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http://dx.doi.org/10.12989/sem.2014.52.4.663

Free vibration analysis of bidirectional functionally graded annular plates resting on elastic foundations using differential quadrature method  

Tahouneh, Vahid (Department of Mechanical Engineering, Islamshahr Branch, Islamic Azad University)
Publication Information
Structural Engineering and Mechanics / v.52, no.4, 2014 , pp. 663-686 More about this Journal
Abstract
This paper deals with free vibration analysis of bidirectional functionally graded annular plates resting on a two-parameter elastic foundation. The formulations are based on the three-dimensional elasticity theory. This study presents a novel 2-D six-parameter power-law distribution for ceramic volume fraction of 2-D functionally graded materials that gives designers a powerful tool for flexible designing of structures under multi-functional requirements. Various material profiles along the thickness and in the in-plane directions are illustrated by using the 2-D power-law distribution. The effective material properties at a point are determined in terms of the local volume fractions and the material properties by the Mori-Tanaka scheme. The 2-D differential quadrature method as an efficient and accurate numerical tool is used to discretize the governing equations and to implement the boundary conditions. The fast rate of convergence of the method is shown and the results are compared against existing results in literature. Some new results for natural frequencies of the plates are prepared, which include the effects of elastic coefficients of foundation, boundary conditions, material and geometrical parameters. The interesting results indicate that a graded ceramic volume fraction in two directions has a higher capability to reduce the natural frequency than conventional 1-D functionally graded materials.
Keywords
nonlinear distribution of material profiles; 3-D vibration analysis of plates; bidirectional functionally graded materials; two-parameter elastic foundations; differential quadrature method;
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Times Cited By KSCI : 2  (Citation Analysis)
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1 Prakash, T. and Ganapathi, M. (2006), "Asymmetric flexural vibration and thermoelastic stability of FGM circular plates using finite element method", Compos Part B, 37(7-8), 642-649.   DOI   ScienceOn
2 Shafiee, A.A., Daneshmand, F., Askari, E., Mahzoon, M. (2014), "Dynamic behavior of a functionally graded plate resting on Winkler elastic foundation and in contact with fluid", Struct. Eng. Mech., 50(1), 53-71.   DOI   ScienceOn
3 Shu, C. (2000), Differential Quadrature and its Application in Engineering, Springer, Berlin, Germany.
4 Shu, C. and Wang, C.M. (1999), "Treatment of mixed and nonuniform boundary conditions in GDQ vibration analysis of rectangular plates", Eng. Struct., 21(2), 125-134.   DOI   ScienceOn
5 Sobhani Aragh, B. and Yas, M.H. (2010), "Static and free vibration analyses of continuously graded fiberreinforced cylindrical shells using generalized power-law distribution", Acta Mech., 215(1-4), 155-173.   DOI
6 Tahouneh, V. and Yas, M.H. (2012), "3-D free vibration analysis of thick functionally graded annular sector plates on Pasternak elastic foundation via 2-D differential quadrature method", Acta Mech., 223(9), 1879-1897.   DOI
7 Tornabene, F. (2009), "Free vibration analysis of functionally graded conical, cylindrical shell and annular plate structures with a four-parameter power-law distribution", Comput. Meth. Appl. Mech. Eng., 198(37-40), 2911-2935.   DOI   ScienceOn
