Interaction and multiscale mechanics

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Changes of modal properties of simply-supported plane beams due to damages

  • Xiang, Zhihai (Department of Engineering Mechanics, Tsinghua University) ;
  • Zhang, Yao (Department of Engineering Mechanics, Tsinghua University)
  • Received : 2009.04.06
  • Accepted : 2009.05.04
  • Published : 2009.06.25
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Abstract

Damage detection methods using structural dynamic responses have received much attention in the past decades. For bridge and offshore structures, these methods are usually based on beam models. To ensure the successful application of these methods, it is necessary to examine the sensitivity of modal properties to structural damages. To this end, an analytic solution is presented of the modal properties of simply-supported Euler-Bernoulli beams that contain a general damage with no additional assumptions. The damage can be a reduction in the bending stiffness or a loss of mass within a beam segment. This solution enables us to thoroughly discuss the sensitivities of different modal properties to various damages. It is observed that the lower natural frequencies and mode shapes do not change so much when a section of the beam is damaged, while the mode of rotation angle and curvature modes show abrupt change near the damaged region. Although similar observations have been reported previously, the analytical solution presented herein for clarifying the mechanism involved is considered a contribution to the literature. It is helpful for developing new damage detection methods for structures of the beam type.

Keywords

Acknowledgement

Supported by : National Science Foundation of China

References

  1. Abdo, M. A. B. and Hori, M. (2002), "A numerical study of structural damage detection using changes in the rotation of mode shapes", J. Sound Vibration 251, 227-239. https://doi.org/10.1006/jsvi.2001.3989
  2. Allemang, R. J. and Brown, D. L. (1982), "Correlation coefficient for modal vector analysis", Proceedings of the 1st International Modal Analysis Conference, Society for Experimental Mechanics, Orlando, 110-116.
  3. Carden, E. P. and Fanning, P. (2004), "Vibration based condition monitoring: a review", Struct. Health Monitor., 3, 355-377. https://doi.org/10.1177/1475921704047500
  4. Chondros, 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
  5. Christides, S. and Barr, A. D. S. (1984), "One-dimensional theory of cracked Bernoulli-Euler beams", Int. J. Mech. Sci., 26, 639-648. https://doi.org/10.1016/0020-7403(84)90017-1
  6. Dimarogonas, A. D. and Paipetis, S. A. (1983), Analytical methods in rotor dynamics, Applied Science Publishers, London and New York.
  7. Dimarogonas, A. D. (1996), "Vibration of cracked structures: a state of the art review", Eng. Fract. Mech., 55, 831-857. https://doi.org/10.1016/0013-7944(94)00175-8
  8. Farrar, C. R. and Jauregui, D. A. (1998), "Comparative study of damage identification algorithms applied to a bridge: I. experiment", Smart Mater. Struct., 7, 704-719. https://doi.org/10.1088/0964-1726/7/5/013
  9. Humar, J. L. (1990), Dynamics of structures, Prentice Hall, New Jersey.
  10. Li, Y. Q., Zhou, M. S, Xiang, Z. H. and Cen, Z. Z. (2008), "Multi-type sensor placement design for damage detection", Interact. Multiscale Mech., 1, 357-368. https://doi.org/10.12989/imm.2008.1.3.357
  11. Lieven, N. A. J. and Ewins, D. J. (1988), "Spatial correlation of modespaces: the coordinate modal assurance criterion (COMAC)", Proceedings of the 6th International Modal Analysis Conference, Society for Experimental Mechanics, Kissimmee, 1063-1070.
  12. Mazanoglu, K., Yesilyurt, I. and Sabuncu, M. (2009), "Vibration analysis of multiple-cracked non-uniform beams", J. Sound Vib., 320, 977-989 https://doi.org/10.1016/j.jsv.2008.09.010
  13. Owolabi, G. M., Swamidas, A. S. J. and Seshadri, R. (2003), "Crack detection in beams using changes in frequencies and amplitudes of frequency response functions", J. Sound Vib., 265, 1-22. https://doi.org/10.1016/S0022-460X(02)01264-6
  14. Patil, D. P. and Maiti, S. K. (2005), "Vibration analysis of multiple-cracked non-uniform beams", J. Sound Vib., 281, 439-451. https://doi.org/10.1016/j.jsv.2004.03.035
  15. Pandey, A. K., Biswas, M. and Samman, M. M. (1991), "Damage detection from changes in curvature mode shapes", J. Sound Vib., 145, 321-332. https://doi.org/10.1016/0022-460X(91)90595-B
  16. Rizos, P. F., Aspragathos, N. and Dimarogonas, A. D. (1990), "Identification of crack location and magnitude in a cantilever beam from the vibration modes", J. Sound Vib., 138, 381-388. https://doi.org/10.1016/0022-460X(90)90593-O
  17. Salawu, O. S. (1997), "Detection of structural damage through changes in frequency: a review", Eng. Struct., 19, 718-723. https://doi.org/10.1016/S0141-0296(96)00149-6
  18. Sinha, J. K., Friswell, M. I. and Edwards, S. (2002), "Simplified models for the location of cracks in beam structures using measured vibration data", J. Sound Vib., 251, 13-38. https://doi.org/10.1006/jsvi.2001.3978
  19. Thomson, M. T. (1949), "Vibration of slender bars with discontinuities in stiffness", J. Appl. Mech., 16, 203-207.
  20. Wang, J. and Qiao, P. (2007), "Vibration of beams with arbitrary discontinuities and boundary conditions", J. Sound Vib., 308, 12-27. https://doi.org/10.1016/j.jsv.2007.06.071
  21. Yuen, M. M. F. (1985), "A numerical study of the eigenparameters of a damaged cantilever", J. Sound Vib., 103, 301-310. https://doi.org/10.1016/0022-460X(85)90423-7
  22. Zheng, D. Y. and Fan, S. C. (2001), "Natural frequencies of a non-uniform beam with multiple cracks via modified Fourier series", J. Sound Vib., 242, 701-717. https://doi.org/10.1006/jsvi.2000.3360
  23. Zou, Y., Tong, L. and Steven, G. P. (2000), "Vibration-based model-dependent damage (delamination) identification and health monitoring for composite structures - a review", J. Sound Vib., 230, 357-378. https://doi.org/10.1006/jsvi.1999.2624

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