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http://dx.doi.org/10.7734/COSEIK.2015.28.5.553

3-D Free Vibration Analysis of Exponential and Power-law Functionally Graded Material(FGM) Plates  

Lee, Won-Hong (Department of Civil Engineering, Gyeongnam National University of Science and Technology)
Han, Sung-Cheon (Department of Civil & Railroad Engineering, Daewon University College)
Ahn, Jin-Hee (Department of Civil Engineering, Gyeongnam National University of Science and Technology)
Park, Weon-Tae (Division of Construction and Environmental Engineering Kongju National University)
Publication Information
Journal of the Computational Structural Engineering Institute of Korea / v.28, no.5, 2015 , pp. 553-561 More about this Journal
Abstract
The exponential and power law functionally graded material(FGM) theory is reformulated considering the refined shear and normal deformation theory. This theory has ability to capture the both normal deformation effect and exponential and power law function in terms of the volume fraction of the constituents for material properties through the plate thickness. Navier's method has been used to solve the governing equations for all edges simply supported plates on Pasternak elastic foundation. Numerical solutions of vibration analysis of FGM plates are presented using this theory to illustrate the effects of power law index and 3-D theory of exponential and power law function on natural frequency. The relations between 3-D and 2-D higher-order shear deformation theory are discussed by numerical results. Further, effects of (i) power law index, (ii) side-to-thickness ratio, and (iii) elastic foundation parameter on nondimensional natural frequency are studied. To validate the present solutions, the reference solutions are discussed.
Keywords
3-D free vibration analysis; exponential and power law functionally graded material(FGM); elastic foundation; power law index; side-to-thickness ratio;
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Times Cited By KSCI : 2  (Citation Analysis)
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1 Aydogdu, M. (2009) A New Shear Deformation Theory for Laminated Composite Plates, Compos. Struct., 89, pp.94-101.   DOI
2 Bao, G., Wang, L. (1995) Multiple Cracking in Functionally Graded Ceramic/Metal Coatings, Int. J. Solids Struct., 32, pp.2853-2871.   DOI
3 Belabed, Z., Houari, M.S.A., Tounsi, A., Mahmoud, S.R., Beg, O.A. (2014) An Efficient and Simple Higher Order Shear and Normal Deformation Theory for Functionally Graded Material (FGM) Plates, Compos. Part B: Eng., 60, pp.274-283.   DOI
4 Benachour, A., Daouadji, T.H., Ait Atmanea, H., Tounsi, A., Ahmed, M.S. (2011) A Four Variable Refined Plate Theory for Free Vibrations of Functionally Graded Plates with Arbitrary Gradient, Compos. Part B: Eng., 42, pp.1386-1394.   DOI
5 Bourada, M., Tounsi, A., Houari, M.S.A. (2012) A New Four-variable Refined Plate Theory for Thermal Buckling Analysis of Functionally Graded Sandwich Plates, J. Sandwich Struct. & Mater., 14, pp.5-33.   DOI
6 Carrera, E., Brischetto, S., Cinefra, M., Soave, M. (2011) Effects of Thickness Stretching in Functionally Graded Plates and Shells, Compos. Part B: Eng., 42, pp.123-133.
7 Delale, F., Erdogan, F. (1983) The Crack Problem for a Nonhomogeneous Plane, J. Appl. Mech. (ASME), 50, pp.609-614.   DOI
8 Han, S.C., Park, W.T., Jung, W.Y. (2015) A Four-variable Refined Plate Theory for Dynamic Stability Analysis of S-FGM Plates based on Physical Neutral Surface, Compos. Struct., 131, pp.1081-1089.   DOI
9 Hirano, T., Yamada, T. (1988) Multi-paradigm Expert System Architecture based upon the Inverse Design Concept, International Workshop on Artificial Intelligence for Industrial Applications, Hitachi, Japan.
