Structural Engineering and Mechanics

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A generalized algorithm for the study of bilinear vibrations of cracked structures

  • Luo, Tzuo-Liang (Institute of Mechanical Engineering, National Chung-Hsing University) ;
  • Wu, James Shih-Shyn (Institute of Mechanical Engineering, National Chung-Hsing University) ;
  • Hung, Jui-Pin (Institute of Precision Machinery and Manufacturing Technology, National chin-Yi Institute of Technology)
  • Received : 2005.02.24
  • Accepted : 2006.01.23
  • Published : 2006.05.10
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Abstract

Structural cracks may cause variations in structural stiffness and thus produce bilinear vibrations to structures. This study examines the dynamic behavior of structures with breathing cracks. A generalized algorithm based on the finite element method and bilinear theory was developed to study the influence of a breathing crack on the vibration characteristic. All the formulae derived in the time domain were applied to estimate the period of the overall bilinear motion cycle, and the contact effect was considered in the calculations by introducing the penetration of the crack surface. Changes in the dynamic characteristics of cracked structures are investigated by assessing the variation of natural frequencies under different crack status in either the open or closed modes. Results in estimation with vibrational behavior variation are significant compared with the experimental results available in the literature as well as other numerical calculations.

Keywords

References

  1. Bovsunovsky, A.P. and Matveev,V.V. (2000), ' Analytical approach to the detennination of dynamic characteristics of a beam with a closing crack', J. Sound Vib., 235(3), 415-434 https://doi.org/10.1006/jsvi.2000.2930
  2. Butcher, E.A. (1999), ' Clearance effects on bilinear normal mode frequencies', J .Sound Vib., 224(2), 305-328 https://doi.org/10.1006/jsvi.1999.2168
  3. Carson, R.L. (1974), ' An experimental study of the parametric excitation of a tensioned sheet with a crack like opening' , Exp. Mech., 14(2),452-458 https://doi.org/10.1007/BF02324026
  4. Chatti, M., Rand, R. and Mukherjee, S. (1997),' Modal analysis of a cracked beam' , J. Sound Vib., 207(2), 249-270 https://doi.org/10.1006/jsvi.1997.1099
  5. Chen, M. and Tang, R. (1997), ' Approximate method of response analysis of vibrations for cracked beams' , Appl. Math. Mech., 18(3), 221-228 https://doi.org/10.1007/BF02453364
  6. Chondros, T.G and Dimarogonas, A.D. (1980),' Identification of cracks in welded joints of complex structures' , J. Sound Vib., 69(4), 531-538 https://doi.org/10.1016/0022-460X(80)90623-9
  7. Chondros, T.G and Dimarogonas, A.D. (1989), ' Dynamic sensitivity of structure to cracks' , J. Vib., Acoustics, Stress, and Reliability in Design, 111, 251-256 https://doi.org/10.1115/1.3269849
  8. Chondros, T.G, Dimarogonas, A.D. and Yao, J. (1998), ' A continuous cracked beam vibration theory' , J. Sound Vib., 215(1), 17-34 https://doi.org/10.1006/jsvi.1998.1640
  9. Chondros, T.G, Dimarogonas, A.D. and Yao, J. (2001), ' Vibration of a beam with a breathing crack' , J. Sound Vib., 239( 1), 57-67 https://doi.org/10.1006/jsvi.2000.3156
  10. Dimarogonas, A.D. (1996), ' Vibration of cracked structure - A state of the art review ' , Eng. Fracture Mech., 5, 831-857
  11. Fernandez, S.J. and Navarro, C. (2002),' Fundamental frequency of cracked beams in bending vibrations: An analytical approach ', J .Sound Vib., 256(1), 17-31 https://doi.org/10.1006/jsvi.2001.4197
