SHAPE EFFECT ON FREE VIBRATION OF FUNCTIONALLY GRADED PLATES

Year 2014, , 52 - 67, 01.12.2014

Hasan Kurtaran

https://doi.org/10.24107/ijeas.251237

Cited By: 3

Abstract

In this article, shape effect on free vibration behavior of functionally graded plates is investigated. Square, rectangular, skew, circular, elliptical, annular and equilateral triangular plates with the same surface area and thickness are considered. Frequency values of these plates are compared for simply supported and clamped boundary conditions. Finite element method (FEM) is used in calculating frequency values and mode shapes. Since commercial codes do not allow inputting functionally graded material properties directly, MATLAB code was developed for FEM solution. Findings of this study can be useful for designers that have freedom to choose the plate shape in engineering applications

Keywords

Free Vibration, Plate, Functionally Graded Material, Finite Element Analyses

References

• [1] Yang, J. and Shen, H. S., Dynamic response of initially stressed functionally graded rectangular thin plates, Composite Structures, 54(4), 497-508, 2001.
• [2] Hosseini-Hashemi, Sh., Fadaee, M. and Atashipour, S.R., A new exact analytical approach for free vibration of Reissner–Mindlin functionally graded rectangular plates, International Journal of Mechanical Sciences, 53(1), 11-22, 2011.
• [3] Hosseini-Hashemi, Sh., Fadaee, M. and Atashipour, S.R., Study on the free vibration of thick functionally graded rectangular plates according to a new exact closed-form procedure, Composite Structures, 93(2), 722-735, 2011.
• [4] Sheikholeslami, S.A. and Saidi, A.R., Vibration analysis of functionally graded rectangular plates resting on elastic foundation using higher-order shear and normal deformable plate theory, Composite Structures, 106, 350-361, 2013.
• [5] Huang, C.S., McGee, III O.G. and Wang, K.P., Three-dimensional vibrations of cracked rectangular parallelepipeds of functionally graded material, International Journal of Mechanical Sciences, 70, 1-25, 2013.
• [6] Latifi, M., Farhatnia, F. and Kadkhodaei, M., Buckling analysis of rectangular functionally graded plates under various edge conditions using Fourier series expansion, European Journal of Mechanics-A/Solids, 41, 16–27, 2013.
• [7] Kim, Y. W., Temperature dependent vibration analysis of functionally graded rectangular plates, Journal of Sound and Vibration, 284(3-5), 531–549, 2005.
• [8] Sundararajana, N., Prakashb, T. and Ganapathic, M., Nonlinear free flexural vibrations of functionally graded rectangular and skew plates under thermal environments, Finite Elements in Analysis and Design, 42(2), 152–168, 2005.
• [9] Upadhyay, A.K. and Shukla, K.K., Geometrically nonlinear static and dynamic analysis of functionally graded skew plates, Communications in Nonlinear Science and Numerical Simulation, 18(8), 2252-2279, 2013.
• [10] Singha, M.K. and Daripa, R., Nonlinear vibration of symmetrically laminated composite skew plates by finite element method, International Journal of Non-Linear Mechanics, 42(9), 1144-1152, 2007.
• [11] Ganapathia, M. and Prakashb, T., Thermal buckling of simply supported functionally graded skew plates, Composite Structures, 74(2), 247-250, 2006.
• [12] Nie, G.J. and Zhong, Z., Semi-analytical solution for three-dimensional vibration of functionally graded circular plates, Computer Methods in Applied Mechanics and Engineering, 196(49-52), 4901-4910, 2007.
• [13] Allahverdizadeh, A., Naei, M.H. and Bahrami, M. N., Nonlinear free and forced vibration analysis of thin circular functionally graded plates, Journal of Sound and Vibration, 310(4-5), 966-984, 2008.
• [14] Allahverdizadeh, A., Naei, M.H. and Bahrami, M. N., Vibration amplitude and thermal effects on the nonlinear behavior of thin circular functionally graded plates, International Journal of Mechanical Sciences, 50(3), 445-454, 2008.
• [15] Zhu, P. and Liew, K.M., A local Krigingmeshless method for free vibration analysis of functionally graded circular plates in thermal environments, International Conference on Advances in Computational Modeling and Simulation Procedia Engineering, 31, 1089-1094, 2012.
• [16] Talabi, M. R. and Saidi, A. R., An explicit exact analytical approach for free vibration of circular/annular functionally graded plates bonded to piezoelectric actuator/sensor layers based on Reddy’s plate theory, Applied Mathematical Modelling, 37(14-15), 7664-7684, 2013.
• [17] Matsunaga, H., Free vibration and stability of functionally graded circular cylindrical shells according to a 2D higher-order deformation theory, Composite Structures, 88(4), 519- 531, 2009.
• [18] Hosseini-HashemiSh., Fadaee M. and Es'haghi, M., A novel approach for in-plane/outof-plane frequency analysis of functionally graded circular/annular plates, International Journal of Mechanical Sciences, 52(8), 1025-1035, 2010.
• [19] Patel, B.P., Gupta, S.S., Loknath, M.S. and Kadu, C.P., Free vibration analysis of functionally graded elliptical cylindrical shells using higher-order theory, Composite Structures, 69(3), 259-270, 2005.
• [20] Hsieh, J. J. and Lee, L. T., An inverse problem for a functionally graded elliptical plate with large deflection and slightly disturbed boundary, International Journal of Solids and Structures, 43(20), 5981-5993, 2006.
• [21] Zhang, D-G, Non-linear bending analysis of super elliptical thin plates, International Journal of Non-Linear Mechanics, 55, 180-185, 2013.
• [22] Çeribaşı, S., Altay, G. and Dökmeci, M. C., Static analysis of superelliptical clamped plates by Galerkin's method, Thin-Walled Structures, 46(2), 122-127, 2008.
• [23] Nie, G.J. and Zhong, Z., Vibration analysis of functionally graded annular sectorial plates with simply supported radial edges, Composite Structures, 84(2), 167-176, 2008.
• [24] Nie, G. and Zhong, Z., Dynamic analysis of multi-directional functionally graded annular plates, Applied Mathematical Modelling, 34(3), 608-616, 2010.
• [25] Hosseini-Hashemi, S., Derakhshani, M. and Fadaee, M., An accurate mathematical study on the free vibration of stepped thickness circular/annular Mindlin functionally graded plates, Applied Mathematical Modelling, 37(6), 4147-4164, 2013.
• [26] Jodaeia, A., Jalalb, M. and Yasa, M.H., Free vibration analysis of functionally graded annular plates by state-space based differential quadrature method and comparative modeling by ANN, Composites Part B: Engineering, 43(2), 340-353, 2012.
• [27] Ebrahimi, F., Rastgoo, A. and Atai, A.A., A theoretical analysis of smart moderately thick shear deformable annular functionally graded plate, European Journal of Mechanics - A/Solids, 28(5), 962-973, 2009.
• [28] Tajeddini, V., Ohadi, A. and Sadighi, M., Three-dimensional free vibration of variable thickness thick circular and annular isotropic and functionally graded plates on Pasternak foundation, International Journal of Mechanical Sciences, 53(4), 300-308, 2011.
• [29] Belalia, S.A. and Houmat, A., Nonlinear free vibration of functionally graded shear deformable sector plates by a curved triangular p-element, European Journal of Mechanics - A/Solids, 35, 1-9, 2012.
• [30] Reddy, J.N., Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press; 2nd edition, 2004.