The Study of the Vibration Characteristics of the Cantilever Beam with a Surface Crack

Abstract:

In this paper, the physical model of the cantilever beam with a surface crack is established to study the free vibration of the cracked beam from three aspects that are theoretical analysis, FEM analysis, and experiment. At the same time, the relation between the crack parameter and the vibration characteristics, which are natural frequencies and the modes of each order, is obtained through analysis. The theoretical analysis is on the basis of the mode analysis theory and applied mechanics. The crack is regarded as a flexible hinge. Utilizing the external boundary conditions and internal boundary conditions at the crack, the free vibration characteristics are obtained combining with the vibration mechanics. With the ANSYS software, a finite element model of the cracked beam is established by the beam element. During the process of calculation, it calculates the natural frequencies and the modes of cracked beam with different parameters of crack. The results obtained from the experiment are in agreement with the results obtained from the theoretical and the FEM analysis. So the accuracy of the theoretical analysis and the numerical simulation is verified by the experiment. At last, the effects of the crack location and depth on the natural frequencies and modes of each order are shown, and it could provide the theoretical, numerical and experimental basis for the identification of cracked materials and the relevant study.

• Periodical: Applied Mechanics and Materials (Volume 394)
• Pages: 121-127
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.394.121
• Online since: September 2013
• Authors: Li Hua Chen, Jian Wei Duan, Yue Sun, Jing Li
• Keywords: Cantilever Beam, Crack, Mode, Natural Frequency

References

[1] George D．Gounarisa，Chris A．Papadopoulos. Crack identification in rotating shafts by coupled response measurements，Engineering Fracture Mechanics，2002, 69：339-352.

DOI: 10.1016/s0013-7944(01)00076-5

[2] Rizos P，Aspragathos N，Dimarogonas A．Identification of crack location and magnitude in a cantilever beam from the vibration modes. Journal of Sound and Vibration，1990，138: 381-388.

DOI: 10.1016/0022-460x(90)90593-o

[3] Li Bing, Chen Xuefeng, Hu Qiao, He ZhengJia. Identification of cracks in cantilever beam based on wavelet finite element methods. Journal of Vibration Engineering, 2004，17(2): 159-164.

[4] 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

[5] D．Y．Zheng，S．C．Fan. Natural frequencies of a non-uniform beam with multiple cracks via modified Fourier-Series. Journal of Sound and Vibration，2001, 242(4)：701-717.

DOI: 10.1006/jsvi.2000.3360

[6] D．Y．Zheng，S．C．Fan. Natural frequency changes of a cracked Timoshenko Beam by modified Fourier-Series. Journal of Sound and Vibration，2001, 246(2)：297-317.

DOI: 10.1006/jsvi.2001.3632

[7] Rice J R，Levy N．The part-through surface crack in an elastic plate．J．of Appl．Mech，1972, 39：184-194.

[8] Tang Guojin, Zhou Jianping. The line spring model of cracked beam. ACTA ARMAMENTARII, 1998, 19(1)：64-68.

[9] G. Gotmmas and A. D. Dimarogonas. A finite element of a cracked prismatic beam for structural analysis．Comp．＆ Struct, 1988, (28)：309-313.

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

[10] N. Papaeconomou, A. Dimarogonas. Vibration of cracked beams. Computational Mechanics, 1989, 5(2-3): 88-94.

DOI: 10.1007/bf01046477