Continuous model for flexural vibration analysis of a Timoshenko cracked beam

• Autorzy: Heydari M. , Ebrahimi A. , Behzad M.
• Języki publikacji: EN

Abstrakty

EN

In this paper, a continuous model for vibration analysis of a beam with an open edge crack including the effects of shear deformation and rotary inertia is presented. A displacement field is suggested for the beam and the strain, and stress fields are calculated. The governing equation of motion for the beam has been obtained using Hamilton’s principle. The equation of motion is solved with a modified Galerkin method and the natural frequencies and mode shapes are obtained. A good agreement has been observed between the results of this research and the results of previous work done in this fiels. The results are also compared to results of a similar model with Euler-Bernoulli assumptions to confirm the advantages of the proposed model in the case of short beams.

Słowa kluczowe

EN

vibration analysis; cracked beam; Timoshenko beam; Galerkin's method; continuous model

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2013
• Tom: Vol. 65, nr 4
• Strony: 265–--288
• Opis fizyczny: Bibliogr. 25 poz., rys., wykr.

Twórcy

autor

Heydari M.

• Sharif University of Technology Mechanical Engineering Department P.O. Box 11365-9567, Azadi Ave. Tehran, Iran

autor

Ebrahimi A.

• Sharif University of Technology Mechanical Engineering Department P.O. Box 11365-9567, Azadi Ave. Tehran, Iran

autor

Behzad M.

• Sharif University of Technology Mechanical Engineering Department P.O. Box 11365-9567, Azadi Ave. Tehran, Iran

Bibliografia

• 1. A.D. Dimarogonas, Vibration of cracked structures: a state of the art review, Engineering Fracture Mechanics, 5 , 831–857, 1996.
• 2. J. Wauer, On the dynamics of cracked rotors: a literature survey, Applied Mechanics Reviews, 43, 1, 13–17, 1990.
• 3. R. Gasch, A survey of the dynamic behavior of a simple rotating shaft with a transverse crack, Journal of Sound and Vibration, 160, 2, 313–332, 1993.
• 4. A.D. Dimarogonas, S.A. Paipetis, Analytical methods in rotor Dynamics, Applied Science Publisher, London, 1983.
• 5. D.Y. Zheng, S.C. Fan, Vibration and stability of cracked hollow-sectional beams, Journal of Sound and Vibration, 267, 933–954, 2003.
• 6. J. Yang, Y. Chen, Y. Xiang, X.L. Jia, Free and forced vibration of cracked inhomogeneous beams under an axial force and a moving load, Journal of Sound and Vibration, 312, 166–181, 2008.
• 7. H.P. Lin, Direct and inverse methods on free vibration analysis of simply supported beams with a crack , Engineering Structures, 26 , 4, 427–436, 2004.
• 8. D.Y. Zheng, S.C. Fan, Vibration and stability of cracked hollow-sectional beams, Journal of Sound and Vibration, 267, 933–954, 2003.
• 9. J.A. Loya, L. Rubio, J. Fernandez-Saez, Natural frequencies for bending vibrations of Timoshenko cracked beams, Journal of Sound and Vibration, 290, 640–653, 2006.
• 10. S. Orhan, Analysis of free and forced vibration of a cracked cantilever beam, NDT&E International, 40, 443–450, 2007.
• 11. X.F. Yang, A.S.J. Swamidas, R. Seshadri, Crack identification in vibrating beams using the energy method , Journal of Sound and Vibration, 244, 2, 339–357, 2001.
• 12. J. Wang, P. Qiao, Vibration of beams with arbitrary discontinuities and boundary conditions, Journal of Sound and Vibration, 308, 12–27, 2007.
• 13. S. Christades, A.D.S. Bar, One-dimensional theory of cracked Bernoulli-Euler beams, Journal of Mechanical Science, 26, 639–648, 1984.
• 14. M.H.H. Shen, C. Pierre, Natural modes of Bernoulli-Euler beams with symmetric cracks, Journal of Sound and Vibration, 138, 1, 115–134, 1990.
• 15. M.H.H. Shen, C. Pierre, Free vibrations of beams with a single-edge crack, Journal of Sound and Vibration, 170 , 2, 237–259, 1994.
• 16. S.H.S. Carneiro, D.J. Iinman, Comments on the free vibration of beams with a single-edge crack , Journal of Sound and Vibration, 244, 4, 729–737, 2001.
• 17. T.G. Chondros, A. D. Dimarogonas, J. Yao, A continuous cracked beam vibration theory, Journal of Sound and Vibration, 215, 1, 17–34, 1998.
• 18. T.G. Chondros, A.D. Dimarogonas, J. Yao, Vibration of a beam with breathing crack, Journal of Sound and Vibration, 239, 1, 57–67, 2001.
• 19. S.H.S. Carneiro, D.J. Inman, Continuous model for the transverse vibration of cracked Timoshenko beams , Journal of Vibration and Acoustics, 124, 310–320, 2002.
• 20. M. Behzad, A. Meghdari, A. Ebrahimi, A linear theory for bending stress–strain analysis of a beam with an edge crack , Engineering Fracture Mechanics, 75, 16, 4695–4705, 2008.
• 21. M. Behzad, A. Meghdari, A. Ebrahimi, A new continuous model for flexural vibration analysis of a cracked beam , Polish Maritime Research, 15, 2, 32–39, 2008.
• 22. M. Behzad, A. Meghdari, A. Ebrahimi, A new approach for vibration analysis of a cracked beam, International Journal of Engineering, 18, 4, 319–330, 2005.
• 23. M. Behzad, A. Meghdari, A. Ebrahimi, A continuous model for forced vibration analysis of a cracked beam, ASME International Mechanical Engineering Congress and Exposition, IMECE 2005, Orlando, Florida, 2005.
• 24. M. Behzad, A. Ebrahimi, A. Meghdari, A continuous vibration theory for beams with a vertical edge crack, Scientica Iranica Transaction B: Mechanical Engineering, 17, 3, 194–204, 2010.
• 25. ANSYS User’s Manual for rev. 8, ANSYS Inc., 2004.