Browse > Article
http://dx.doi.org/10.12989/scs.2015.18.1.187

Free vibration analysis of functionally graded plates with temperature-dependent properties using various four variable refined plate theories  

Attia, Amina (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
Bedia, E.A. Adda (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
Mahmoud, S.R. (Department of Mathematics, Faculty of Science, King Abdulaziz University)
Publication Information
Steel and Composite Structures / v.18, no.1, 2015 , pp. 187-212 More about this Journal
Abstract
In this paper, various four variable refined plate theories are presented to analyze vibration of temperature-dependent functionally graded (FG) plates. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations for the present model is reduced, significantly facilitating engineering analysis. These theories account for parabolic, sinusoidal, hyperbolic, and exponential distributions of the transverse shear strains and satisfy the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. Power law material properties and linear steady-state thermal loads are assumed to be graded along the thickness. Uniform, linear, nonlinear and sinusoidal thermal conditions are imposed at the upper and lower surface for simply supported FG plates. Equations of motion are derived from Hamilton's principle. Analytical solutions for the free vibration analysis are obtained based on Fourier series that satisfy the boundary conditions (Navier's method). Non-dimensional results are compared for temperature-dependent and temperature-independent FG plates and validated with known results in the literature. Numerical investigation is conducted to show the effect of material composition, plate geometry, and temperature fields on the vibration characteristics. It can be concluded that the present theories are not only accurate but also simple in predicting the free vibration responses of temperature-dependent FG plates.
Keywords
functionally graded plate; higher-order plate theory; vibration; temperature-dependent properties;
Citations & Related Records
Times Cited By KSCI : 4  (Citation Analysis)
연도 인용수 순위
1 Ait Atmane Meziane, H., Tounsi, A. and Adda Bedia, E.A. (2010), "Free vibration analysis of functionally graded plates resting on Winkler-Pasternak elastic foundations using a new shear deformation theory", International Journal of Mechanics and Materials in Design, 6(2), 113-121.   DOI
2 Ait Atmane Meziane, M., Abdelaziz, H.H. and Tounsi, A. (2014), "An efficient and simple refined theory for buckling and free vibration of exponentially graded sandwich plates under various boundary conditions", J. Sandwich Struct. Mater., 16(3), 293-318.   DOI
3 Akavci, S. (2010), "Two new hyperbolic shear displacement models for orthotropic laminated composite plates", Mech. Compos. Mater., 46(2), 215-226.   DOI
4 Bouazza, M., Tounsi, A., Adda Bedia, E.A. and Megueni, A. (2009), "Buckling analysis of functionally graded plates with simply supported edges", Leonardo Journal of Sciences, 15(8), 2-32.
5 Bouderba, B., Houari, M.S.A. and Tounsi, A. (2013), "Thermomechanical bending response of FGM thick plates resting on Winkler-Pasternak elastic foundations", Steel Compos. Struct., Int. J., 14(1), 85-104.   DOI   ScienceOn
6 Bourada, M., Tounsi, A., Houari, M.S.A. and Adda Bedia, E.A. (2012), "A new four-variable refined plate theory for thermal buckling analysis of functionally graded sandwich plates", J. Sandwich Struct. Mater., 14(1), 5-33.   DOI
7 Chi, S. and Chung, Y. (2006a), "Mechanical behavior of functionally graded material plates under transverse load. Part I: Analysis", Int. J. Sol. Struct., 43(13), 3657-3674.   DOI
8 Chi, S. and Chung, Y. (2006b), "Mechanical behavior of functionally graded material plates under transverse load. Part II: Numerical results", Int. J. Sol. Struct., 43(13), 3675-3691.   DOI
