Research Article
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Stability of A Non-Homogenous Porous Plate by Using Generalized Differantial Quadrature Method

Year 2017, Volume: 9 Issue: 2, 147 - 155, 04.07.2017
https://doi.org/10.24107/ijeas.322375

Abstract

This
paper presents
stability analysis of
a non-homogeneous plate
wit
porosity effect. Material properties of the plate vary in the thickness
direction and depend on the porosity.
In the solution of the problem, the
Generalized
Differential Quadrature method is used
. In the porosity model, uniform porosity
distribution is considered. The effects of the
porosity and material
distribution parameters
on the critical buckling of the non-homogeneous
plate are investigated.

References

  • [1] Reddy, J.N., and Chin, C.D., Thermomechanical analysis of functionally graded cylinders and plates, Journal of Thermal Stresses, 21, 6,.593-626, 1998.
  • [2] Reddy, J.N., Analysis of functionally graded plates, International Journal for Numerical Methods in Engineering, 47, 1-3, 663-684, 2000.
  • [3] Yanga, J. and Shen, H.S., Non-linear analysis of functionally graded plates under transverse and in-plane loads, International Journal of Non-Linear Mechanics, 38, 4, 467-482,2003.
  • [4] Lanhe, Wu., Thermal buckling of a simply supported moderately thick rectangular FGM plate, Composite Structures, 64, 2, 211-218,2004.
  • [5] Abrate, S., Free vibration, buckling, and static deflections of functionally graded plates, Composites Science and Technology, 66, 14, 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, 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, 433-439,2007.
  • [8] Zhao, X., Lee, Y.Y. and Liew, K.M., Mechanical and thermal buckling analysis of functionally graded plates, Composite Structures, 90, 2, 161-171,2009.
  • [9] Akbaş, Ş.D., Static analysis of a functionally graded beam with edge cracks on elastic foundation, Proceedings of the 9 th International Fracture Conference, Istanbul, Turkey, 2011.
  • [10] 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, 918-939,2009.
  • [11] Mohammadi, M., Saidi, A.R. and Jomehzadeh, E., Levy solution for buckling analysis of functionally graded rectangular plates, Applied Composite Materials, 17, 2, 81-93,2010.
  • [12] 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, 1523-1539,2011.
  • [13] Akbaş, Ş.D. and Kocatürk, T., Post-buckling analysis of a simply supported beam under uniform thermal loading, Scientific Research and Essays, 6,5, 1135-1142, 2011.
  • [14] 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, 557-560, 2010.
  • [15] Kocatürk, T. and Akbas, Ş.D., Post-buckling analysis of Timoshenko beams with various boundary conditions under non-uniform thermal loading, Structural Engineering and Mechanics, 40,3,, 347-371, 2011.
  • [16] Kocatürk, T., Eskin ,A. and Akbaş Ş.D. Wave propagation in a piecewise homegenous cantilever beam under impact force, International Journal of Physical Sciences, 6, 16, 3867-3874, 2011.
  • [17] 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, 105-111,2011.
  • [18] Jadhav, P.A. and Bajoria, K.M., Buckling of piezoelectric functionally graded plate subjected to electro-mechanical loading, Smart Materials and Structures, 21,.10, 105005,2012.
  • [19] Akbaş, Ş.D. Free vibration characteristics of edge cracked functionally graded beams by using finite element method. International Journal of Engineering Trends and Technology, 4(10), 4590-4597,2013.
  • [20] 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, 1819-1827,2012.
  • [21] Kocatürk and Akbas, Ş.D., Thermal post-buckling analysis of functionally graded beams with temperature-dependent physical properties. Steel and Composite Structures, 15, 5, 481-505, 2013.
  • [22] Daouadji, T.H., Tounsi and Adda Bedia, E-A., Analytical solution for bending analysis of functionally graded plates, Scientia Iranica, 20, 3, 516-523, 2013.
  • [23] Akbaş, Ş.D.. Geometrically nonlinear static analysis of edge cracked Timoshenko beams composed of functionally graded material, Mathematical Problems in Engineering, 2013, 2013.
  • [24] 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, 235-249,2013.
  • [25] Akbaş, Ş. D. and Kocatürk, T., Post-buckling analysis of functionally graded three-dimensional beams under the influence of temperature. Journal of Thermal Stresses, 36, 12, 1233-1254, 2013.
