Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30761
Analytical Study and Modeling of Free Vibrations of Functionally Graded Plates Using a Higher Shear Deformation Theory

Authors: A. Meftah, D. Zarga, M. Yahiaoui


In this paper, we have used an analytical method to analyze the vibratory behavior of plates in materials with gradient of properties, simply supported, proposing a refined non polynomial theory. The number of unknown functions involved in this theory is only four, as compared to five in the case of other higher shear deformation theories. The transverse shearing effects are studied according to the thickness of the plate. The motion equations for the FGM plates are obtained by the Hamilton principle application, the solutions are obtained using the Navier method, and then the fundamental frequencies are found, solving an eigenvalue equation system, the results of this analysis are presented and compared to those available in the literature.

Keywords: FGM plates, Navier method, vibratory behavior

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 285


[1] Koizumi (1993), Koizumi, M. (1993), “The concept of FGM Ceramic transactions”, Funct Grad Mater, 34, 3–10.
[2] Tounsi et al (2013), Tounsi, A., Houari, M.S.A., Benyoucef, S. and Adda Bedia, E.A. (2013), “A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates”, Aerosp. Sci. Technol., 24(1), 209-220.
[3] Turan (2016), Turan, M., Adiyaman, G., Kahya, V., Birinci, A. (2016), "Axisymmetric analysis of a functionally graded layer resting on elastic substrate", Structural Engineering and Mechanics, 58(3), 423 - 442.
[4] El-Hassar (2016), El-Hassar, S.M., Benyoucef, S., Heireche, H., Tounsi, A. (2016), "Thermal stability analysis of solar functionally graded plates on elastic foundation using an efficient hyperbolic shear deformation theory", Geomechanics and Engineering, 10(3), 357-386.
[5] Vel (2004), Vel, SS, Batra, RC. (2004), “Three-dimensional exact solution for the vibration of functionally graded rectangular plates”, J Sound Vib, 272, 703–730.
[6] Ferreira (2006), Ferreira, AJM, Batra, RC, Roque, CMC, Qian, LF, Jorge, RMN. (2006), “Natural frequencies of functionally graded plates by a meshless method”, Compos Struct, 75, 593–600.
[7] Qian (2004), Qian, LF, Batra, RC, Chen, LM. (2004), “Static and dynamic deformations of thick functionally graded elastic plates by using higher-order shear and normal deformable plate theory and meshless local Petrov–Galerkin method”, Composites: Part B, 35, 685–697.
[8] Matsunaga (2008), Matsunaga, H. (2008), “Free vibration and stability of functionally graded plates according to a 2-D higher-order deformation theory”, Compos Struct, 82, 499–512.
[9] Meftah et al (2017), A. Meftah , A. Bakora , F. Z. Zaoui ,A. Tounsi and E. A. Adda Bedia , A non-polynomial four variable refined plate theory for free vibration of functionally graded thick rectangular plates on elastic foundation, Steel and Composite Structures, Vol. 23, No. 3 (2017) 317-330
[10] Reddy, J. (2000).Analysis of functionally graded plates. Int.J. Numer. Methods Eng,47, 663–684.
[11] Zenkour, A. (2007) Benchmark trigonometric and 3D elasticity solutions for an exponentially graded thick rectangular plate.
[12] Benferhat Rabia (2017) Analyse et modélisation de l’influence du cisaillement transverse sur le comportement mécanique des plaques en matériaux à gradient de propriété , thèse de doctorat 184p.
[13] Uymaz, B., Aydogdu, M.: Three-dimensional vibration analyses of functionally graded plates under various boundary conditions. J. Reinf. Plast. Compos. 26(18), 1847–1863 (2007)
[14] Trung-Kien Nguyen.(2014). A higher-order hyperbolic shear deformation plate model for analysis of functionally graded materials. Int J Mech Mater Des, 014-9260-3.
[15] Miyamoto Y (1999) “Functionally graded materials: design, processing, and applications. Kluwer, Boston”