Journal of Applied and Computational Mechanics
Vibration and Static Analysis of Functionally Graded Porous Plates
Document Type : Research Paper
Author
Department of Civil Engineering, Bursa Technical University, Bursa, 16330, Turkey
Abstract
This research deals with free vibration and static bending of a simply supported functionally graded (FG) plate with the porosity effect. Material properties of the plate which are related to its change are position-dependent. Governing equations of the FG plate are obtained by using the Hamilton’s principle within first-order shear deformation plate theory. In solving the problem, the Navier solution is also used. In this study, the effect of the porosity and material distribution parameters on the static and vibration responses of the FG plate is presented and discussed.
Keywords
Main Subjects
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[15] Jadhav, P.A. and Bajoria, K.M., “Buckling of piezoelectric functionally graded plate subjected to electro-mechanical loading”, Smart Materials and Structures, 21(10), pp. 105005, 2012.
[16] Singh, J. and Shukla, K. K., “Nonlinear flexural analysis of functionally graded plates under different loadings using RBF based meshless method”, Engineering Analysis with Boundary Elements, 36(12), pp. 1819-1827, 2012.
[17] Daouadji, T.H., Tounsi and Adda Bedia, E-A. “Analytical solution for bending analysis of functionally graded plates”, Scientia Iranica, 20(3), pp. 516-523, 2013.
[18] Asemi, K. and Shariyat, M., “Highly accurate nonlinear three-dimensional finite element elasticity approach for biaxial buckling of rectangular anisotropic FGM plates with general orthotropy directions”, Composite Structures. 106, pp. 235-249, 2013.
[19] Czechowski, L. and Kowal-Michalska, K. “Static and dynamic buckling of rectangular functionally graded plates subjected to thermal loading”, Strength of Materials, 45(6), pp. 666-673, 2013.
[20] Civalek, Ö., Korkmaz, A. and Demir,C. “Discrete singular convolution approach for buckling analysis of rectangular Kirchhoff plates subjected to compressive loads on two-opposite edges” Advances in Engineering Software, 41(4), pp. 557-560, 2010.
[21] Tahouneh, V., “Free vibration analysis of thick CGFR annular sector plates resting on elastic foundations”, Structural Engineering and Mechanics, 50(6), pp. 773-796, 2013.
[22] Swaminathan, K., and Naveenkumar, D. T. “Assessment of First Order Computational Model for Free Vibration Analysis of FGM Plates”, International Journal of Scientific and Engineering Research, 4(5), pp. 115-118, 2013.
[23] Jin, G., Su, Z., Ye, T. and Gao, S., “Three-dimensional free vibration analysis of functionally graded annular sector plates with general boundary conditions”, Composites Part B: Engineering, 83, pp. 352-366, 2015.
[24] AkbaÅŸ, Åž.D., “Termo-Mechanical Vibration of Functionally Graded Nano Plates and Beams Based on Couple Stress Theory”, 3rd International Conference on Advanced Technology Sciences, Konya/Turkey, 01-03 September, 2016.
[25] Van Long, N., Quoc, T.H. and Tu, T.M., “Bending and free vibration analysis of functionally graded plates using new eight-unknown shear deformation theory by finite-element method”, International Journal of Advanced Structural Engineering, 8(4), pp. 391-399, 2016.
[26] Civalek, Ö. “Free vibration of carbon nanotubes reinforced (CNTR) and functionally graded shells and plates based on FSDT via discrete singular convolution method” Composites Part B: Engineering, 111, pp. 45-59, 2017.
[27] Barati, M.R. and Zenkour, A.M., “Electro-thermoelastic vibration of plates made of porous fuctionally graded piezoelectric materials under various boundary conditions”, Journal of Vibration and Control, doi: 10.1177/1077546316672788, 2016.
[28] Mercan, K., Demir, Ç. And Civalek, Ö. “Vibration analysis of FG cylindrical shells with power-law index using discrete singular convolution technique”Curved and Layered Structures, 3(1), 2016.
[29] Wattanasakulpong, N. and Ungbhakorn, V., “Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities”, Aerospace Science and Technology, 32(1), pp. 111-120, 2014.
[30] Mechab, I., Mechab, B., Benaissa, S., Serier, B., Bouiadjra, B.B., “Free vibration analysis of FGM nanoplate with porosities resting on Winkler Pasternak elastic foundations based on two-variable refined plate theories”, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 38(8), pp. 2193–2211, 2016.
[31] Mechab, B., Mechab, I., Benaissa, S., Ameri, M. and Serier, B., “Probabilistic analysis of effect of the porosities in functionally graded material nanoplate resting on Winkler–Pasternak elastic foundations”, Applied Mathematical Modelling, 40(2), pp. 738-749, 2016.
