How to cite this paper
Dehghany, M & Farajpour, A. (2014). Free vibration of simply supported rectangular plates on Pasternak foundation: An exact and three-dimensional solution.Engineering Solid Mechanics, 2(1), 29-42.
Refrences
Akhavan, H., Hashemi, S. H., Taher, H., Alibeigloo, A., & Vahabi, S. (2009). Exact solutions for rectangular Mindlin plates under in-plane loads resting on Pasternak elastic foundation. Part II: Frequency analysis. Computational Materials Science, 44(3), 951-961.
Hanna, N. F., & Leissa, A. W. (1994). A higher order shear deformation theory for the vibration of thick plates. Journal of Sound and Vibration, 170(4), 545-555.
Hasani Baferani, A., Saidi, A. R., & Ehteshami, H. (2011). Accurate solution for free vibration analysis of functionally graded thick rectangular plates resting on elastic foundation. Composite Structures, 93(7), 1842-1853.
Hasheminejad, S. M., & Gheshlaghi, B. (2012). Three-dimensional elastodynamic solution for an arbitrary thick FGM rectangular plate resting on a two parameter viscoelastic foundation. Composite Structures, 94(9), 2746-2755.
Hosseini Hashemi, S., Karimi, M., & Rokni Damavandi Taher, H. (2010). Vibration analysis of rectangular Mindlin plates on elastic foundations and vertically in contact with stationary fluid by the Ritz method. Ocean Engineering, 37(2), 174-185.
Lam, K. Y., Wang, C. M., & He, X. Q. (2000). Canonical exact solutions for Levy-plates on two-parameter foundation using Green & apos; s functions. Engineering Structures, 22(4), 364-378.
Levinson, M. (1985). Free vibrations of a simply supported, rectangular plate: an exact elasticity solution. Journal of Sound and Vibration, 98(2), 289-298.
Lim, C. W., Liew, K. M. & Kitipornchai, S. (1998 a). Numerical aspects for free vibration of thick plates Part I: formulation and verification. Computer Methods in Applied Mechanics and Engineering, 156(1), 15-29.
Lim, C. W., Kitipornchai, S., & Liew, K. M. (1998 b). Numerical aspects for free vibration of thick plates Part II: Numerical efficiency and vibration frequencies. Computer Methods in Applied Mechanics and Engineering, 156(1), 31-44.
Malekzadeh, P. (2009). Three-dimensional free vibration analysis of thick functionally graded plates on elastic foundations. Composite Structures, 89(3), 367-373.
Matsunaga, H. (2000). Vibration and stability of thick plates on elastic foundations. Journal of Engineering Mechanics, 126(1), 27-34.
Mindlin, R. D. (1951). Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates. J. of Appl. Mech., 18, 31-38.
Mindlin, R. D., & Deresiewicz, H. (1954). Thickness?Shear and Flexural Vibrations of a Circular Disk. Journal of Applied Physics, 25(10), 1329-1332.
Mindlin, R. D., Schaknow, A. & Deresiewicz, H. (1956). Flexural Vibration of Rectangular Plates. Journal of Applied Mechanics, 23, 430-436.
Omurtag, M. H., ?zütok, A., Ak?z, A. Y., & OeZCEL?KOeRS, Y. U. N. U. S. (1997). Free vibration analysis of Kirchhoff plates resting on elastic foundation by mixed finite element formulation based on Gateaux differential. International Journal for Numerical Methods in Engineering, 40(2), 295-317.
Pasternak, P. L. (1954). On a new method of analysis of an elastic foundation by means of two foundation constants. Gosudarstvennoe Izdatel’stvo Litearturi po Stroitel’stvu i Arkhitekture, Moscow, USSR (in Russian).
Reddy, J. N. (1984). A simple higher-order theory for laminated composite plates. Journal of applied mechanics, 51(4), 745-752.
Reissner, E. (1945). The effect of transverse shear deformation on the bending of elastic plates. Journal of Applied Mechanics, 12(2), 69-77.
Saidi, A. R., Atashipour, S. R., & Jomehzadeh, E. (2009). Reformulation of Navier equations for solving three-dimensional elasticity problems with applications to thick plate analysis. Acta Mechanica, 208(3-4), 227-235.
Sobhy, M. (2013). Buckling and free vibration of exponentially graded sandwich plates resting on elastic foundations under various boundary conditions. Composite Structures.99, 76-87.
Srinivas, S., Joga Rao, C. V., & Rao, A. K. (1970). An exact analysis for vibration of simply-supported homogeneous and laminated thick rectangular plates. Journal of Sound and Vibration, 12(2), 187-199.
Tajeddini, V., Ohadi, A., & Sadighi, M. (2011). 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.
Timoshenko, S. P., & Goodier, J. N. (1951). Theory of elasticity. McGraw-Hill, New York
Timoshenko, S., & Woinowsky-Krieger, S. (1970). Theory of plates and shells . New York: McGraw-Hill.
Wen, P. H. (2008). The fundamental solution of Mindlin plates resting on an elastic foundation in the Laplace domain and its applications. International Journal of Solids and Structures, 45(3), 1032-1050.
Winkler, E. (1867). Die Lehre von der Elasticitaet und Festigkeit. Prag, Dominicus.
Xiang, Y., Wang, C. M., & Kitipornchai, S. (1994). Exact vibration solution for initially stressed Mindlin plates on Pasternak foundations. International Journal of Mechanical Sciences, 36(4), 311-316.
Zhong, Y., & Yin, J. H. (2008). Free vibration analysis of a plate on foundation with completely free boundary by finite integral transform method. Mechanics Research Communications, 35(4), 268-275.
