A new approach for free vibration of axially functionally graded beams with non-uniform cross-section

Journal of Sound and Vibration

Volumn 329, Issue 11, 2010, Pages 2291-2303

  Huang, Yong ^a   Li, Xian Fang ^a  

^a CENTRAL SOUTH UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

CONSTITUENT PHASIS; FAST CONVERGENCE; FLEXURAL RIGIDITIES; FREDHOLM INTEGRAL EQUATIONS; FREE END; FREE VIBRATION; FUNCTIONALLY GRADED BEAMS; FUNDAMENTAL FREQUENCIES; GOVERNING EQUATIONS; GRADIENT PARAMETER; MASS DENSITIES; MATERIAL PROPERTY; NEW APPROACHES; NON-HOMOGENEOUS; NONHOMOGENEITY; NONTRIVIAL SOLUTION; NONUNIFORM; NUMERICAL RESULTS; OPTIMUM DESIGNS; SIMPLE APPROACH; SIMPLY SUPPORTED; TAPERED BEAM; VARIABLE WIDTH; VARYING COEFFICIENTS;

CONVERGENCE OF NUMERICAL METHODS; INTEGRAL EQUATIONS; NUMERICAL ANALYSIS; ZIRCONIA;

NATURAL FREQUENCIES;

EID: 75749124983     PISSN: 0022460X     EISSN: 10958568     Source Type: Journal    
DOI: 10.1016/j.jsv.2009.12.029     Document Type: Article

References (30)

1. Koizumi M. The concept of FGM. Ceramic Transactions on Functional Grade Materials 34 (1993) 3-10
2. Birman V., and Byrd L.W. Modeling and analysis of functionally graded materials and structures. Applied Mechanics Review 60 (2007) 195-216
3. Sankar B.V. An elasticity solution for functionally graded beams. Composite Science and Technology 61 (2001) 689-696
4. Kapuria S., Bhattacharyya M., and Kumar A.N. Bending and free vibration response of layered functionally graded beams: a theoretical model and its experimental validation. Composite Structures 82 (2008) 390-402
5. Li X.-F. A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler-Bernoulli beams. Journal of Sound and Vibration 318 (2008) 1210-1229
6. Benatta M.A., Mechab I., Tounsi A., and Bedia E.A.A. Static analysis of functionally graded short beams including warping and shear deformation effects. Computational Materials Science 44 (2008) 765-773
7. Sina S.A., Navazi H.M., and Haddadpour H. An analytical method for free vibration analysis of functionally graded beams. Materials and Designs 30 (2009) 741-747
8. Kang Y.-A., and Li X.-F. Bending of functionally graded cantilever beam with power-law non-linearity subjected to an end force. International Journal of Non-Linear Mechanics 44 (2009) 696-703
9. Elishakoff I., and Candan S. Apparently first closed-form solutions for vibrating inhomogeneous beams. International Journal of Solids and Structures 38 (2001) 3411-3441
10. Elishakoff I., and Candan S. Apparently first closed-form solution for frequencies of deterministically and/or stochastically inhomogeneous simply supported beams. Journal of Applied Mechanics 68 (2001) 176-185
11. Elishakoff I., and Guede Z. Analytical polynomial solutions for vibrating axially graded beams. Mechanics of Advanced Materials and Structures 11 (2004) 517-533
12. Wu L., Wang Q., and Elishakoff I. Semi-inverse method for axially functionally graded beams with an anti-symmetric vibration mode. Journal of Sound and Vibration 284 (2005) 1190-1202
13. Calio I., and Elishakoff I. Closed-form trigonometric solutions for inhomogeneous beam-columns on elastic foundation. International Journal of Structural Stability and Dynamics 4 (2004) 139-146
14. Calio I., and Elishakoff I. Closed-form solutions for axially graded beam-columns. Journal of Sound and Vibration 280 (2005) 1083-1094
15. Li Q.S. A new exact approach for determining natural frequencies and mode shapes of non-uniform shear beams with arbitrary distribution of mass or stiffness. International Journal of Solids and Structures 37 (2000) 5123-5141
16. Li Q.S. Classes of exact solutions for buckling of multi-step non-uniform columns with an arbitrary number of cracks subjected to concentrated and distributed axial loads. International Journal of Engineering Science 41 (2003) 569-586
17. Laura P.A.A., De Greco B.V., Utjes J., and Carnicer R. Numerical experiments on free and forced vibrations of beams of non-uniform cross section. Journal of Sound and Vibration 120 (1988) 587-596
18. Abrate S. Vibration of non-uniform rods and beams. Journal of Sound and Vibration 185 (1995) 703-716
19. Mabie H.H., and Rogers C.B. Transverse vibrations of tapered cantilever beams with end loads. Journal of the Acoustical Society of America 36 (1964) 463-469
20. Kumar B.M., and Sujith R.I. Exact solutions for the longitudinal vibration of non-uniform rods. Journal of Sound and Vibration 207 (1997) 721-729
21. Naguleswaran S. Vibration of an Euler-Bernoulli beam of constant depth and with linearly varying breadth. Journal of Sound and Vibration 153 (1992) 509-522
22. Naguleswaran S. A direct solution for the transverse vibration of Euler Bernoulli wedge and cone beams. Journal of Sound and Vibration 172 (1994) 289-304
23. Singh K.V., Li G., and Pang S.S. Free vibration and physical parameter identification of non-uniform composite beams. Composite Structures 74 (2006) 37-50
24. Nachum S., and Altus E. Natural frequencies and mode shapes of deterministic and stochastic non-homogeneous rods and beams. Journal of Sound and Vibration 302 (2007) 903-924
25. Keer L.M., and Stahl B. Eigenvalue problems of rectangular plates with mixed edge conditions. ASME Journal of Applied Mechanics 39 (1972) 513-520
26. Melnikov Y.A. Influence Functions and Matrices (1999), Marcel Dekker, New York
27. Weaver Jr. W., Timoshenko S.P., and Young D.H. Vibration Problems in Engineering (1990), Wiley-Interscience, New York
28. Hodges D.H., Chung Y.Y., and Shang X.Y. Discrete transfer matrix method for non uniform rotating beams. Journal of Sound and Vibration 169 (1994) 276-283
29. Cortinez V.H., and Laura P.A.A. An extension of Timoshenko's method and its application to buckling and vibration problems. Journal of Sound and Vibration 169 (1994) 141-144
30. Vel S.S., and Batra R.C. Three-dimensional exact solution for the vibration of functionally graded rectangular plates. Journal of Sound and Vibration 272 (2004) 703-730