Free Vibration of Cracked Cantilever Beams: Analytical and Experimental Modelling
Year 2018,
Volume: 13 Issue: 1, 1 - 7, 01.03.2018
Volkan Kahya
,
Sebahat Karaca
Abstract
This study presents free
vibration of cantilever beams with multiple cracks. The problem is solved
analytically by the transfer matrix method, and is validated experimentally by
the operational modal analysis. Six damage scenarios are considered to study
crack effect on the natural frequencies and corresponding mode shapes. Graphs
and tables for numerical results are given and discussed. Results show that
crack occurrence in a beam significantly changes its dynamic behavior.
References
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2. Dimarogonas, A.D. and Paipetis, S.A. (1983). Analytical Methods in Rotor Dynamics, Applied Science Publisher, London.
3. Shifrin, E.I. and Ruotolo, R.. (1999). Natural frequencies of a beam with an arbitrary number of cracks. Journal of Sound and Vibration, 222(3): 409-423.
4. Lin, H.P., Chang, S.C. and Wu, J.D. (2002). Beam vibrations with an arbitrary number of cracks. Journal of Sound and Vibration, 258(5): 987-999.
5. Zheng, D.Y. and Fan, S.C. (2003). Vibration and stability of cracked hollow-sectional beams. Journal of Sound and Vibration, 267: 933-954.
6. Lin, H.P. (2004). Direct and inverse methods on free vibration analysis of simply supported beams with a crack. Engineering Structures, 26: 427–436.
7. Loya, J.A., Rubio, L. and Fernández-Sáez, J. (2006). Natural frequencies for bending vibrations of Timoshenko cracked beams. Journal of Sound and Vibration, 290: 640-653.
8. Attar, M. (2012). A transfer matrix method for free vibration analysis and crack identification of stepped beams with multiple edge cracks and different boundary conditions. International Journal of Mechanical Sciences, 57: 19-33.
9. Viola, E., Ricci, P. and Aliabadi, M.H. (2007). Free vibration analysis of axially loaded cracked Timoshenko beam structures using the dynamic stiffness method. Journal of Sound and Vibration, 304: 124-153.
10. Ruotolo, R. and Surace, C. (2004). Natural frequencies of a bar with multiple cracks. Journal of Sound and Vibration, 272: 301-316.
11. Lee, J. (2009). Identification of multiple cracks in a beam using natural frequencies. Journal of Sound and Vibration, 320: 482-490.
12. Nandakumar, P. and Shankar, K. (2014). Multiple crack damage detection of structures using the two-crack transfer matrix. Structural Health Monitoring, 13(5): 548–561.
13.Neves, A.C., Simões, F.M.F. and Pinto da Costa, A. (2016). Vibrations of cracked beams: Discrete mass and stiffness models. Computers and Structures, 168: 68–77.
14. Sinha, J.K., Friswell, M.I. and Edwards, S. (2002). Simplified models for the location of cracks in beam structure using measured vibration data, Journal of Sound and Vibration, 251: 13-38.
15. Patil, D.P. and Maiti, S.K. (2005). Experimental verification of a method of detection of multiple cracks in beams based on frequency measurements. Journal of Sound and Vibration, 281: 439-451.
16.Nandakumar, P. and Shankar, K. (2015). Structural crack damage detection using transfer matrix and state vector. Measurement, 68: 310–327.
17. PULSE (2006). Analyzers and Solutions, Release 11.2. Bruel and Kjaer, Sound and Vibration Measurement A/S, Denmark.
18.OMA (2006). Operational Modal Analysis, Release 4.0. Structural Vibration Solution A/S, Denmark.
19. Ewins, D.J. (1995). Modal Testing: Theory and Practice, John Wiley & Sons, Inc, New York.
Year 2018,
Volume: 13 Issue: 1, 1 - 7, 01.03.2018
Volkan Kahya
,
Sebahat Karaca
References
- 1.Dimarogonas, A.D. (1996). Vibration of cracked structures: a state of the art review. Engineering Fracture Mechanics, 55(5): 831-857.
2. Dimarogonas, A.D. and Paipetis, S.A. (1983). Analytical Methods in Rotor Dynamics, Applied Science Publisher, London.
3. Shifrin, E.I. and Ruotolo, R.. (1999). Natural frequencies of a beam with an arbitrary number of cracks. Journal of Sound and Vibration, 222(3): 409-423.
4. Lin, H.P., Chang, S.C. and Wu, J.D. (2002). Beam vibrations with an arbitrary number of cracks. Journal of Sound and Vibration, 258(5): 987-999.
5. Zheng, D.Y. and Fan, S.C. (2003). Vibration and stability of cracked hollow-sectional beams. Journal of Sound and Vibration, 267: 933-954.
6. Lin, H.P. (2004). Direct and inverse methods on free vibration analysis of simply supported beams with a crack. Engineering Structures, 26: 427–436.
7. Loya, J.A., Rubio, L. and Fernández-Sáez, J. (2006). Natural frequencies for bending vibrations of Timoshenko cracked beams. Journal of Sound and Vibration, 290: 640-653.
8. Attar, M. (2012). A transfer matrix method for free vibration analysis and crack identification of stepped beams with multiple edge cracks and different boundary conditions. International Journal of Mechanical Sciences, 57: 19-33.
9. Viola, E., Ricci, P. and Aliabadi, M.H. (2007). Free vibration analysis of axially loaded cracked Timoshenko beam structures using the dynamic stiffness method. Journal of Sound and Vibration, 304: 124-153.
10. Ruotolo, R. and Surace, C. (2004). Natural frequencies of a bar with multiple cracks. Journal of Sound and Vibration, 272: 301-316.
11. Lee, J. (2009). Identification of multiple cracks in a beam using natural frequencies. Journal of Sound and Vibration, 320: 482-490.
12. Nandakumar, P. and Shankar, K. (2014). Multiple crack damage detection of structures using the two-crack transfer matrix. Structural Health Monitoring, 13(5): 548–561.
13.Neves, A.C., Simões, F.M.F. and Pinto da Costa, A. (2016). Vibrations of cracked beams: Discrete mass and stiffness models. Computers and Structures, 168: 68–77.
14. Sinha, J.K., Friswell, M.I. and Edwards, S. (2002). Simplified models for the location of cracks in beam structure using measured vibration data, Journal of Sound and Vibration, 251: 13-38.
15. Patil, D.P. and Maiti, S.K. (2005). Experimental verification of a method of detection of multiple cracks in beams based on frequency measurements. Journal of Sound and Vibration, 281: 439-451.
16.Nandakumar, P. and Shankar, K. (2015). Structural crack damage detection using transfer matrix and state vector. Measurement, 68: 310–327.
17. PULSE (2006). Analyzers and Solutions, Release 11.2. Bruel and Kjaer, Sound and Vibration Measurement A/S, Denmark.
18.OMA (2006). Operational Modal Analysis, Release 4.0. Structural Vibration Solution A/S, Denmark.
19. Ewins, D.J. (1995). Modal Testing: Theory and Practice, John Wiley & Sons, Inc, New York.