Zhou, D., Cheung, Y. K., Lo, S. H., & Au, F. T. K. (2004). Three?dimensional vibration analysis of rectangular thick plates on Pasternak foundation. International Journal for Numerical Methods in Engineering, 59(10), 1313-1334.
Hanna, N. F., & Leissa, A. W. (1994). A higher order shear deformation theory for the vibration of thick plates. Journal of Sound and Vibration, 170(4), 545-555.
Hasani Baferani, A., Saidi, A. R., & Ehteshami, H. (2011). Accurate solution for free vibration analysis of functionally graded thick rectangular plates resting on elastic foundation. Composite Structures, 93(7), 1842-1853.
Hasheminejad, S. M., & Gheshlaghi, B. (2012). Three-dimensional elastodynamic solution for an arbitrary thick FGM rectangular plate resting on a two parameter viscoelastic foundation. Composite Structures, 94(9), 2746-2755.
Hosseini Hashemi, S., Karimi, M., & Rokni Damavandi Taher, H. (2010). Vibration analysis of rectangular Mindlin plates on elastic foundations and vertically in contact with stationary fluid by the Ritz method. Ocean Engineering, 37(2), 174-185.
Lam, K. Y., Wang, C. M., & He, X. Q. (2000). Canonical exact solutions for Levy-plates on two-parameter foundation using Green & apos; s functions. Engineering Structures, 22(4), 364-378.
Levinson, M. (1985). Free vibrations of a simply supported, rectangular plate: an exact elasticity solution. Journal of Sound and Vibration, 98(2), 289-298.
Lim, C. W., Liew, K. M. & Kitipornchai, S. (1998 a). Numerical aspects for free vibration of thick plates Part I: formulation and verification. Computer Methods in Applied Mechanics and Engineering, 156(1), 15-29.
Lim, C. W., Kitipornchai, S., & Liew, K. M. (1998 b). Numerical aspects for free vibration of thick plates Part II: Numerical efficiency and vibration frequencies. Computer Methods in Applied Mechanics and Engineering, 156(1), 31-44.
Malekzadeh, P. (2009). Three-dimensional free vibration analysis of thick functionally graded plates on elastic foundations. Composite Structures, 89(3), 367-373.
Matsunaga, H. (2000). Vibration and stability of thick plates on elastic foundations. Journal of Engineering Mechanics, 126(1), 27-34.
Mindlin, R. D. (1951). Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates. J. of Appl. Mech., 18, 31-38.
Mindlin, R. D., & Deresiewicz, H. (1954). Thickness?Shear and Flexural Vibrations of a Circular Disk. Journal of Applied Physics, 25(10), 1329-1332.
Mindlin, R. D., Schaknow, A. & Deresiewicz, H. (1956). Flexural Vibration of Rectangular Plates. Journal of Applied Mechanics, 23, 430-436.
Omurtag, M. H., ?zütok, A., Ak?z, A. Y., & OeZCEL?KOeRS, Y. U. N. U. S. (1997). Free vibration analysis of Kirchhoff plates resting on elastic foundation by mixed finite element formulation based on Gateaux differential. International Journal for Numerical Methods in Engineering, 40(2), 295-317.
Pasternak, P. L. (1954). On a new method of analysis of an elastic foundation by means of two foundation constants. Gosudarstvennoe Izdatel’stvo Litearturi po Stroitel’stvu i Arkhitekture, Moscow, USSR (in Russian).
Reddy, J. N. (1984). A simple higher-order theory for laminated composite plates. Journal of applied mechanics, 51(4), 745-752.
Reissner, E. (1945). The effect of transverse shear deformation on the bending of elastic plates. Journal of Applied Mechanics, 12(2), 69-77.
Saidi, A. R., Atashipour, S. R., & Jomehzadeh, E. (2009). Reformulation of Navier equations for solving three-dimensional elasticity problems with applications to thick plate analysis. Acta Mechanica, 208(3-4), 227-235.
Sobhy, M. (2013). Buckling and free vibration of exponentially graded sandwich plates resting on elastic foundations under various boundary conditions. Composite Structures.99, 76-87.
Srinivas, S., Joga Rao, C. V., & Rao, A. K. (1970). An exact analysis for vibration of simply-supported homogeneous and laminated thick rectangular plates. Journal of Sound and Vibration, 12(2), 187-199.
Tajeddini, V., Ohadi, A., & Sadighi, M. (2011). 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.
Timoshenko, S. P., & Goodier, J. N. (1951). Theory of elasticity. McGraw-Hill, New York
Timoshenko, S., & Woinowsky-Krieger, S. (1970). Theory of plates and shells . New York: McGraw-Hill.
Wen, P. H. (2008). The fundamental solution of Mindlin plates resting on an elastic foundation in the Laplace domain and its applications. International Journal of Solids and Structures, 45(3), 1032-1050.
Winkler, E. (1867). Die Lehre von der Elasticitaet und Festigkeit. Prag, Dominicus.
Xiang, Y., Wang, C. M., & Kitipornchai, S. (1994). Exact vibration solution for initially stressed Mindlin plates on Pasternak foundations. International Journal of Mechanical Sciences, 36(4), 311-316.
Zhong, Y., & Yin, J. H. (2008). Free vibration analysis of a plate on foundation with completely free boundary by finite integral transform method. Mechanics Research Communications, 35(4), 268-275.
Zhou, D., Cheung, Y. K., Lo, S. H., & Au, F. T. K. (2004). Three?dimensional vibration analysis of rectangular thick plates on Pasternak foundation. International Journal for Numerical Methods in Engineering, 59(10), 1313-1334.