International Journal of Precision Engineering and Manufacturing

Korean Society for Precision Engineering (한국정밀공학회)
권호 표지

Effects of a Moving Mass on the Dynamic Behavior of Cantilever Beams with Double Cracks

  • Son, In-Soo (School of Mechanical Engineering, Dong-eui University) ;
  • Cho, Jeong-Rae (Department of Car-Electronics, Korea Polytechnic VI College Dalseong Campus) ;
  • Yoon, Han-Ik (School of Mechanical Engineering, Dong-eui University)
  • Published : 2008.07.01
Download PDF
⟨ Previous Next ⟩

Abstract

The effects of a double crack and tip masses on the dynamic behavior of cantilever beams with a moving mass are studied using numerical methods. The cantilever beams are modeled by applying Euler-Bernoulli beam theory. The cracked sections are represented by a local flexibility matrix connecting three undamaged beam segments. The influences of the crack, moving mass, and tip mass, and the coupling of these factors on the vibration mode and the frequencies of the double-cracked cantilever beams are determined analytically. The methodology provides a basis for analyzing the dynamic behavior of a beam with an arbitrary number of cracks and a moving mass.

Keywords

References

  1. Stanisic, M. M., "On a New Theory of the Dynamic Behavior of the Structures Carrying Moving Masses," Ingenieur-Archiv, Vol. 55, No. 3, pp. 176-185, 1985 https://doi.org/10.1007/BF00536412
  2. Lee, H. P., "The Dynamic Response of a Timoshenko Beam Subjected to a Moving Mass," Journal of Sound and Vibration, Vol. 198, No. 2, pp. 249-256, 1996 https://doi.org/10.1006/jsvi.1996.0567
  3. Yoon, H. I., Jin, J. T. and Son, I. S., "A Study on Dynamic Behavior of Simply Supported Fluid Flow Pipe with Crack and Moving Mass," Proceedings of the 11th International Congress on Sound and Vibration, pp. 2215-2222, 2004
  4. Mahmoud, M. A. and Zaid, C. S. A., "Dynamic Response of a Beam with a Crack Subject to a Moving Mass," Journal of Sound and Vibration, Vol. 256, No. 4, pp. 591-603, 2002 https://doi.org/10.1006/jsvi.2001.4213
  5. Chondros, T. G., and Dimarogonas, A. D., "Dynamic Sensitivity of Structures to Cracks," Journal of Vibration and Acoustics, Stress, and Reliability in Design, Vol. 111, No. 3, pp. 251-256, 1989 https://doi.org/10.1115/1.3269849
  6. Chondros, T. G. and Dimarogonas, A. D., "Vibration of a Cracked Cantilever Beam," Journal of Vibration and Acoustics, Vol. 120, No. 3, pp. 742-746, 1998 https://doi.org/10.1115/1.2893892
  7. Narkis, Y., "Identification of Crack Location in Vibrating Simply Supported Beams," Journal of Sound and Vibration, Vol. 172, No. 4, pp. 549-558, 1994 https://doi.org/10.1006/jsvi.1994.1195
  8. Lin, H. P., "Direct and Inverse Methods on Free Vibration Analysis of Simply Supported Beams with a Crack," Engineering Structures, Vol. 26, No. 4, pp. 427-436, 2004 https://doi.org/10.1016/j.engstruct.2003.10.014
  9. Liu, D., Gurgenci, H. and Veidt, M., "Crack Detection in Hollow Section Structures Through Coupled Response Measurements," Journal of Sound and Vibration, Vol. 261, No. 1, pp. 17-29, 2003 https://doi.org/10.1016/S0022-460X(02)00922-7
  10. Yoon, H. I., Choi, C. S. and Son, I. S., "Influence of Moving Mass on Dynamic Behavior of Simply Supported Timoshenko Beam with Crack," International Journal of Precision Engineering and Manufacturing, Vol. 7, No. 1, pp. 24-29, 2006
  11. Ruotole, R., Surace, C. and Mares, C., "Theoretical and Experimental Study of the Dynamic Behaviour of a Double-Cracked Beam," Proceedings of the 14th International Model Analysis Conference, pp. 1560-1564, 1996
  12. Sekhar, A., "Vibration Characteristics of a Cracked Rotor with Two Open Cracks," Journal of Sound and Vibration, Vol. 223, No. 4, pp. 497-512, 1999 https://doi.org/10.1006/jsvi.1998.2120
  13. Ostachowicz, W. and Krawczuk, M., "Analysis of the Effect of Cracks on the Natural Frequencies of a Cantilever Beam," Journal of Sound and Vibration, Vol. 150, No. 2, pp. 191-201, 1991 https://doi.org/10.1016/0022-460X(91)90615-Q
  14. Shen, M. H. H. and Pierre, C., "Natural Modes of Bernoulli-Euler Beams with Symmetric Cracks," Journal of Sound and Vibration, Vol. 138, No. 1, pp. 115-134, 1990 https://doi.org/10.1016/0022-460X(90)90707-7
  15. Christides, S. and Barr, A. D. S., "One-Dimensional Theory of Cracked Bernoulli-Euler Beams," International Journal of Mechanical Sciences, Vol. 26, No. 11, pp. 639-648, 1984 https://doi.org/10.1016/0020-7403(84)90017-1
  16. Douka, E., Bamnios, G. and Trochidis, A., "A Method for Determining the Location and Depth of Cracks in Double-Cracked Beams," Applied Acoustics, Vol. 65, No. 10, pp. 997-1008, 2004 https://doi.org/10.1016/j.apacoust.2004.05.002
  17. Takahashi, I., "Vibration and Stability of a Cracked Shaft Simultaneously Subjected to a Follower Force with an Axial Force," International Journal of Solids and Structures, Vol. 35, No. 23, pp. 3071-3080, 1998 https://doi.org/10.1016/S0020-7683(97)00364-8
  18. Yoon, H. I. and Son, I. S., "Dynamic Behavior of Cracked Simply Supported Pipe Conveying Fluid with Moving Mass," Journal of Sound and Vibration, Vol. 292, No. 3/5, pp. 941-953, 2006 https://doi.org/10.1016/j.jsv.2005.09.030
  19. Meirovitch, L., "Principles and Techniques of Vibrations," Prentice Hall, pp.400-430, 1997
  20. Inman, D. J., "Engineering Vibration," Prentice-Hall, pp. 329-340, 1994
  21. 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, Issue 1, pp. 1-18, 2000 https://doi.org/10.1006/jsvi.2000.3099