Smart Structures and Systems

  • 제9권4호
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  • Pages.355-371
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  • 2012
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  • 1738-1584(pISSN)
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  • 1738-1991(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Vibration analysis of a cracked beam with axial force and crack identification

  • Lu, Z.R. (Department of Mechanics, Sun Yat-sen University) ;
  • Liu, J.K. (Department of Mechanics, Sun Yat-sen University)
  • 투고 : 2011.05.25
  • 심사 : 2012.03.18
  • 발행 : 2012.04.25
⟨ 이전 논문 다음 논문 ⟩

초록

A composite element method (CEM) is presented to analyze the free and forced vibrations of a cracked Euler-Bernoulli beam with axial force. The cracks are introduced by using Christides and Barr crack model with an adjustment on one crack parameter. The effects of the cracks and axial force on the reduction of natural frequencies and the dynamic responses of the beam are investigated. The time response sensitivities with respect to the crack parameters (i.e., crack location, crack depth) and the axial force are calculated. The natural frequencies obtained from the proposed method are compared with the analytical results in the literature, and good agreement is found. This study shows that the cracks in the beam may have significant effects on the dynamic responses of the beam. In the inverse problem, a response sensitivity-based model updating method is proposed to identify both a single crack and multiple cracks from measured dynamic responses. The cracks can be identified successfully even using simulated noisy acceleration responses.

