. Loya, J.A., Rubio, L. and Fernandez-Saez, J. (2006), "Natural frequencies for bending vibrations of Timoshenko cracked beams", J. Sound Vib., 290, 640-653. https://doi.org/10.1016/j.jsv.2005.04.005
  20. Qian, G.L., Gu, S.N. and Jiung, J.S. (1990), "The dynamic behavior and crack detection of a beam with a crack", J. Sound Vib., 138, 233-243. https://doi.org/10.1016/0022-460X(90)90540-G
  21. Shen, M.H. and Pierre, C. (1990), "Natural modes of Bernoulli-Euler beams with symmetric cracks", J. Sound Vib., 138, 115-134. https://doi.org/10.1016/0022-460X(90)90707-7

Cited by

  1. An inverse approach for the calculation of flexibility coefficient of open-side cracks in beam type structures vol.41, pp.2, 2012, https://doi.org/10.12989/sem.2012.41.2.285
  2. Vibration analysis of a cracked beam with axial force and crack identification vol.9, pp.4, 2010, https://doi.org/10.12989/sss.2012.9.4.355