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Original Articles

Extended three-dimensional generalized differential quadrature method: The basic equations and thermal vibration analysis of functionally graded fiber orientation rectangular plates

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Pages 854-870 | Received 20 Jun 2015, Accepted 05 May 2016, Published online: 02 Dec 2016

References

  • S. Subra, A. Mortenzen, and S. Suresh, Fundamentals of Functionally Graded Materials, Institute of Material, London, 1998.
  • D.B. Miracle, Metal matrix composites—From science to technological significance, Compos. Sci. Technol., vol. 65, pp. 2526–2540, 2005.
  • H. Matsunaga, Free vibration and stability of functionally graded circular cylindrical shells according to a 2D higher-order deformation theory, Compos. Struct., vol. 88, no. 4, pp. 519–531, 2009.
  • X.D. Zhang, D.Q. Liu, and C.C. Ge, Thermal stress analysis of axial symmetry functionally gradient materials under steady temperature field, J. Funct. Mater., vol. 25, pp. 452–455, 1994.
  • H.S. Shen, and Z.X. Wang, Nonlinear vibration of hybrid laminated plates resting on elastic foundations in thermal environments, Appl. Math. Modell., vol. 36, pp. 6275–6290, 2012.
  • Y. Xiang, S. Kitipornchai, and K.M. Liew, Buckling and vibration of thick laminates on Pasternak foundations, J. Eng. Mech., vol. 122, pp. 54–63, 1996.
  • H.S. Shen, and C.L. Zhang, Non-linear analysis of functionally graded fiber reinforced composite laminated plates, Part I: Theory and solutions, Int. J. Non Linear Mech., vol. 47, pp. 1045–1054, 2012.
  • F. Ebrahimi, and A. Rastgo, An analytical study on the free vibration of smart circular thin FGM plate based on classical plate theory, Thin Walled Struct., vol. 46, pp. 1402–1408, 2008.
  • Sh. Hosseini-Hashemi, H. Rokni Damavandi Taher, H. Akhavan, and M. Omidi, Free vibration of functionally graded rectangular plates using first-order shear deformation plate theory, Appl. Math. Modell., vol. 34, pp. 1276–1291, 2010.
  • U.S. Gupta, R. Lal, and R. Sagar, Effect of an elastic foundation on axisymmetric vibrations of polar orthotropic Mindlin circular plates, Indian J. Pure Appl. Math., vol. 25, pp. 1317–1317, 1994.
  • M. Farid, P. Zahedinejad, and P. Malekzadeh, Three-dimensional temperature dependent free vibration analysis of functionally graded material curved panels resting on two-parameter elastic foundation using a hybrid semi-analytic, differential quadrature method, Mater. Des., vol. 31, pp. 2–13, 2010.
  • P. Malekzadeh, and N. Safaeian Hamzehkolaei, A 3D discrete layer-differential quadrature free vibration of multi-layered FG annular plates in thermal environment, Mech. Adv. Mater. Struct., vol. 20, pp. 316–330, 2013.
  • R.C. Batra, and J. Jin, Natural frequencies of a functionally graded anisotropic rectangular plate, J. Sound Vib., vol. 282, pp. 509–516, 2005.
  • B. Sobhani Aragh, and M.H. Yas, Three-dimensional free vibration of functionally graded fiber orientation and volume fraction cylindrical panels, Mater. Des., vol. 31, pp. 4543–4552, 2010.
  • B. Sobhani Aragh, and M.H. Yas, Effect of continuously grading fiber orientation face sheets on vibration of sandwich panels with FGM core, Int. J. Mech. Sci., vol. 53, pp. 628–638, 2011.
  • M. Nejati, K. Malekzadeh Fard, and A.H. Eslampanah, Effects of fiber orientation and temperature on natural frequencies of a functionally graded beam reinforced with fiber, J. Mech. Sci. Technol., vol. 29, pp. 3363–3371, 2015.
  • F. Tornabene, N. Fantuzzi, F. Ubertini, and E. Viola, Strong formulation finite element method based on differential quadrature: A survey, Appl. Mech. Rev., vol. 67, pp. 1–55, 2015.
  • S.A. Belalia, and A. Houmat, Nonlinear free vibration of functionally graded shear deformable sector plates by a curved triangular element, Eur. J. Mech. A. Solids, vol. 35, pp. 1–9, 2012.
  • A.J.M. Ferreira, R.C. Batra, C.M.C. Roque, L.F. Qian, and R.M.N. Jorge, Natural frequencies of functionally graded plates by a meshless method, Compos. Struct., vol. 75, pp. 593–600, 2006.
  • A.K. Sharma, N.D. Mittal, and A. Sharma, Free vibration analysis of moderately thick antisymmetric angle-ply laminated rectangularplates with elastic edge constraints, Mech. Adv. Mater. Struct., vol. 21, pp. 341–348, 2014.
  • H. Hedayati, M. Hedayati, B. Sobhani Aragh, and E. Borzabadi Farahani, Two-dimensional differential quadrature solution for vibration characteristics of two-dimensional functionally graded metal/ceramic open cylindrical shells, Mech. Adv. Mater. Struct., vol. 21, pp. 305–320, 2014.
  • M.H. Sadd, Elasticity: Theory, Applications, and Numerics, Elsevier, New York, 2009.
  • J.N. Reddy, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press, Boca Raton, 2004.
  • M.H. Yas, and B. Sobhani Aragh, Free vibration analysis of continuous grading fiber reinforced plates on elastic foundation, Int. J. Eng. Sci., vol. 48, pp. 1881–1895, 2010.
  • P. Malekzadeh, Three-dimensional free vibration analysis of thick functionally graded plates on elastic foundations, Compos. Struct., vol. 89, pp. 367–373, 2009.
  • C.W. Bert, and M. Malik, Differential quadrature method in computational mechanics: A review, Appl. Mech. Rev., vol. 49, pp. 1–27, 1996.
  • A. Zarei, M. Nejati, S. Jafari Mehrabadi, and H. Farahani, Using the third order shear deformation theory to examine magnetic-mechanical buckling of a two dimensional functionally graded cylindrical panel with longitudinal and circumferential stiffeners, Mech. Adv. Mater. Struct., 2015. DOI: 10.1080/15376494.2015.1091525.
  • P. Malekzadeh, M. Farid, and P. Zahedinejad, A three-dimensional layerwise differential quadrature free vibration analysis of laminated cylindrical shells, Int. J. Press. Vessels Pip., vol. 85, pp. 450–458, 2008.
  • H. Matsunaga, Free vibration and stability of functionally graded plates according to a 2-D higher-order deformation theory, Compos. Struct., vol. 82, pp. 499–512, 2008.

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