키워드

참고문헌

  1. Ayatollahi, M.R., Hashemi, R. and Rokhi, H. (2010), "New formulation for vibration analysis of Timoshenko beam with double-sided cracks", Struct. Eng. Mech., 34(4), 475-490. https://doi.org/10.12989/sem.2010.34.4.475
  2. Binici, B. (2005), "Vibration of beams with multiple open cracks subjected to axial force", J.Sound Vib., 287(1- 2), 277-295. https://doi.org/10.1016/j.jsv.2004.11.010
  3. Bokaian, H. (1988), "Natural frequencies of beams under axial compressive loads", J. Sound Vib., 126(1), 49-65. https://doi.org/10.1016/0022-460X(88)90397-5
  4. Chen, L.W. and Chen, C.U. (1988), "Vibration and stability of cracked thick rotating blades", Comput. Struct., 28(1), 67-74. https://doi.org/10.1016/0045-7949(88)90093-4
  5. Chaudhari, T.D. and Maiti, S.K. (2000), "A study of vibration geometrically segmented beams with and without crack", Int. J. Solids Struct., 37(5), 761-779. https://doi.org/10.1016/S0020-7683(99)00054-2
  6. Christides, A. and Barr, A.D.S. (1984), "One dimensional theory of cracked Bernoulli-Euler beams", Int. J. Mech. Sci., 26(11-12), 639-648. https://doi.org/10.1016/0020-7403(84)90017-1
  7. Da Silva, L.S., De Lima L.R.O. and Da S. Vellasco, P.C.G. (2004), "Behaviour of flush end-plate beam-tocolumn joints under bending and axial force", Steel Compos. Struct., 4(2), 77-94. https://doi.org/10.12989/scs.2004.4.2.077
  8. Dimarogonas, A.D. (1996), "Vibration of cracked structures: a state of the art review", Eng. Fract. Mech., 55(5), 831-857. https://doi.org/10.1016/0013-7944(94)00175-8
  9. Farghaly, S.H. (1992), "Bending vibrations of an axially cantilever beam with an elastically mounted end mass of finite length", J. Sound Vib., 156(2), 373-380. https://doi.org/10.1016/0022-460X(92)90706-4
  10. Farghaly, S.H. and Shebl, M.G. (1995), "Exact frequency and mode shape formulae for studying vibration and stability of Timoshenko beam system", J. Sound Vib., 180(2), 205-227. https://doi.org/10.1006/jsvi.1995.0075
  11. Gounaris, G.D., Papadopoulos C.A. and Dimarogonas, A.D. (1996), "Crack identification in beams by coupled response measurement", Comput. Struct., 58(2), 299-305. https://doi.org/10.1016/0045-7949(95)00142-4
  12. Hansen, P.C. (1994), "Regularization tools: A Matlab package for analysis and solution of discrete ill-posed problems", Numer. Algorithms, 6(1), 1-35. https://doi.org/10.1007/BF02149761
  13. He, Z.Y. and Lu, Z.R. (2010), "Time domain identification of multiple cracks in a beam", Struct. Eng. Mech., 35(6), 773-789. https://doi.org/10.12989/sem.2010.35.6.773
  14. Kisa, M. and Brandon, J.A. (2000a), "The effects of closure of cracks on the dynamics of a cracked cantilever beam", J. Sound Vib., 238(1), 1-18. https://doi.org/10.1006/jsvi.2000.3099
  15. Kisa, M. and Brandon, J.A. (2000b), "Free vibration analysis of multiple open edge cracked beams by component mode synthesis", Struct. Eng. Mech., 10(1), 81-92. https://doi.org/10.12989/sem.2000.10.1.081
  16. Krawczuk, M. and Ostachowicz, W.M. (1993), "Transverse natural vibrations of a cracked beam loaded with a constant axial force", J. Vib. Acoust., 115(4), 524-528. https://doi.org/10.1115/1.2930381
  17. Kukla, S. and Zamojska, I. (2007), "Frequency analysis of axially loaded stepped beams by Green's function method", J. Sound Vib., 300(3-5), 1034-1041. https://doi.org/10.1016/j.jsv.2006.07.047
  18. Kwon,Y.W. and Christy, C. (1994), "An efficient finite element modeling of dynamic crack propagation using a moving node element", Struct. Eng. Mech., 2(2), 173-184. https://doi.org/10.12989/sem.1994.2.2.173
  19. Lee, H.P. (1995), "Dynamic response of a rotating Timoshenko shaft subject to axial forces and moving loads", J. Sound Vib., 181(1), 169-177. https://doi.org/10.1006/jsvi.1995.0132
  20. Li, Q.S. (2001), "Buckling of multi-step cracked columns with shear deformation", Eng. Struct., 23(4), 356-364. https://doi.org/10.1016/S0141-0296(00)00047-X
  21. Li, J, Hua, H.X. and Li, X.B. (2010), "Dynamic stiffness matrix of an axially loaded slender double-beam element", Struct. Eng. Mech., 35(6), 717-733. https://doi.org/10.12989/sem.2010.35.6.717
  22. Lu, Z.R. and Law, S.S. (2007), "Features of dynamic response sensitivity and its application in damage detection", J. Sound Vib., 303(1-2), 305-329. https://doi.org/10.1016/j.jsv.2007.01.021
  23. Lu, Z.R. and Law, S.S. (2009), "Dynamic condition assessment of a cracked beam with the composite element model", Mech. Syst.Signal Pr., 23(2), 415-431. https://doi.org/10.1016/j.ymssp.2008.02.009
  24. MATLAB 6.5, The MathWorks, Inc. Release 13 User's Manual, 2002.
  25. Meirovitch, L. (1975), Elements of Vibration Analysis, McGraw-Hill, New York.
  26. Naguleswaran, S. (1994), "Transverse vibration and stability of an Euler-Bernoulli beam with step change in cross-section and in axial force", J. Sound Vib., 270(4-5), 1045-1055.
  27. Naguleswaran, S. (2003), "Vibration and stability of an Euler-Bernoulli beam with up to three-step changes in cross-section and axial force", Int. J. Mech. Sci., 45(9), 1563-1579. https://doi.org/10.1016/j.ijmecsci.2003.09.001
  28. Narkis, Y. (1994), "Identification of crack location in vibrating simply supported beams", J. Sound Vib., 172(4), 549-558. https://doi.org/10.1006/jsvi.1994.1195
  29. Ostachowicz, W. and Krawczuk, M. (2001), "On modelling of structural stiffness loss due to damage", Proceedings of 4th International Conference on Damage Assessment of Structures, DAMAS, Cardiff.
  30. Oz, H.R. (2010), "In-plane vibrations of cracked slightly curved beams", Struct. Eng. Mech., 36(6), 679-695. https://doi.org/10.12989/sem.2010.36.6.679
  31. Rosa, M.A. De. (1996), "Free vibration of stepped beams with flexible ends in the presence of follower forces at step", J. Sound Vib., 194(4), 631-635. https://doi.org/10.1006/jsvi.1996.0382
  32. Ruotolo, R., Surace, C., Crespo, P. and Storer, D (1996), "Harmonic analysis of the vibrations of a cantilevered beam with a closing crack", Comput. Struct., 61(6), 1057-1074. https://doi.org/10.1016/0045-7949(96)00184-8
  33. Shifrin, E.I. and Ruotolo, R. (1999), "Natural frequencies of a beam with an arbitrary number of cracks", J. Sound Vib., 222(3), 409-423. https://doi.org/10.1006/jsvi.1998.2083
  34. Yesilce, Y. and Catal, S. (2010), "Free vibration of axially loaded Reddy-Bickford beam on elastic soil using the differential transform method", Struct. Eng. Mech., 31(4), 453-474. https://doi.org/10.12989/sem.2009.31.4.453
  35. Zeng, P. (1998), "Composite element method for vibration analysis of structure, part II: C1element (beam)", J. Sound Vib., 218(4), 619-696. https://doi.org/10.1006/jsvi.1998.1853
  36. Zhou, L. and Huang, Y. (2006), "Crack effect on the elastic buckling behavior of axially and eccentrically loaded columns", Struct. Eng. Mech., 22(2), 169-184. https://doi.org/10.12989/sem.2006.22.2.169
  37. Zhu, X.Q., Law, S.S. and Hao, H. (2009), "Damage assessment of reinforced concrete beams including the load environment", Struct. Eng. Mech., 33(6), 765-779. https://doi.org/10.12989/sem.2009.33.6.765

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