  • [26] Czechowski, L. and Kowal-Michalska, K., Static and dynamic buckling of rectangular functionally graded plates subjected to thermal loading, Strength of Materials, 45, 6, 666-673,2013.
  • [27] Kocatürk, T. and Akbas, Ş.D., Post-buckling analysis of Timoshenko beams made of functionally graded material under thermal loading, Structural Engineering and Mechanics, 41,6, 775-789, 2012.
  • [28] Tahouneh, V., Free vibration analysis of thick CGFR annular sector plates resting on elastic foundations, Structural Engineering and Mechanics, 50, 6, 773-796, 2013.
  • [29] Akbaş, Ş.D., Free vibration of axially functionally graded beams in thermal environment, International Journal of Engineering and Applied Sciences, 6(3), 37-51, 2014.
  • [30] 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, 115-118, 2013.
  • [31] 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, vol. 8., No.4, pp.391-399, 2016.
  • [32] Akbaş, Ş.D., Free vibration and bending of functionally graded beams resting on elastic foundation, Research on Engineering Structures and Materials, 1,1, 2015.
  • [33] Akbaş, Ş.D. On Post-Buckling Behavior of Edge Cracked Functionally Graded Beams Under Axial Loads. International Journal of Structural Stability and Dynamics, 15, 4, 1450065, 2015
  • [34] Akbaş, Ş.D., Post-buckling analysis of axially functionally graded three-dimensional beams. International Journal of Applied Mechanics, 7, 3, 1550047, 2015.
  • [35] 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, 45-59, 2017.
  • [36] Civalek, Ö. (2017). Buckling analysis of composite panels and shells with different material properties by discrete singular convolution (DSC) method. Composite Structures, 161, 93-110, 2017.
  • [37] Mercan, K., Ersoy, H. and Civalek, Ö., Free vibration of annular plates by discrete singular convolution and differential quadrature methods. Journal of Applied and Computational Mechanics, 2,3, 128-133, 2016.
  • [38] Akbaş, Ş.D., Free vibration of edge cracked functionally graded microscale beams based on the modified couple stress theory, International Journal of Structural Stability and Dynamics, 1750033, 2016.
  • [39] 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.
  • [40] Akbaş, Ş.D. (2016). Static Analysis of a Nano Plate by Using Generalized Differential Quadrature Method, International Journal of Engineering and Applied Sciences, 8, 2, 30-39, 2016.
  • [41] 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.
  • [42] Akbaş, Ş.D. (2016). Wave propagation in edge cracked functionally graded beams under impact force, Journal of Vibration and Control, 22, 10, 2443-2457,2016.
  • [43] Wattanasakulpong, N. and Ungbhakorn, V.,Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities, Aerospace Science and Technology, 32, 1, 111-120, 2014.
  • [44] 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, 2193–2211, 2016.
  • [45] 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, 738-749, 2016.
  • [46] Şimşek, 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, 408-421, 2017.
  • [47] 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, 2190-2205, 2016.
  • [48] 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.
  • [49] 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, 223-249, 2016.
  • [50] Chen, D., Yang, J. and Kitipornchai, S., Nonlinear vibration and postbuckling of functionally graded graphene reinforced porous nanocomposite beams, Composites Science and Technology, 142, 235-245, 2017.
  • [51] Kitipornchai, S., Chen, D. and Yang, J., Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets, Materials&Design, 116, 656-665, 2017.
  • [52] Akbaş, Ş.D., Vibration and Static Analysis of Functionally Graded Porous Plates, Doi: 10.22055/jacm.2017.21540.1107, Journal of Applied and Computational Mechanics, 2017.
  • [53] Shu, C. and Du, H., Implementation of clamped and simply supported boundary conditions in the GDQ free vibration analysis of beams and plates, Int. J. Solids Struct. 34, 819–835, 1997.
  • [54] Shu, C., Differential Quadrature and its Application in Engineering, Springer, 2000.
  • [55] Chen, C.N., Discrete element analysis methods of generic differential quadrature, Lecture Notes in Applied and Computational Mechanics, vol. 25, Springer, 2006.
  • [56] Quan, J.R. and Chang, C.T. New insights in solving distributed system equations by the quadrature methods, Comput. Chem. Eng. 13, 779–788, 1989.
Year 2017, Volume: 9 Issue: 2, 147 - 155, 04.07.2017
https://doi.org/10.24107/ijeas.322375