8 Vel, S.S. (2010), "Exact elasticity solution for the vibration of functionally graded anisotropic cylindrical shells", Compos. Struct., 92(11), 2712-2727.   DOI   ScienceOn
9 Vel, S.S. and Batra, R.C. (2002), "Exact solution for thermoelastic deformations of functionally graded thick rectangular plates", AIAA, 40(7), 1421-1433.   DOI   ScienceOn
10 Wang, X. and Wang, Y. (2004), "Free vibration analyses of thin sector plates by the new version of differential quadrature method", Comput. Meth. Appl. Mech. Eng., 193(36-38), 3957-3971.   DOI
11 Xiang, Y., Kitipornchai, S. and Liew, K.M. (1996), "Buckling and vibration of thick laminates on Pasternak foundations", J. Eng. Mech., ASCE, 122(1), 54-63.   DOI
12 Xiang, Y., Wang, C.M. and Kitipornchai, S. (1994), "Exact vibration solution for initially stressed Mindlin plates on Pasternak foundations", Int. J. Mech. Sci., 36(4), 311-316.   DOI   ScienceOn
13 Yas, M.H. and Sobhani Aragh, B. (2010), "Free vibration analysis of continuous grading fiber reinforced plates on elastic foundation", Int. J. Eng. Sci., 48(12), 1881-1895.   DOI   ScienceOn
14 Zhou, D., Cheung, Y.K., Lo, S.H. and Au, F.T.K. (2004), "Three-dimensional vibration analysis of rectangular thick plates on Pasternak foundation", Int. J. Numer. Meth. Eng., 59(10), 1313-1334.   DOI   ScienceOn
15 Zhou, D., Lo, S.H., Au, F.T.K .and Cheung, Y.K. (2006), "Three-dimensional free vibration of thick circular plates on Pasternak foundation", J. Sound Vib., 292(3-5), 726-741.   DOI   ScienceOn
16 Benveniste, Y. (1987), "A new approach to the application of Mori-Tanaka's theory of composite materials", Mech. Mater., 6(2), 147-157.   DOI   ScienceOn
17 Allahverdizadeh, A., Naei, M.H. and Nikkhah Bahrami M. (2008), "Nonlinear free and forced vibration analysis of thin circular functionally graded plates", J. Sound Vib., 310(4-5), 966-984.   DOI   ScienceOn
18 Amini, M.H., Soleimani, M. and Rastgoo, A. (2009), "Three-dimensional free vibration analysis of functionally graded material plates resting on an elastic foundation", Smart Mater. Struct., 18(8), 085015.   DOI   ScienceOn
19 Bellman, R. and Casti, J. (1971), "Differential quadrature and long term integration", J. Math. Anal. Appl., 34(2), 235-238.   DOI
20 Bert, C.W. and Malik, M. (1996), "Differential quadrature method in computational mechanics, a review", Appl. Mech. Rev., 49(1), 1-27.   DOI   ScienceOn
21 Columbia Accident Investigation Board (2003a), Report of Columbia Accident Investigation Board, Vol. I. NASA.
22 Columbia Accident Investigation Board (2003b), In-Flight Options Assessment, Vol. II. NASA, Appendix D.12 (PDF).
23 Dasgupta, A. and Bhandarkar, S.M. (1992), "A generalized self-consistent Mori-Tanaka scheme for fibercomposites with multiple inter-phases", Mech. Mater., 14(1), 67-82.   DOI   ScienceOn
24 Dong, C.Y. (2008), "Three-dimensional free vibration analysis of functionally graded annular plates using the Chebyshev-Ritz method", Mater. Des., 29(8), 1518-1525.   DOI   ScienceOn
25 Ebrahimi, F. and Rastgo, A. (2008), "An analytical study on the free vibration of smart circular thin FGM plate based on classical plate theory", Thin Walled Struct., 46(12), 1402-1408.   DOI   ScienceOn
26 Efraim, E. and Eisenberger, M. (2007), "Exact vibration analysis of variable thickness thick annular isotropic and FGM plates", J. Sound Vib., 299(4-5), 720-738.   DOI   ScienceOn
27 Eraslan, A.N. and Akis, T. (2009), "On the plane strain and plane stress solutions of functionally graded rotating solid shaft and solid disk problems", Acta Mech., 181(1-2), 43-63.
