Crake Effect on the Dynamic Characteristics of Elastically Coupled Beams

Abstract:

Simple mathematical model that describes the lateral vibration of elastically coupled cracked cantilever beams carrying rigid disk at their tips is derived. The derived model is used to study the effect of elastic coupling, crack depth and location on the dynamic characteristics of the system. The cracked beam is presented as two beams connected with torsional spring at the crack location. Model verification is carried out using three dimensional finite element analysis using ANSYS program, the verification results showed good agreement with that obtained from the proposed model. The study reveals that the first system natural frequency is affected by the crack and the elastic coupling.

• Periodical: Applied Mechanics and Materials (Volumes 110-116)
• Pages: 328-336
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.110-116.328
• Online since: October 2011
• Authors: Samer A. M. Al-Said
• Keywords: Coupled Beams, Crack Effect, Cracked Beam, Lateral Vibration

References

[1] D. Dimarogonas, Vibration of cracked structures: a state of the art review, Engineering Fracture Mechanics, 55 (5) (1996) 831-857.

DOI: 10.1016/0013-7944(94)00175-8

[2] S. W. Doebling, C. R. Farrar, and M. B. Prime, 1998, A Summary Review of Vibration-Based Damage Identification Methods, The Shock and Vibration Digest 30 (2), 91-105.

DOI: 10.1177/058310249803000201

[3] C. Chasalevris, and C. A. Papadopoulos, 2006, Identification of multiple cracks in beams under bending, Mechanical Systems and Signal Processing 20, 1631–1673.

DOI: 10.1016/j.ymssp.2006.03.008

[4] Chondros T. G., Dimarogonas A. D., Yao J., Vibration of a beam with a breathing crack, Journal of Sound Vibration, 239 (2001) 57–67.

DOI: 10.1006/jsvi.2000.3156

[5] N. Dharmaraju, R. Tiwari, S. Talukdar, Identification of an open crack model in a beam based on force–response measurements, Computers and Structures, 82 (2004) 167–179.

DOI: 10.1016/j.compstruc.2003.10.006

[6] D.Y. Zheng, N.J. Kessissoglou, Free vibration analysis of a cracked beam by finite element method, Journal of Sound and Vibration, 273 (2004) 457–475.

DOI: 10.1016/s0022-460x(03)00504-2

[7] A.S. Sekhar, Model-based identification of two cracks in a rotor system, Mechanical Systems and Signal Processing, 18 (2004) 977–983.

DOI: 10.1016/s0888-3270(03)00041-4

[8] X. F. Yang, A. S. J. Swamidas and R. Seshadri, Crack identification in vibrating beams using the energy method, Journal of Sound and vibration, 244(2), (2001) 339-357.

DOI: 10.1006/jsvi.2000.3498

[9] M. Dilena, A. Morassi. The use of antiresonances for crack detection in beams, Journal of Sound and Vibration, 276 (2004) 195–214.

DOI: 10.1016/j.jsv.2003.07.021

[10] S. Masoud, M. A. Jarrah, M. Al-Maamory, Effect of crack depth on the natural frequency of a pre-stressed fixed beam, Journal of Sound and Vibration, 214 (1998) 201-212.

DOI: 10.1006/jsvi.1997.1541

[11] J. N. Sundermeter, R. L. Weaver, On Crack Identification and Characterization in a beam by Nonlinear Vibration Analysis, Journal of Sound and Vibration, 183 (1995) 857-871.

DOI: 10.1006/jsvi.1995.0290

[12] T. C. Tsai, Y. Z. Wang, The Vibration of Multi-crack Rotor, International Journal of Mechanical Sciences, 39 (1997) 1037-1053.

DOI: 10.1016/s0020-7403(97)00005-2

[13] T.G. Chondros, Variational formulation of a rod under torsional vibration for crack identification, Theoretical and Applied Fracture Mechanics, 44 (2005).

DOI: 10.1016/j.tafmec.2005.05.008