Abstract

References

  • [1] Reddy, J.N., and Chin, C.D., Thermomechanical analysis of functionally graded cylinders and plates, Journal of Thermal Stresses, 21, 6,.593-626, 1998.
  • [2] Reddy, J.N., Analysis of functionally graded plates, International Journal for Numerical Methods in Engineering, 47, 1-3, 663-684, 2000.
  • [3] Yanga, J. and Shen, H.S., Non-linear analysis of functionally graded plates under transverse and in-plane loads, International Journal of Non-Linear Mechanics, 38, 4, 467-482,2003.
  • [4] Lanhe, Wu., Thermal buckling of a simply supported moderately thick rectangular FGM plate, Composite Structures, 64, 2, 211-218,2004.
  • [5] Abrate, S., Free vibration, buckling, and static deflections of functionally graded plates, Composites Science and Technology, 66, 14, 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, 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, 433-439,2007.
  • [8] Zhao, X., Lee, Y.Y. and Liew, K.M., Mechanical and thermal buckling analysis of functionally graded plates, Composite Structures, 90, 2, 161-171,2009.
  • [9] Akbaş, Ş.D., Static analysis of a functionally graded beam with edge cracks on elastic foundation, Proceedings of the 9 th International Fracture Conference, Istanbul, Turkey, 2011.
  • [10] 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, 918-939,2009.
  • [11] Mohammadi, M., Saidi, A.R. and Jomehzadeh, E., Levy solution for buckling analysis of functionally graded rectangular plates, Applied Composite Materials, 17, 2, 81-93,2010.
  • [12] 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, 1523-1539,2011.
  • [13] Akbaş, Ş.D. and Kocatürk, T., Post-buckling analysis of a simply supported beam under uniform thermal loading, Scientific Research and Essays, 6,5, 1135-1142, 2011.
  • [14] 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, 557-560, 2010.
  • [15] Kocatürk, T. and Akbas, Ş.D., Post-buckling analysis of Timoshenko beams with various boundary conditions under non-uniform thermal loading, Structural Engineering and Mechanics, 40,3,, 347-371, 2011.
  • [16] Kocatürk, T., Eskin ,A. and Akbaş Ş.D. Wave propagation in a piecewise homegenous cantilever beam under impact force, International Journal of Physical Sciences, 6, 16, 3867-3874, 2011.
  • [17] 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, 105-111,2011.
  • [18] Jadhav, P.A. and Bajoria, K.M., Buckling of piezoelectric functionally graded plate subjected to electro-mechanical loading, Smart Materials and Structures, 21,.10, 105005,2012.
  • [19] Akbaş, Ş.D. Free vibration characteristics of edge cracked functionally graded beams by using finite element method. International Journal of Engineering Trends and Technology, 4(10), 4590-4597,2013.
  • [20] 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, 1819-1827,2012.
  • [21] Kocatürk and Akbas, Ş.D., Thermal post-buckling analysis of functionally graded beams with temperature-dependent physical properties. Steel and Composite Structures, 15, 5, 481-505, 2013.
  • [22] Daouadji, T.H., Tounsi and Adda Bedia, E-A., Analytical solution for bending analysis of functionally graded plates, Scientia Iranica, 20, 3, 516-523, 2013.
  • [23] Akbaş, Ş.D.. Geometrically nonlinear static analysis of edge cracked Timoshenko beams composed of functionally graded material, Mathematical Problems in Engineering, 2013, 2013.
  • [24] 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, 235-249,2013.
  • [25] Akbaş, Ş. D. and Kocatürk, T., Post-buckling analysis of functionally graded three-dimensional beams under the influence of temperature. Journal of Thermal Stresses, 36, 12, 1233-1254, 2013.
  • [26] Czechowski, L. and Kowal-Michalska, K., Static and dynamic buckling of rectangular functionally graded plates subjected to thermal loading, Strength of Materials, 45, 6, 666-673,2013.
  • [27] Kocatürk, T. and Akbas, Ş.D., Post-buckling analysis of Timoshenko beams made of functionally graded material under thermal loading, Structural Engineering and Mechanics, 41,6, 775-789, 2012.
  • [28] Tahouneh, V., Free vibration analysis of thick CGFR annular sector plates resting on elastic foundations, Structural Engineering and Mechanics, 50, 6, 773-796, 2013.
  • [29] Akbaş, Ş.D., Free vibration of axially functionally graded beams in thermal environment, International Journal of Engineering and Applied Sciences, 6(3), 37-51, 2014.
  • [30] 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, 115-118, 2013.
  • [31] 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, vol. 8., No.4, pp.391-399, 2016.
  • [32] Akbaş, Ş.D., Free vibration and bending of functionally graded beams resting on elastic foundation, Research on Engineering Structures and Materials, 1,1, 2015.
  • [33] Akbaş, Ş.D. On Post-Buckling Behavior of Edge Cracked Functionally Graded Beams Under Axial Loads. International Journal of Structural Stability and Dynamics, 15, 4, 1450065, 2015
  • [34] Akbaş, Ş.D., Post-buckling analysis of axially functionally graded three-dimensional beams. International Journal of Applied Mechanics, 7, 3, 1550047, 2015.
  • [35] 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, 45-59, 2017.
  • [36] Civalek, Ö. (2017). Buckling analysis of composite panels and shells with different material properties by discrete singular convolution (DSC) method. Composite Structures, 161, 93-110, 2017.
  • [37] Mercan, K., Ersoy, H. and Civalek, Ö., Free vibration of annular plates by discrete singular convolution and differential quadrature methods. Journal of Applied and Computational Mechanics, 2,3, 128-133, 2016.
  • [38] Akbaş, Ş.D., Free vibration of edge cracked functionally graded microscale beams based on the modified couple stress theory, International Journal of Structural Stability and Dynamics, 1750033, 2016.
  • [39] 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.
  • [40] Akbaş, Ş.D. (2016). Static Analysis of a Nano Plate by Using Generalized Differential Quadrature Method, International Journal of Engineering and Applied Sciences, 8, 2, 30-39, 2016.
  • [41] 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.
  • [42] Akbaş, Ş.D. (2016). Wave propagation in edge cracked functionally graded beams under impact force, Journal of Vibration and Control, 22, 10, 2443-2457,2016.
  • [43] Wattanasakulpong, N. and Ungbhakorn, V.,Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities, Aerospace Science and Technology, 32, 1, 111-120, 2014.
  • [44] 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, 2193–2211, 2016.
  • [45] 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, 738-749, 2016.
  • [46] Şimşek, 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, 408-421, 2017.
  • [47] 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, 2190-2205, 2016.
  • [48] 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.
  • [49] 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, 223-249, 2016.
  • [50] Chen, D., Yang, J. and Kitipornchai, S., Nonlinear vibration and postbuckling of functionally graded graphene reinforced porous nanocomposite beams, Composites Science and Technology, 142, 235-245, 2017.
  • [51] Kitipornchai, S., Chen, D. and Yang, J., Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets, Materials&Design, 116, 656-665, 2017.
  • [52] Akbaş, Ş.D., Vibration and Static Analysis of Functionally Graded Porous Plates, Doi: 10.22055/jacm.2017.21540.1107, Journal of Applied and Computational Mechanics, 2017.
  • [53] Shu, C. and Du, H., Implementation of clamped and simply supported boundary conditions in the GDQ free vibration analysis of beams and plates, Int. J. Solids Struct. 34, 819–835, 1997.
  • [54] Shu, C., Differential Quadrature and its Application in Engineering, Springer, 2000.
  • [55] Chen, C.N., Discrete element analysis methods of generic differential quadrature, Lecture Notes in Applied and Computational Mechanics, vol. 25, Springer, 2006.
  • [56] Quan, J.R. and Chang, C.T. New insights in solving distributed system equations by the quadrature methods, Comput. Chem. Eng. 13, 779–788, 1989.
There are 56 citations in total.

