RESONANT SUBHARMONIC VIBRATIONS OF A BEAM WITH A BREATHING FATIGUE CRACK

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DOI https://doi.org/10.15407/pmach2016.02.025
Journal Journal of Mechanical Engineering – Problemy Mashynobuduvannia
Publisher A. Podgorny Institute for Mechanical Engineering Problems
National Academy of Science of Ukraine
ISSN 0131-2928 (Print), 2411-0779 (Online)
Issue Vol. 19, no. 2, 2016 (June)
Pages 25-30
Cited by J. of Mech. Eng., 2016, vol. 19, no. 2, pp. 25-30

 

Authors

K. V. Avramov, A. Podgorny Institute of Mechanical Engineering Problems of NASU (2/10, Pozharsky St., Kharkiv, 61046, Ukraine), e-mail: kvavramov@gmail.com, ORCID: 0000-0002-8740-693X

T. P. Raimberdiyev, Akhmet Yassawi International Kazakh-Turkish University (29, B. Sattarkhanov Ave, Turkestan, Kazakhstan)

E. M. Shekhvatova, National Aerospace University “KhAI” (17, Chkalov St., Kharkov, 61070, Ukraine)

 

Abstract

To describe the vibrations of a beam with a transverse crack, a quasilinear dynamical system with a finite number of degrees of freedom is obtained. To obtain this system, the solution was decomposed according to the forms of linear oscillations. The Galerkin method was applied to partial differential equations describing the vibrations of a beam with a crack. Nonlinear dynamical systems with two and three degrees of freedom with internal resonances were analyzed. In a quasilinear dynamical system, subharmonic vibrations in the region of the second main resonance were studied using the method of multiple scales.

 

Keywords: vibrations of a beam with a breathing crack, Bubnov-Galerkin method, finite degrees of freedom dynamical system, method of multiple scales, principle resonance)

 

References

  1. Luzzato, E. (2003). Approximate computation of non-linear effects in a vibrating cracked beam. J. of Sound and Vibr., vol. 265, pp. 745–763. https://doi.org/10.1016/S0022-460X(02)01562-6
  2. Christides, S. & Barr, A. D. S. (1984). One- dimensional theory of cracked Bernoulli- Euler beams. J. Mech. Sci., vol. 26, pp. 639–648. https://doi.org/10.1016/0020-7403(84)90017-1
  3. Shen, M.-H. H. & Pierre, C. (1994). Free vibrations of beams with a single-edge crack. J. of Sound and Vibr., vol. 170, pp. 237–259. https://doi.org/10.1006/jsvi.1994.1058
  4. Shen, M.-H. H. & Chu, Y. C. (1992). Vibrations of beams with a fatigue crack. Comp. and Struc., vol. 45, pp. 79–93. https://doi.org/10.1016/0045-7949(92)90347-3
  5. Chu, Y. C. & Shen, M.-H. H. (1992). Analysis of forced bilinear oscillators and the application to cracked beam dynamics. AIAA Journal, vol. 30, pp. 2512–2519. https://doi.org/10.2514/3.11254
  6. Chondros, T. G., Dimarogonas, A. D, & Yao, J. (1998). A continuous cracked beam vibration theory. J. of Sound and Vibr., vol. 215, pp. 17–34. https://doi.org/10.1006/jsvi.1998.1640
  7. Nayfeh, A. H. & Mook, D. T. (1988). Nonlinear oscillations. New York: Wiley, 865 p.

 

Received 01 February 2016

Published 30 June 2016