[32] ÅžimÅŸek, M. and Aydın, M., “Size-dependent forced vibration of an imperfect functionally graded (FG) microplate with porosities subjected to a moving load using the modified couple stress theory”, Composite Structures, 160, pp. 408-421, 2017.
[33] Al Jahwari, F.and Naguib, H.E., “Analysis and homogenization of functionally graded viscoelastic porous structures with a higher order plate theory and statistical based model of cellular distribution”, Applied Mathematical Modelling, 40(3), pp. 2190-2205, 2016.
[34] Ebrahimi,F. and Jafari, A., “A Higher-Order Thermomechanical Vibration Analysis of Temperature-Dependent FGM Beams with Porosities”, Journal of Engineering, doi:10.1155/2016/9561504, 2016.
[35] Ebrahimi, F., Ghasemi, F. and Salari, E., “Investigating thermal effects on vibration behavior of temperature-dependent compositionally graded Euler beams with porosities”, Meccanica, 51(1), pp. 223-249, 2016.
[36] Chen, D., Yang, J. and Kitipornchai, S., “Nonlinear vibration and postbuckling of functionally graded graphene reinforced porous nanocomposite beams”, Composites Science and Technology, 142, pp. 235-245, 2017.
[37] Kitipornchai, S., Chen, D. and Yang, J., “Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets”, Materials & Design, 116, pp. 656-665, 2017.
[2] Reddy, J. N. “Analysis of functionally graded plates”. International Journal for Numerical Methods in Engineering, 47(1-3), pp. 663-684, 2000.
[3] Yanga, J. and Shen, H.S. (2003), “Non-linear analysis of functionally graded plates under transverse and in-plane loads”, International Journal of Non-Linear Mechanics, 38(4) pp.467-482, 2003.
[4] Lanhe, W. “Thermal buckling of a simply supported moderately thick rectangular FGM plate”, Composite Structures, 64(2), pp.211-218, 2004.
[5] Abrate, S., “Free vibration, buckling, and static deflections of functionally graded plates”, Composites Science and Technology. 66(14), pp.2383-2394, 2006.
[6] Chi, S.H. and Chung, Y.L., “Mechanical behavior of functionally graded material plates under transverse load—Part I: Analysis”, International Journal of Solids and Structures, 43(13), pp. 3657-3674, 2006
[7] Samsam Shariat, B.A. and Eslami M.R., “Buckling of thick functionally graded plates under mechanical and thermal loads”, Composite Structures. 78(3), pp. 433-439, 2007.
[8] Civalek, Ö. “Analysis of thick rectangular plates with symmetric cross-ply laminates based on first-order shear deformation theory”, Journal of Composite Materials, 42(26), pp. 2853-2867, 2008.
[9] Zhao, X., Lee, Y.Y. and Liew, K.M., “Mechanical and thermal buckling analysis of functionally graded plates”, Composite Structures, 90(2), pp. 161-171, 2009.
[10] Oyekoya, O.O., Mba, D.U. and El-Zafrany, A.M., “Buckling and vibration analysis of functionally graded composite structures using the finite element method”, Composite Structures, 89(1), pp. 134-142, 2009.
[11] Zhao, X., Lee, Y. Y. and Liew, K. M., “Free vibration analysis of functionally graded plates using the element-free kp-Ritz method”, Journal of sound and Vibration, 319(3), pp. 918-939, 2009.
[12] Mohammadi, M., Saidi, A.R. and Jomehzadeh, E., “Levy solution for buckling analysis of functionally graded rectangular plates”, Applied Composite Materials, 17(2), pp. 81-93, 2010.
[13] Fereidoon, A., Asghardokht Seyedmahalle, M. and Mohyeddin, A., “Bending analysis of thin functionally graded plates using generalized differential quadrature method”, Archive of Applied Mechanics, 81(11), pp. 1523-1539, 2011.
[14] Kumar, J.S., Reddy, B.S., Reddy, C.E. and Reddy, K.V.K., “Higher order theory for free vibration analysis of functionally graded material plates”, ARPN J. Eng. Appl. Sci., 6(10), pp. 105-111, 2011.
[15] Jadhav, P.A. and Bajoria, K.M., “Buckling of piezoelectric functionally graded plate subjected to electro-mechanical loading”, Smart Materials and Structures, 21(10), pp. 105005, 2012.
[16] Singh, J. and Shukla, K. K., “Nonlinear flexural analysis of functionally graded plates under different loadings using RBF based meshless method”, Engineering Analysis with Boundary Elements, 36(12), pp. 1819-1827, 2012.
[17] Daouadji, T.H., Tounsi and Adda Bedia, E-A. “Analytical solution for bending analysis of functionally graded plates”, Scientia Iranica, 20(3), pp. 516-523, 2013.
