Vibration Analysis of a Multi-Span Continuous Beam with Cracks

Abstract:

This paper deals with dynamic analysis of a multi-span continuous beam with an arbitrary number of cracks. This problem is solved by a hybrid analytical/ numerical method that is the basis for applying to a method of damage detection in the multi-span continuous beam later. In this paper, we calculate in detail about vibration frequencies, vibration mode shape of beam structure with cracks. The proposed method is the method that improved the transfer matrix method combined with the mode-superposition method. Only need to use two unknowns, this method can solve the problem of multi-span continuous beam with an arbitrary number of cracks. Calculation cases of beam with cracks and beam without cracks are compared with previous studies.

• Periodical: Applied Mechanics and Materials (Volumes 256-259)
• Pages: 964-972
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.256-259.964
• Online since: December 2012
• Authors: Han Bing Liu, Huu Hung Nguyen, Yi Ming Xiang
• Keywords: Cracked Beam, Mode Shape, Mode Superposition, Multi-Span, Uncraked Beam

References

[1] M. H. Shen, C. Pierre, Modes of free vibrations of cracked beams, Thesis, UM-MEAN-86-37 (1986)

[2] M.-H. H. Shen and C. Pierre, Natural modes of Bernoulli-Euler beams with symmetric cracks, Journal of Sound and Vibration (1990) 138(l), 115-134.

DOI: 10.1016/0022-460x(90)90707-7

[3] N. Papaeconomou, A. Dimarogonas, Vibration of cracked beams, Computational Mechanics (1989) 5, 88-9

DOI: 10.1007/bf01046477

[4] H. P. Lee and T. Y. Ng, Dynamic response of a cracked beam subject to a moving load, Acta Mechanica 106, 221-230 (1994)

DOI: 10.1007/bf01213564

[5] H. P. Lee and T. Y. Ng, Natural Frequencies and Modes for the Flexural Vibration of a Cracked Beam, Applied Acoustics 42 (1994) 151-163

DOI: 10.1016/0003-682x(94)90004-3

[6] H. P. Lee, Dynamic response of a multi-span beam on one-sided point constraints subject to a moving load, Computers & Structures Vol55. No. 4. pp.615-623, (1995)

DOI: 10.1016/0045-7949(94)00492-l

[7] T. G. CHONDROS, A. D. DIMAROGONAS, A continuous cracked beam vibration theory, Journal of Sound and Vibration (1998) 215(1),17-34

DOI: 10.1006/jsvi.1998.1640

[8] E. I. SHIFRIN, R. RUOTOLO, Natural frequencies of a beam with an arbitrary number of cracks, Journal of Sound and Vibration (1999) 222 (3), 409-423

DOI: 10.1006/jsvi.1998.2083

[9] T. G. CHONDROS, A. D. DIMAROGONAS, Vibration of a beam with a breathing crack, Journal of Sound and Vibration (2001) 239(1), 57-67

DOI: 10.1006/jsvi.2000.3156

[10] H. P. Lin ,S.C. Chang and J. D. Wu, Beam vibrations with an arbitrary number of cracks, Journal of Sound and Vibration (2002) 258(5), 987–999

DOI: 10.1006/jsvi.2002.5184

[11] Hai-Ping Lin, S.C. Chang, Free vibration analysis of multi-span beams with intermediate flexible constraints, Journal of Sound and Vibration 281 (2005) 155–169

DOI: 10.1016/j.jsv.2004.01.010

[12] Hai-Ping Lin, Shun-Chang Chang, Forced responses of cracked cantilever beams subjected to a concentra ted moving load, International Journal of Mechanical Sciences 48 (2006) 1456 – 1463

DOI: 10.1016/j.ijmecsci.2006.06.014

[13] N. Roveri, A. Carcaterra, Damage detection in structures under traveling loads by Hilbert-Huang transform, Mechanical Systems and Signal Processing 28 (2012) 128–144.

DOI: 10.1016/j.ymssp.2011.06.018

[14] A. Ariaei, S. Ziaei-Rad, M. Ghayour, Vibration analysis of beams with open and breathing cracks subjected to moving masses, Journal of Sound and Vibration 326 (2009) 709–724

DOI: 10.1016/j.jsv.2009.05.013

[15] K. Mazanoglu, M. Sabuncu, Flexural vibration of non-uniform beams having double-edge breathing cracks, Journal of Sound and Vibration 329 (2010) 4181–4191

DOI: 10.1016/j.jsv.2010.04.011

[16] Mousa Rezaee, Reza Hassannejad, Free vibration analysis of simply supported beam with breathing crack using perturbation method, Acta Mechanica Solida Sinica, Vol. 23, No. 5, October, (2010)

DOI: 10.1016/s0894-9166(10)60048-1

[17] Mousa Rezaee, Reza Hassannejad, A new approach to free vibration analysis of a beam with a breathing crack based on mechanical energy balance method, Acta Mechanica Solida Sinica, Vol. 24, No. 2, April, (2011)

DOI: 10.1016/s0894-9166(11)60020-7

[18] R. W. Clough, J. Penzien, Dynamics of structures, Computers & Structures, Inc 2003, pp.365-423

[19] M. Ichikawa, Y. Miyakawa and A. Matsuda, Vibration analysis of the continuous beam subjected to a moving mass, Journal of Sound and Vibration (2000) 230(3), 493-506

DOI: 10.1006/jsvi.1999.2625