10 Hosseini-Hashemi, S., Fadaee, M., Atashipour, S.R. (2011a) Study on the Free Vibration of Thick Functionally Graded Rectangular Plates according to a New Exact Closed-form Procedure, Compos. Struct., 93, pp.722-735.   DOI   ScienceOn
11 Hosseini-Hashemi, S., Fadaee, M., Atashipour, S.R. (2011b) A New Exact Analytical Approach for Free Vibration of Reissner-Mindlin Functionally Graded Rectangular Plates, Int. J. Mech. Sci., 53, pp.11-22.   DOI   ScienceOn
12 Jung, W.Y., Han, S.C. (2014) Transient Analysis of FGM and Laminated Composite Structures using a Refined 8-node ANS Shell Element, Compos.: Part B, 56, pp.372-383.   DOI
13 Jung, W.Y., Han, S.C. (2015) Static and Eigenvalue Problems of Sigmoid Functionally Graded Materials (S-FGM) Micro-scale Plates using the Modified Couple Stress Theory, Appl. Math. Model., 39, pp.3506-3524.   DOI
14 Karama, M., Afaq, K.S., 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, pp.1525-1546.   DOI
15 Lee, W.H., Han, S.C., Park, W.T. (2008) Bending, Vibration and Buckling Analysis of Functionally Graded Material Plates, J. Korea Academic-Industrial coop. Soc., 9(4), pp.1043-1049.   DOI
16 Lee, W.H., Han, S.C., Park, W.T. (2015) A Study of Dynamic Instability for Sigmoid Functionally Graded Material Plates on Elastic Foundation, J. Comput. Struct. Eng. Inst.Korea, 28(1), pp.85-92.   DOI
17 Mantari, J.L., Guedes Soares, C. (2014) Optimized Sinusoidal Higher Order Shear Deformation Theory for the Analysis of Functionally Graded Plates and Shells, Compos. Part B: Eng., 56, pp.126-136.   DOI
18 Lu, C.F., Lim, C.W., Chen, W.Q. (2009) Exact Solutions for Free Vibrations of Functionally Graded Thick Plates on Elastic Foundations, Mech. Adv. Mater. & Struct., 16, pp.576-584.   DOI
19 Malekzadeh, P., Monajjemzadeh, S.M. (2013) Dynamic Response of Functionally Graded Plates in Thermal Environment under Moving Load, Compos. Part B: Eng., 45, pp.1521-1533.   DOI
20 Malekzadeh, P., Shojaee, M. (2013) Free Vibration of Nanoplates based on a Nonlocal Two-variable Refined Plate Theory, Compos. Struct., 95, pp.443-452.   DOI
21 Matsunaga, H. (2008) Free Vibration and Stability of Functionally Graded Plates according to a 2-D Higher-order Deformation Theory, Compos. Struct., 82, pp.499-512.   DOI   ScienceOn
22 Mechab, I., Mechab, B., Benaissa, S. (2013) Static and Dynamic Analysis of Functionally Graded Plates using Four-variable Refined Plate Theory by the New Function, Compos. Part B: Eng., 45, 748-757.   DOI
23 Reddy, J.N. (2000) Analysis of Functionally Graded Plates, Int. J. Numer. Methods Eng., 47, pp.663-684.   DOI
24 Reddy, J.N. (2007) Theory and Analysis of Elastic Plates and Shells, CRC Press, London.
25 Senthilnathan, N.R., Chow, S.T., Lee, K.H., Lim, S.P. (1987) Buckling of Shear-deformable Plates, AIAA J., 25, pp.1268-1271.   DOI
26 Shimpi, R.P., Patel, H.G. (2006a) Free Vibrations of Plate using Two Variable Refined Plate Theory, J. Sound & Vib., 296, pp.979-999.   DOI
27 Zenkour, A.M. (2006) Generalized Shear Deformation Theory for Bending Analysis of Functionally Graded Plates, Appl. Math. Model., 30, pp.67-84.   DOI
28 Shimpi, R.P., Patel, H.G. (2006b) A Two Variable Refined Plate Theory for Orthotropic Plate Analysis, Int. J. Solids & Struct., 43, pp.6783-6799.   DOI
29 Thai, H.T., Kim, S.E. (2010) Free Vibration of Laminated Composite Plates using Two Variable Refined Plate Theory, Int. J. Mech. Sci., 52, pp.626-633.   DOI
30 Tran, L.V., Ferreira, A.J.M., Nguyen-Xuan, H. (2013) Isogeometric Analysis of Functionally Graded Plates using Higher-order Shear Deformation Theory, Compos. Part B: Eng., 51, pp.368-383.   DOI