[18] Asemi, K. and Shariyat, M., “Highly accurate nonlinear three-dimensional finite element elasticity approach for biaxial buckling of rectangular anisotropic FGM plates with general orthotropy directions”, Composite Structures. 106, pp. 235-249, 2013.
[19] Czechowski, L. and Kowal-Michalska, K. “Static and dynamic buckling of rectangular functionally graded plates subjected to thermal loading”, Strength of Materials, 45(6), pp. 666-673, 2013.
[20] Civalek, Ö., Korkmaz, A. and Demir,C. “Discrete singular convolution approach for buckling analysis of rectangular Kirchhoff plates subjected to compressive loads on two-opposite edges” Advances in Engineering Software, 41(4), pp. 557-560, 2010.
[21] Tahouneh, V., “Free vibration analysis of thick CGFR annular sector plates resting on elastic foundations”, Structural Engineering and Mechanics, 50(6), pp. 773-796, 2013.
[22] Swaminathan, K., and Naveenkumar, D. T. “Assessment of First Order Computational Model for Free Vibration Analysis of FGM Plates”, International Journal of Scientific and Engineering Research, 4(5), pp. 115-118, 2013.
[23] Jin, G., Su, Z., Ye, T. and Gao, S., “Three-dimensional free vibration analysis of functionally graded annular sector plates with general boundary conditions”, Composites Part B: Engineering, 83, pp. 352-366, 2015.
[24] AkbaÅŸ, Åž.D., “Termo-Mechanical Vibration of Functionally Graded Nano Plates and Beams Based on Couple Stress Theory”, 3rd International Conference on Advanced Technology Sciences, Konya/Turkey, 01-03 September, 2016.
[25] Van Long, N., Quoc, T.H. and Tu, T.M., “Bending and free vibration analysis of functionally graded plates using new eight-unknown shear deformation theory by finite-element method”, International Journal of Advanced Structural Engineering, 8(4), pp. 391-399, 2016.
[26] Civalek, Ö. “Free vibration of carbon nanotubes reinforced (CNTR) and functionally graded shells and plates based on FSDT via discrete singular convolution method” Composites Part B: Engineering, 111, pp. 45-59, 2017.
[27] Barati, M.R. and Zenkour, A.M., “Electro-thermoelastic vibration of plates made of porous fuctionally graded piezoelectric materials under various boundary conditions”, Journal of Vibration and Control, doi: 10.1177/1077546316672788, 2016.
[28] Mercan, K., Demir, Ç. And Civalek, Ö. “Vibration analysis of FG cylindrical shells with power-law index using discrete singular convolution technique”Curved and Layered Structures, 3(1), 2016.
[29] Wattanasakulpong, N. and Ungbhakorn, V., “Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities”, Aerospace Science and Technology, 32(1), pp. 111-120, 2014.
[30] Mechab, I., Mechab, B., Benaissa, S., Serier, B., Bouiadjra, B.B., “Free vibration analysis of FGM nanoplate with porosities resting on Winkler Pasternak elastic foundations based on two-variable refined plate theories”, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 38(8), pp. 2193–2211, 2016.
[31] Mechab, B., Mechab, I., Benaissa, S., Ameri, M. and Serier, B., “Probabilistic analysis of effect of the porosities in functionally graded material nanoplate resting on Winkler–Pasternak elastic foundations”, Applied Mathematical Modelling, 40(2), pp. 738-749, 2016.
[32] ÅžimÅŸek, M. and Aydın, M., “Size-dependent forced vibration of an imperfect functionally graded (FG) microplate with porosities subjected to a moving load using the modified couple stress theory”, Composite Structures, 160, pp. 408-421, 2017.
[33] Al Jahwari, F.and Naguib, H.E., “Analysis and homogenization of functionally graded viscoelastic porous structures with a higher order plate theory and statistical based model of cellular distribution”, Applied Mathematical Modelling, 40(3), pp. 2190-2205, 2016.
[34] Ebrahimi,F. and Jafari, A., “A Higher-Order Thermomechanical Vibration Analysis of Temperature-Dependent FGM Beams with Porosities”, Journal of Engineering, doi:10.1155/2016/9561504, 2016.
[35] Ebrahimi, F., Ghasemi, F. and Salari, E., “Investigating thermal effects on vibration behavior of temperature-dependent compositionally graded Euler beams with porosities”, Meccanica, 51(1), pp. 223-249, 2016.
[36] Chen, D., Yang, J. and Kitipornchai, S., “Nonlinear vibration and postbuckling of functionally graded graphene reinforced porous nanocomposite beams”, Composites Science and Technology, 142, pp. 235-245, 2017.
[37] Kitipornchai, S., Chen, D. and Yang, J., “Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets”, Materials & Design, 116, pp. 656-665, 2017.
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