Stability of a cracked Timoshenko beam column by modified Fourier series

Journal of Sound and Vibration

Volumn 264, Issue 2, 2003, Pages 475-484

  Fan, S C ^a   Zheng, D Y ^a  

^a NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

Author keywords

[No Author keywords available]

Indexed keywords

BUCKLING; COLUMNS (STRUCTURAL); CRACKS; FOURIER TRANSFORMS; STABILITY; STIFFNESS MATRIX; STRUCTURAL LOADS;

BUCKLING LOAD; MODIFIED FOURIER SERIES; TIMOSHENKO BEAM COLUMN;

BEAMS AND GIRDERS;

EID: 0037805080     PISSN: 0022460X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-460X(02)01487-6     Document Type: Letter

References (20)

1. T. Irie, G. Yamada, I. Takahashi, Vibration and stability of a non-uniform Timoshenko beam subjected to a follower force, Journal of Sound and Vibration 70 (1980) 503-512.
2. N. Antifantis, A. Dimarogonas, Stability of columns with a single crack subjected to follower and vertical loads, International Journal of Solids and Structures 19 (1983) 281-291.
3. S.Y. Lee, Y.H. Kuo, F.Y. Lin, Stability of a Timoshenko beam resting on a Winkler elastic foundation, Journal of Sound and Vibration 153 (1992) 193-202.
4. I. Takahashi, Vibration and stability of non-uniform cracked Timoshenko beam subjected to follower force, Computers and Structures 71 (1999) 585-591.
5. A.D. Dimarogonas, Vibration of cracked structures: a state of the art review, Engineering Fracture Mechanics 55 (1996) 831-857.
6. G. Gounaris, A.D. Dimarogonas, A finite element of a cracked prismatic beam for structural analysis, Computers and Structures 28 (1988) 309-313.
7. G.L. Qian, S.N. Gu, J.S. Jiang, The dynamic behaviour and crack detection of a beam with a crack, Journal of Sound and Vibration 138 (1990) 233-243.
8. A. Morassi, Crack-induced changes in eigenfrequencies of beam structures, Journal of Engineering Mechanics 119 (1993) 1768-1803.
9. E.I. Shifrin, R. Routolo, Natural frequencies of a beam with an arbitrary number of cracks, Journal of Sound and Vibration 222 (1999) 409-423.
10. D.Y. Zheng, Y.K. Cheung, F.T.K. Au, Y.S. Cheng, Vibration of multi-span non-uniform beams under moving loads by using modified beam vibration functions, Journal of Sound and Vibration 212 (1998) 455-467.
11. 0 modified beam vibration functions, Applied Mathematical Modeling 29 (1999) 19-34.
12. 1 continuous displacement functions, Thin Walled Structures 32 (1998) 289-303.
13. Y.K. Cheung, F.T.K. Au, D.Y. Zheng, Y.S. Cheng, Vibration of multi-span non-uniform bridges under moving vehicles and trains by using modified beam vibration functions, Journal of Sound and Vibration 228 (1999) 611-628.
14. D.Y. Zheng, Vibration and Stability Analysis of Plate-type Structures under Moving Loads by Analytical and Numerical Methods, Ph.D. Thesis, The University of Hong Kong, 1999.
15. Y.K. Cheung, F.T.K. Au, D.Y. Zheng, Finite strip method for the free vibration and buckling analysis of plates with abrupt changes in thickness and complex support conditions, Thin-Walled Structures 36 (2000) 89-110.
16. 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 242 (4) (2001) 701-717.
17. S.C. Fan, D.Y. Zheng, F.T.K. Au, Gibbs phenomenon free Fourier series for vibration and stability of complex beams, American Institute of Aeronautics and Astronautics Journal 39 (10) (2001) 1977-1984.
18. D.Y. Zheng, S.C. Fan, Natural frequency changes of a cracked Timoshenko beam by modified Fourier series, Journal of Sound and Vibration 246 (2) (2001) 297-317.
19. J.Y. Liu, D.Y. Zheng, Z.J. Mei, Practical Integral Transforms in Engineering, Huazhong University of Science and Technology Press, Wuhan, P.R. China, 1995 (in Chinese).
20. D.Y. Zheng, S.C. Fan, Vibration and stability of cracked hollow-sectional beams, Journal of Sound and Vibration, in press.