9 Grover, N., Maiti, D.K. and Singh, B.N. (2013), "A new inverse hyperbolic shear deformation theory for static and buckling analysis of laminated composite and sandwich plates", Compos. Struct., 95, 667-675.   DOI   ScienceOn
10 Fekrar, A., El Meiche, N., Bessaim, A., Tounsi, A. and Adda Bedia, E.A. (2012), "Buckling analysis of functionally graded hybrid composite plates using a new four variable refined plate theory", Steel Compos. Struct., Int. J., 13(1), 91-107.   DOI   ScienceOn
11 Huang, X. and Shen, H. (2004), "Nonlinear vibration and dynamic response of functionally graded plates in thermal environments", Int. J. Solid. Struct., 41(9-10), 2403-2427.   DOI
12 Karama, M., Afaq, K.S. and Mistou, S. (2003), "Mechanical behaviour of laminated composite beam by the new multi-layered laminated composite structures model with transverse shear stress continuity", Int. J. Solids Struct., 40(6), 1525-1546.   DOI
13 Kettaf, F.Z., Houari, M.S.A., Benguediab, M. and Tounsi, A. (2013), "Thermal buckling of functionally graded sandwich plates using a new hyperbolic shear displacement model", Steel Compos. Struct., Int. J., 15(4), 399-423.   과학기술학회마을   DOI
14 Kim, Y. (2005), "Temperature dependent vibration analysis of functionally graded rectangular plates", J. Sound Vib., 284(3-5), 531-549.   DOI
15 Li, Q., Iu, V. and Kou, K. (2009), "Three-dimensional vibration analysis of functionally graded material plates in thermal environment", J. Sound Vib., 324(3-5), 733-750.   DOI
16 Mantari, J.L., Oktem, A.S. and Guedes Soares, C. (2012), "A new trigonometric shear deformation theory for isotropic, laminated composite and sandwich plates", Int. J. Solids Struct., 49(1), 43-53.   DOI   ScienceOn
17 Mindlin, R.D. (1951), "Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates", J. Appl.Mech., 18(1), 31-38.
18 Reddy, J.N. (2000), "Analysis of functionally graded plates", Int. J. Numer. Method. Eng., 47(1-3), 663-684.   DOI
19 Pradyumna, S. and Bandyopadhyay, J.N. (2008), "Free vibration analysis of functionally graded curved panels using a higher-order finite element formulation", J. Sound Vib., 318(1-2), 176-192.   DOI
20 Reddy, J.N. (1984), "A simple higher-order theory for laminated composite plates", J. Appl. Mech., 51(4), 745-752.   DOI
21 Reddy, J.N. (2004), Mechanics of Laminated Composite Plates and Shells, CRC Press.
22 Reissner, E. (1945), "The effect of transverse shear deformation on the bending of elastic plates", J. Appl. Mech., 12(2), 69-72.
23 Ren, J.G. (1986), "A new theory of laminated plate", Compos. Sci. Technol., 26(3), 225-239.   DOI
24 Shahrjerdi, A., Mustapha, F., Bayat, M. and Majid, D.L.A. (2011), "Free vibration analysis of solar functionally graded plates with temperature-dependent material properties using second order shear deformation theory", J. Mech. Sci. Techol., 25(9), 2195-2209.   DOI
25 Soldatos, K.P. (1992), "A transverse shear deformation theory for homogeneous monoclinic plates", Acta Mech., 94(3), 195-220.   DOI
26 Touratier, M. (1991), "An efficient standard plate theory", Int. J. Eng. Sci., 29(8), 901-916.   DOI
27 Xiang, S., Wang, K.M., Ai, Y.T., Sha, Y.D. and Shi, H. (2009), "Analysis of isotropic, sandwich and laminated plates by a meshless method and various shear deformation theories", Compos. Struct., 91(1), 31-37.   DOI
28 Yaghoobi, H. and Yaghoobi, P. (2013), "Buckling analysis of sandwich plates with FGM face sheets resting on elastic foundation with various boundary conditions: An analytical approach", Meccanica, 48(8), 2019-2035.   DOI   ScienceOn
29 Yaghoobi, H. and Torabi, M. (2013a), "Post-buckling and nonlinear free vibration analysis of geometrically imperfect functionally graded beams resting on nonlinear elastic foundation", Appl. Math. Model., 37(18-19), 8324-8340.   DOI
30 Yaghoobi, H. and Torabi, M., (2013b), "An analytical approach to large amplitude vibration and postbuckling of functionally graded beams rest on non-linear elastic foundation", J. Theor. Appl. Mech., 51(1), 39-52.