Abstract
In the present paper, the higher order shear deformation theory is used to analyze the natural frequencies of simply supported functionally graded plate composed of a mixture of Titanium (Ti-6Al-4 V) and zirconia (ZrO2) resting on elastic foundation. This theory accounts for adequate distribution of the transverse shear strains in the thickness of the plate and satisfies the traction free boundary conditions on the top and bottom surface of the plates, thus a shear correction factor is not required. The material properties change within the plate thickness according to the power law distribution of the volume fraction of the constituents (Titanium and zirconia). The equations of motion are derived employing the principle of Hamilton. Navier type solutions are proposed to obtain the natural frequencies of functionally graded plate and efficiency of the theory is ensured by comparing the results with the existing results. Numerical results are computed to examine the effects of different geometrical parameters such the power-law index, aspect ratio, elastic foundation parameters, and side-to-thickness ratio, on the natural frequencies of simply supported functionally graded plate. It can be concluded that the presence of the elastic foundation increases the non dimensional natural frequencies. It can be found also that the normalized natural frequencies of the plate decrease with increasing the volume fraction exponent and slenderness ratio.
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References
Zenkour, A.M.A.: Comprehensive analysis of functionally graded sandwich plates: part 2—Buckling and free vibration. Int. J. Solids Struct. 42, 5243–5258 (2005)
Kashtalyan, M., Menshykova, M.: Three-dimensional elasticity solution for sandwich panels with a functionally graded core. Compos. Struct. 87, 36–43 (2009)
Zenkour, A.M., Alghamdi, N.A.: Bending analysis of functionally graded sandwich plates under the effect of mechanical and thermal loads. Mech. Adv. Mater. Struct. 17, 419–432 (2010)
Cinefra, M., Soave, M.: Accurate vibration analysis of multilayered plates made of functionally graded materials. Mech. Adv. Mater. Struct. 18, 3–13 (2011)
Daouadji, T.H., Adim, B., Benferhat, B.: Bending analysis of an imperfect FGM plates under hygro-thermo-mechanical loading with analytical validation. Adv. Mater. Res. 5(1), 35–53 (2016)
Akbas, S.D.: Thermal effects on the vibration of functionally graded deep beams with porosity. Int. J. Appl. Mech. 9(5), 1750076 (2017)
El-Zafrany, A., Fadhil, S., Al-Hosani, K.A.: New fundamental solution for boundary element analysis of thick plates on winkler foundation. Int. J. Numer. Meth. Eng. 38, 887–903 (1995)
Omurtag, M.H., Kadioglu, F.: Free vibration analysis of orthotropic plates resting on pasternak foundation by mixed finite element formulation. Comput. Struct. 67, 253–265 (1998)
Setoodeh, A.R., Karami, G.: Static, free vibration and buckling analysis of anisotropic thick laminated composite plates on distributed and point elastic supports using a 3-D layer-wise FEM. Eng. Struct. 26, 211–220 (2004)
Xiang, Y., Kitipornchai, S., Liew, K.M.: Buckling and vibration of thick laminates on pasternak foundation. J. Eng. Mech. ASCE 122(1), 54–63 (1996)
Hui-Shen, S., Zheng, J.J., Huang, X.L.: Dynamic response of shear deformable laminated plates under thermo-mechanical loading and resting on elastic foundations. Compos. Struct. 60, 57–66 (2003)
Bennai, R., Fourn, H., Ait Atmane, H., Tounsi, A., Bessaim, A.: A dynamic and wive propagation investigation of FGM plates with porosities using a four variable plate theory. Wind Struct. 28(1), 49–62 (2019)
Hayat, S., Tounsi, A., Bousahla, A.A.: A simple hyperbolic shear deformation theory for vibration analysis of thick functionally graded rectangular plates resting on elastic foundations. Geomech. Eng. An Int’l J. 11(2), 289–307 (2016)
Hosseini-Hashemi, S.H., Rokni Damavandi Taher, H., Akhavan, H., Omidi, M.: Free vibration of functionally graded rectangular plates using first-order shear deformation plate theory. Appl. Math. Model. 34, 1276–1291 (2010)
Akavci, S.S.: An efficient shear deformation theory for free vibration of functionally graded thick rectangular plates on elastic foundation. Compos. Struct. 108, 667–676 (2014)
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Saidi, H., Sahla, M., Tounsi, A. (2020). Natural Frequencies of Functionally Graded Plate Composed of a Mixture of Titanium (Ti-6Al-4V) and Zirconia (ZrO2). In: Benmounah, A., Abadlia, M.T., Saidi, M., Zerizer, A. (eds) Proceedings of the 4th International Symposium on Materials and Sustainable Development. ISMSD 2019. Springer, Cham. https://doi.org/10.1007/978-3-030-43268-3_18
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DOI: https://doi.org/10.1007/978-3-030-43268-3_18
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