Determination of Structural Flaws in Beams

A nondestructive experimental technique for determination of structural flaws in cantilever beams is presented. The proposed method is capable of detecting location of cracks and other possible structural flows on a beam using its natural frequencies and vibration mode shapes measured on a roving mass on the beam. To verify the validity of the proposed method, vibration response of a cracked cantilever beam with a stationary roving mass is investigated. The beam is modeled as an Euler-Bernoulli beam with rectangular cross section. The axial and transverse deformations of the cracked beam are coupled through a stiffness matrix determined using the fracture mechanics principles. The developed model is used to determine analytical solutions for the variation of natural frequencies and mode shapes of a cracked cantilever beam versus the position of the roving mass. The analysis indicates that the variation of the natural frequencies versus position of the roving mass can drastically change when the roving mass is close to the position of a flaw. Moreover, the effects of the location and depth of the crack, the location and the weight of the roving mass on the natural frequencies, and mode shapes of the beam are investigated. The analytical results show that the coupling between the axial and transverse vibrations for moderate values of crack depth and/or roving mass is weak. Increasing the crack depth, the mass and the rotary inertia increases the coupling effect.

References
1. Zhong, S., S.O. Oyadiji and K. Ding, “Response-only method for damage detection of beam-like structures using high accuracy frequencies with auxiliary mass spatial probing,” Journal of Sound and Vibration, 311, 1075-1099, 2008. 2. Lu, Y. and F. A. Gao, “Novel time-domain auto-regressive model for structural damage diagnosis,” Journal of Sound and Vibration, 283, 1031-1049, 2005. 3. Hadjileontiadis, L.J., E. Douka and A. Trochidis, “Crack detection in beams using kurtosis,” Computers and Structures, 83, 909-919, 2005. 4. Parloo, E., S. Vanlanduit, P. Guillaume and P. Verboven, “Increased reliability of referenced-based damage identification techniques by using output-only data,” Journal of Sound and Vibration, 270, 813-832, 2004. 5. Choi, S. and N. Stubbs, “Damage identification in structures using the time-domain response,” Journal of Sound and Vibration, 275, 577-590, 2004. 6. Zhong, S. and S.O. Oyadiji, “Analytical prediction of natural frequencies of cracked simply supported beams with a stationary roving mass,” Journal of Sound and Vibration, 311, 328-352, 2008. 7. Lin, H.P. and S.C. Chang, “Forced response of cracked cantilever beams subjected to a concentrated moving load,” International Journal of Mechanical Sciences, 48, 1456-1463, 2006. 8. Dong, G.M., J. Chen and J. Zou, “Parameter identification of a rotor with an open crack,” European Journal of Mechanics A/Solids, 23, 325-333, 2004. 9. Dado, M.H.F. and O. Abuzeid, “Coupled transverse and axial vibratory behaviour of cracked beam with end mass and rotary inertia,” Journal of Sound and Vibration, 261, 675-696, 2003. 10. Mahmoud, M.A.M. and M.A. Abou Zaid, “Dynamic response of a beam with a crack subject to a moving mass,” Journal of Sound and Vibration, 256, 591-603, 2002. 11. Dimarogonas, A.D. and C.A. Paradopoulos, “Vibration of cracked shafts in bending,” Journal of Sound and Vibration, 914, 583-593, 1983. 12. Paradopoulos, C.A. and A.D. Dimarogonas, “Coupled longitudinal and bending vibrations of a cracked shaft,” Journal of Vibration and acoustics stress and reliability in design, 110, 1-8, 1988. 13. Chondros, T.G., A.D. Dimarogonas and J. Yao, “A continuous cracked beam vibration theory,” Journal of Sound and Vibration, 215, 17-34, 1998. 14. Chondros, T.G. and A.D. Dimarogonas, “Vibration of a cracked cantilever beam,” Journal of Vibration and Acoustics, 120, 742-746, 1998. 15. Masoud, S., M.A. Jarrah and M. Al-Maamory, “Effect of crack depth on the natural frequency of a pre-stressed fixedfixed beam,” Journal of Sound and Vibration, 214, 201-212, 1998. 16. Low, K.H., “Comparisons of experimental and numerical frequencies for classical beams carrying a mass in-span,” International Journal of Mechanical Science, 41, 1515-1531, 1999. 17. Chondros T.G., A.D. Dimarogonas and J. Yao, “Vibration of a beam with a breathing crack,” Journal of Sound and Vibration, 239, 57-67, 2001. 18. Zhong, S. and S.O. Oyadiji, “Response-only frequency-domain method for structure damage detection,” Proceedings of the ASME 2009 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, August 30-September 2, 2009, San Diego, California, 1-8.
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