28 Genin, G.M. and Birman, V. (2009), "Micromechanics and Structural Response of Functionally Graded, Particulate-Matrix, Fiber-Reinforced Composites", Int. J. Solids Struct., 46(10), 2136-2150.   DOI   ScienceOn
29 Gupta, U.S., Lal, R. and Sharma, S. (2006), "Vibration analysis of non-homogeneous circular plate of nonlinear thickness variation by differential quadrature method", J. Sound Vib., 298(4-5), 892-906.   DOI   ScienceOn
30 Gupta, U.S., Lal, R. and Jain, S.K. (1990), "Effect of elastic foundation on axisymmetric vibrations of polar orthotropic circular plates of variable thickness", J. Sound Vib., 139(3), 503-513.   DOI   ScienceOn
31 Hosseini Hashemi, S., Omidi, M. and Rokni Damavandi Taher, H. (2009), "The validity range of CPT and Mindlin plate theory in comparison with 3-D vibration analysis of circular plates on the elastic foundation", Eur. J. Mech. A Solids, 28(3-5), 289-304.   DOI   ScienceOn
32 Hosseini Hashemi, S., Rokni Damavandi Taher, H. and Akhavan, H. (2010), "Vibration analysis of radially FGM sectorial plates of variable thickness on elastic foundations", Compos. Struct., 92(7), 1734-1743.   DOI   ScienceOn
33 Hosseini Hashemi, S., Rokni Damavandi Taher, H. and Omidi, M. (2008), "3-D free vibration analysis of annular plates on Pasternak elastic foundation via p-Ritz method", J. Sound Vib., 311(3), 1114-1140.   DOI
34 Hu, G.K. and Weng, G.J. (2000), "The Connections between the double-inclusion model and the Ponte Castaneda- Willis, Mori-Tanaka, and Kuster-Toksoz models", Mech. Mater., 32(8), 495-503.   DOI   ScienceOn
35 Liew, K.M. and Liu, F.L. (2000), "Differential quadrature method for vibration analysis of shear deformable annular sector plates", J. Sound Vib., 230(2), 335-356.   DOI   ScienceOn
36 Liew, K.M., Han, J.B., Xiao, Z.M. and Du, H. (1996), "Differential quadrature method for Mindlin plates on Winkler foundation", Int. J. Mech. Sci., 38(4), 405-421.   DOI   ScienceOn
37 Matsunaga, H. (2000), "Vibration and stability of thick plates on elastic foundations", J. Eng. Mech., ASCE, 126(1), 27-34.   DOI   ScienceOn
38 Liu, F.L. and Liew, K.M. (1999), "Free vibration analysis of Mindlin sector plates numerical solutions by differential quadrature method", Comput. Meth. Appl. Mech. Eng., 177(1-2), 77-92.   DOI   ScienceOn
39 Malekzadeh, P. (2009), "Three-dimensional free vibration analysis of thick functionally graded plates on elastic foundations", Compos. Struct., 89(3), 367-373.   DOI   ScienceOn
40 Malekzadeh, P. and Karami, G. (2004), "Vibration of non-uniform thick plates on elastic foundation by differential quadrature method", Eng. Struct., 26(10), 1473-1482.   DOI   ScienceOn
41 Ming Hung, H. (2010), "Vibration analysis of orthotropic rectangular plates on elastic foundations", Compos. Struct., 92(4), 844-852.   DOI   ScienceOn
42 Mori, T. and Tanaka, K. (1973), "Average stress in matrix and average elastic energy of materials with misfitting inclusions", Acta Metall., 21(5), 571-574.   DOI   ScienceOn
43 Nie, G.J. and Zhong, Z. (2007), "Semi-analytical solution for three-dimensional vibration of functionally graded circular plates", Comput. Mech. Appl., 196(49-52), 4901-4910.   DOI   ScienceOn
44 Nie, G.J. and Zhong, Z. (2010), "Dynamic analysis of multi-directional functionally graded annular plates", Appl. Math. Modell., 34(3), 608-616.   DOI   ScienceOn
45 Ponnusamy, P. and Selvamani, R. (2012), "Wave propagation in a generalized thermo elastic plate embedded in elastic medium", IMM, An Int. J., 5(1), 13-26.