  12. Gounaris, G. and Dimarogonas, A.D. (1988), ' A finite element of a cracked prismatic beam for structural analysis ', Comput. Struct., 28(3), 309-313 https://doi.org/10.1016/0045-7949(88)90070-3
  13. Gudmundson, P. (1983), ' The dynamic behavior of slender structures with cross-sectional cracks', J. Mech. Phy. Solids, 31(1), 329-345 https://doi.org/10.1016/0022-5096(83)90003-0
  14. Hjeimstad, K.D. and Shin, S. (1996), ' Crack identifcation in a cantilever beam from modal response ', J . Sound Vib., 198(1), 527-545 https://doi.org/10.1006/jsvi.1996.0587
  15. Khiem, N.T and Lien, T.V. (2001),' A simplified method for natural frequency analysis of a multiple cracked beam ', J .Sound Vib., 245(4), 737-751 https://doi.org/10.1006/jsvi.2001.3585
  16. Khiem, N.T. and Lien, TY. (2002), ' The dynamic stiffuess matrix method in forced vibration analysis of multiple-cracked beam ' , J. Sound Vib., 254(3), 541-555 https://doi.org/10.1006/jsvi.2001.4109
  17. Kikidis, M.L. (1992), ' Slenderness ratio effect on cracked beam ', J. Sound Vib., 155( 1) 1-11 https://doi.org/10.1016/0022-460X(92)90641-A
  18. Kisa, M. (2004), ' Free vibration analysis of a cantilever composite beam with multiple cracks ' , J. Camp. Sci.Tech., 64(9), 1391-1402 https://doi.org/10.1016/j.compscitech.2003.11.002
  19. Kisa, M. and Brandon, J. (2000), ' 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
  20. Krawczuk, M. and Ostachowicz, W.M. (1993), ' Transverse natural vibrations of a cracked beam loaded with a constant axial force ', J. Vib. and Acoustics Transactions of the ASME., 115(4), 524-528 https://doi.org/10.1115/1.2930381
  21. Lee, H.P. and Ng, T.Y. (1994), ' Natural frequencies and modes for the flexural vibration of a cracked beam ', J.Appl. Acoustics., 42(2), 151-163 https://doi.org/10.1016/0003-682X(94)90004-3
  22. Liew, K.M. and Wang, Q. (1998), ' Application of wavelet theory for crack identification in structures ' , J. Eng. Mech., 124(2), 152-157 https://doi.org/10.1061/(ASCE)0733-9399(1998)124:2(152)
  23. Lin, H.P. (2004), ' Direct and inverse methods on free vibration analysis of simply supported beams with a crack ' , Eng. Struct., 26(4), 427-436 https://doi.org/10.1016/j.engstruct.2003.10.014
  24. Murphy, K.D. and Zhang, Y. (2000), ' Vibration and stability of a cracked translating beam ', J. Sound Vib., 237(2), 319-335 https://doi.org/10.1006/jsvi.2000.3058
  25. Nandi, A. and Neogy, S. (2002), ' Modelling of a beam with a breathing edge crack and some observations for crack detection ', J. Vib. Control., 8(5), 673-693 https://doi.org/10.1177/1077546029296
  26. 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
  27. Qian, G.L., Gu, S.N. and Jian, J.S. (1990), ' The dynamics behavior and crack detection of a beam with a crack ', J. Sound Vib., 138(1),233-243 https://doi.org/10.1016/0022-460X(90)90540-G
  28. Shen, M.H. and Pierre, C. (1990), ' Natural modes of Bemoulli-Euler beams with symmetric cracks ', J. Sound Vib., 138(1), 115-134 https://doi.org/10.1016/0022-460X(90)90707-7
  29. Todd, M.D. and Virgin, L.N. (1996), ' Natural frequency computations of impact oscillator ', J. Sound Vib., 194(3), 452-460 https://doi.org/10.1006/jsvi.1996.0370
  30. Yokoyama, T and Chen, M.C. (1998), ' Vibration analysis of edge-cracked beams using a line-spring model ', Eng. Fracture Mech., 59(3), 403-409 https://doi.org/10.1016/S0013-7944(97)80283-4

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