Details

Subjects Engineering
Journal Section Articles
Authors

Şeref Doğuşcan Akbaş 0000-0001-5327-3406

Publication Date July 4, 2017
Acceptance Date July 2, 2017
Published in Issue Year 2017 Volume: 9 Issue: 2

Cite

APA Akbaş, Ş. D. (2017). Stability of A Non-Homogenous Porous Plate by Using Generalized Differantial Quadrature Method. International Journal of Engineering and Applied Sciences, 9(2), 147-155. https://doi.org/10.24107/ijeas.322375
AMA Akbaş ŞD. Stability of A Non-Homogenous Porous Plate by Using Generalized Differantial Quadrature Method. IJEAS. July 2017;9(2):147-155. doi:10.24107/ijeas.322375
Chicago Akbaş, Şeref Doğuşcan. “Stability of A Non-Homogenous Porous Plate by Using Generalized Differantial Quadrature Method”. International Journal of Engineering and Applied Sciences 9, no. 2 (July 2017): 147-55. https://doi.org/10.24107/ijeas.322375.
EndNote Akbaş ŞD (July 1, 2017) Stability of A Non-Homogenous Porous Plate by Using Generalized Differantial Quadrature Method. International Journal of Engineering and Applied Sciences 9 2 147–155.
IEEE Ş. D. Akbaş, “Stability of A Non-Homogenous Porous Plate by Using Generalized Differantial Quadrature Method”, IJEAS, vol. 9, no. 2, pp. 147–155, 2017, doi: 10.24107/ijeas.322375.
ISNAD Akbaş, Şeref Doğuşcan. “Stability of A Non-Homogenous Porous Plate by Using Generalized Differantial Quadrature Method”. International Journal of Engineering and Applied Sciences 9/2 (July 2017), 147-155. https://doi.org/10.24107/ijeas.322375.
JAMA Akbaş ŞD. Stability of A Non-Homogenous Porous Plate by Using Generalized Differantial Quadrature Method. IJEAS. 2017;9:147–155.
MLA Akbaş, Şeref Doğuşcan. “Stability of A Non-Homogenous Porous Plate by Using Generalized Differantial Quadrature Method”. International Journal of Engineering and Applied Sciences, vol. 9, no. 2, 2017, pp. 147-55, doi:10.24107/ijeas.322375.
Vancouver Akbaş ŞD. Stability of A Non-Homogenous Porous Plate by Using Generalized Differantial Quadrature Method. IJEAS. 2017;9(2):147-55.

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