Detection of Cracks in Beam Structures Using Modal Analysis

Abstract:

In the present study, the modal parameters of cracked plain cement concrete beams have been studied theoretically. A crack in a beam element introduces considerable local flexibility, which has been expressed by local flexibility matrix, the dimension of which depends upon the numbers of degree of freedom considered. An approach based on linear fracture mechanics theory has been used to find flexibility matrix for the cracked element. The FEM program has been developed for eigen-value problems to determine the modal parameters of the cracked beams. Changes in natural frequencies and mode shapes between the damaged and intact beam have been observed. Numerical studies are performed by considering simply supported beam with single and multiple cracks at different locations with different crack depths.

• Periodical: Applied Mechanics and Materials (Volumes 105-107)
• Pages: 689-694
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.105-107.689
• Online since: September 2011
• Authors: Pallab Das
• Keywords: Crack, Finite Element Method (FEM), Flexibility Matrix, Natural Frequency

References

[1] Cerri M.N., Ruta G.C.: Detection of localized damage in plane circular arches by frequency data, Journal of sound and vibration, Vol. 270 (2004), pp.39-59.

DOI: 10.1016/s0022-460x(03)00482-6

[2] Dutta Anjan, Talukdar S.: Damage detection in bridges using accurate modal parameters, Finite elements in analysis and design, Vol. 40(3) (2004) pp.287-304.

DOI: 10.1016/s0168-874x(02)00227-5

[3] Gounarist G., Dimargonas A.: A finite element of a cracked prismatic beam for structural  analysis, Journal of computers and structures, Vol. 28 (3) (1988) pp.309-313.

DOI: 10.1016/0045-7949(88)90070-3

[4] Inman Deniel J.: Engineering Vibration, Prentice Hall, Inc., second edition 2001.

[5] Khiem N.T., Lien T.V.: A simplified method for natural frequency analysis of a multiple  cracked beam, Journal of sound and vibration, Vol. 245(4) (2001) pp.737-751.

DOI: 10.1006/jsvi.2001.3585

[6] Saavedra P.N. and Cuitino L.A.: Crack detection and vibration behavior of cracked beams, Journal of computers and structures, Vol. 79 (2001) pp.1451-1459.

DOI: 10.1016/s0045-7949(01)00049-9

[7] Liberatore S. and Carman G.P.: Power spectral density analysis for damage identification and location, Journal of sound and vibration, Vol. 274(3-5) (2004) pp.761-776.

DOI: 10.1016/s0022-460x(03)00785-5

[8] Liebowitz H. and Claus W.D.: Failure of notched columns, Engineering Fracture Mechanics, Vol. 1(1968) pp.379-383.

DOI: 10.1016/0013-7944(68)90010-6

[9] Kisa M. and Brandon J.: The effects of closure of cracks on the dynamics of a cracked cantilever beam, Journal of sound and vibration, Vol. 238(1) (2000) pp.1-18.

DOI: 10.1006/jsvi.2000.3099

[10] Armon Dror, Ben-Haim Yakov and Braun Simon: Crack detection in beams by rank ordering of eigenfrequency shifts, Journal of sound and vibration, Vol. 8(1) (1994) pp.81-91.

DOI: 10.1006/mssp.1994.1006

[11] Owolabi G.M., Swamidas A.S.J. and Seshadri R.: Crack detection in beams using changes in frequencies and amplitudes of frequency response functions, Journal of sound and vibration, Vol. 265 (2003) pp.1-22.

DOI: 10.1016/s0022-460x(02)01264-6

[12] Ndambi J.M., Vantomme J. and Harri K.: Damage assessment in reinforced concrete beams using eigenfrequencies and mode shape derivatives, Journal of sound and vibration, Vol. 24 (2002) pp.501-515.

DOI: 10.1016/s0141-0296(01)00117-1