A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler-Bernoulli beams

Journal of Sound and Vibration

Volumn 318, Issue 4-5, 2008, Pages 1210-1229

  Li, X F ^a  

^a CENTRAL SOUTH UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

PARTICLE BEAMS; SHEAR DEFORMATION; SHEAR FLOW;

DEFLECTION AND STRESS; EULER BERNOULLI BEAMS; FUNCTIONALLY GRADED BEAMS; NATURAL FREQUENCIES AND MODES; PHYSICAL QUANTITIES; SIMPLY SUPPORTED BEAMS; STATIC AND DYNAMIC BEHAVIORS; TIMOSHENKO BEAM THEORY;

VIBRATION ANALYSIS;

EID: 55349145939     PISSN: 0022460X     EISSN: 10958568     Source Type: Journal    
DOI: 10.1016/j.jsv.2008.04.056     Document Type: Article

References (30)

1. S. Suresh, A. Mortensen, Fundamentals of Functionally Graded Materials, ASM International and The Institute of Materials, Cambridge, 1995.
2. B. Kieback, A. Neubrand, H. Riedel, Processing techniques for functionally graded materials, Material Science and Engineering A 362 (2003) 81-106.
3. B.V. Sankar, An elasticity solution for functionally graded beams, Composites Science and Technology 61 (2001) 689-696.
4. M. Aydogdu, V. Taskin, Free vibration analysis of functionally graded beams with simply supported edges, Materials and Design 28 (2007) 1651-1656.
5. A. Chabraborty, S. Gopalakrishnan, J.N. Reddy, A new beam finite element for the analysis of functionally graded materials, International Journal of Mechanical Science 45 (2003) 519-539.
6. Z. Zhong, T. Yu, Analytical solution of a cantilever functionally grade beam, Composites Science and Technology 67 (2007) 481-488.
7. C.-F. Lu, W.Q. Chen, Free vibration of orthotropic functionally graded beams with various end conditions, Structural Engineering and Mechanics 20 (2005) 465-476.
8. S.P. Timoshenko, On the transverse vibrations of bars of uniform cross-section, Philosophical Magazine 43 (1922) 125-131.
9. R.Y. Cheng, Vibration of Timoshenko beams and frameworks, ASCE Journal of Structural Division 96 (1970) 551-571.
10. W.P. Howson, F.W. Williams, Natural frequencies of frames with axially loaded Timoshenko members, Journal of Sound and Vibration 26 (1973) 503-515.
11. H. Abramovich, I. Elishakoff, Application of the Krein's method for determination of natural frequencies of periodically supported beam based on simplified Bresse-Timoshenko equations, Acta Mechanica 66 (1987) 39-59.
12. K. Chandrashekhara, K. Krishnamurthy, S. Roy, Free vibration of composite beams including rotary inertia and shear deformation, Composite Structures 14 (1990) 269-279.
13. G. Oliveto, Dynamic stiffness and flexibility functions for axially strained Timoshenko beams, Journal of Sound and Vibration 154 (1992) 1-23.
14. W.Q. Chen, C.F. Lv, Z.G. Bian, Elasticity solution for free vibration of laminated beams, Composite Structures 62 (2003) 75-82.
15. A.M. Horr, L.C. Schmidt, Closed-form solution for the Timoshenko beam theory using a computer-based mathematical package, Computers and Structures 55 (1995) 405-412.
16. J.R. Banerjee, Frequency equation and mode shape formulae for composite Timoshenko beams, Composite Structures 51 (2001) 381-388.
17. T.C. Huang, The effect of rotatory inertia and of shear deformation on the frequency and normal mode equation beams with simple end conditions, ASME Journal of Applied Mechanics 28 (1961) 579-584.
18. A.M. Chervyakov, V.V. Nesterenko, Is it possible to assign physical meaning to field theory with higher derivatives?, Physical Review D 48 (1993) 5811-5817.
19. N.G. Stephen, The second spectrum of Timoshenko beam theory - further assessment, Journal of Sound and Vibration 292 (2006) 372-389.
20. C.M. Wang, Timoshenko beam-bending solutions in terms of Euler-Bernoulli solutions, Journal of Engineering Mechanics 121 (1995) 763-765.
21. J.F. Doyle, Wave Propagation in Structures, Springer, New York, 1989.
22. C.R. Fuller, S.J. Elliott, P.A. Nelson, Active Control of Vibration, Academic, London, 1996.
23. M. Levinson, D.W. Cooke, On the two frequency spectra of Timoshenko beams, Journal of Sound and Vibration 84 (1982) 319-326.
24. K.T. Chan, X.Q. Wang, R.M.C. So, S.R. Reid, Superposed standing waves in a Timoshenko beam, Proceedings of Royal Society London A 458 (2002) 83-108.
25. B. Geist, J.R. McLaughlin, Double eigenvalues for the uniform Timoshenko beam, Applied Mathematics Letters 10 (1997) 129-134.
26. E. Kausel, Nonclassical modes of unrestrained shear beams, Journal of Engineering Mechanics 128 (2002) 663-667.
27. N.F.J. van Rensberg, A.J. van der Merwe, Natural frequencies and modes of a Timoshenko beam, Wave Motion 44 (2006) 58-69.
28. X.-F. Li, S.-H. Guo, Effects of nonhomogeneity on dynamic stress intensity factors for an anti-plane interface crack in a functionally graded material bonded to an elastic semi-strip, Computational Material Science 38 (2006) 432-441.
29. A.J. Markworth, K.S. Ramesh, W.P. Parks Jr., Modelling studies applied to functionally graded materials, Journal of Material Science 30 (1995) 2183-2193.
30. M. Grujicic, H. Zhao, Optimization of 316 stainless steel/alumina functionally graded material for reduction of damage induced by thermal residual stresses, Material Science Engineering A 252 (1998) 117-132.