Free vibration of functionally graded rectangular plates using first-order shear deformation plate theory

Abrate, 2008, Functionally graded plates behave like homogeneous plates, Compos. Part B-Eng., 39, 151, 10.1016/j.compositesb.2007.02.026 Zhang, 2008, A theoretical analysis of FGM thin plates based on physical neutral surface, Comp. Mater. Sci., 44, 716, 10.1016/j.commatsci.2008.05.016 Woo, 2006, Nonlinear free vibration behavior of functionally graded plates, J. Sound Vib., 289, 595, 10.1016/j.jsv.2005.02.031 Reddy, 2003, Frequency of functionally graded plates with three-dimensional asymptotic approach, J. Eng. Mech. ASCE, 129, 896, 10.1061/(ASCE)0733-9399(2003)129:8(896) Qian, 2004, Static and dynamic deformations of thick functionally graded elastic plate by using higher-order shear and normal deformable plate theory and meshless local Petrov–Galerkin method, Compos. Part B-Eng., 35, 685, 10.1016/j.compositesb.2004.02.004 Vel, 2004, Three-dimensional exact solution for the vibration of functionally graded rectangular plates, J. Sound Vib., 272, 703, 10.1016/S0022-460X(03)00412-7 Zhong, 2006, Vibration of a simply supported functionally graded piezoelectric rectangular plate, Smart. Mater. Struct., 15, 1404, 10.1088/0964-1726/15/5/029 Roque, 2007, A radial basis function approach for the free vibration analysis of functionally graded plates using a refined theory, J. Sound Vib., 300, 1048, 10.1016/j.jsv.2006.08.037 Pradyumna, 2008, Free vibration analysis of functionally graded curved panels using a higher-order finite element formulation, J. Sound Vib., 318, 176, 10.1016/j.jsv.2008.03.056 Matsunaga, 2008, Free vibration and stability of functionally graded plates according to a 2-D higher-order deformation theory, Compos. Struct., 82, 499, 10.1016/j.compstruct.2007.01.030 Abrate, 2006, Free vibration, buckling, and static deflections of functionally graded plates, Compos. Sci. Technol., 66, 2383, 10.1016/j.compscitech.2006.02.032 Ferreira, 2006, Natural frequencies of functionally graded plates by a meshless method, Compos. Struct., 75, 593, 10.1016/j.compstruct.2006.04.018 Zhao, 2009, Free vibration analysis of functionally graded plates using the element-free kp-Ritz method, J. Sound Vib., 319, 918, 10.1016/j.jsv.2008.06.025 Timoshenko, 1922, On the transverse vibrations of bars of uniform cross-section, Philos. Mag., 43, 125, 10.1080/14786442208633855 Efraim, 2007, Exact vibration analysis of variable thickness thick annular isotropic and FGM plates, J. Sound Vib., 299, 720, 10.1016/j.jsv.2006.06.068 Nguyen, 2008, First-order shear deformation plate models for functionally graded materials, Compos. Struct., 83, 25, 10.1016/j.compstruct.2007.03.004 Xiang, 1994, Exact vibration solution for initially stressed Mindlin plates on Pasternak foundation, Int. J. Mech. Sci., 36, 311, 10.1016/0020-7403(94)90037-X Xiang, 2003, Vibration of rectangular Mindlin plates resting on non-homogenous elastic foundations, Int. J. Mech. Sci., 45, 1229, 10.1016/S0020-7403(03)00141-3 Lam, 2000, Canonical exact solutions for Levy-plates on two-parameter foundation using Green’s functions, Eng. Struct., 22, 364, 10.1016/S0141-0296(98)00116-3 Zhou, 2004, Three-dimensional vibration analysis of rectangular thick plates on Pasternak foundation, Int. J. Numer. Meth. Eng., 59, 1313, 10.1002/nme.915 Akhavan, 2009, Exact solutions for rectangular Mindlin plates under in-plane loads resting on Pasternak elastic foundation. Part I: buckling analysis, Comp. Mater. Sci., 44, 968, 10.1016/j.commatsci.2008.07.004 Akhavan, 2009, Exact solutions for rectangular Mindlin plates under in-plane loads resting on Pasternak elastic foundation. Part II: frequency analysis, Comp. Mater. Sci., 44, 951, 10.1016/j.commatsci.2008.07.001 Cheng, 1999, Membrane analogy of buckling and vibration of inhomogeneous plates, J. Eng. Mech. ASCE, 125, 1293, 10.1061/(ASCE)0733-9399(1999)125:11(1293) Yang, 2001, Dynamic response of initially stressed functionally graded rectangular thin plates, Compos. Struct., 54, 497, 10.1016/S0263-8223(01)00122-2 Yang, 2005, Second-order statistics of the elastic buckling of functionally graded rectangular plates, Compos. Sci. Technol., 65, 1165, 10.1016/j.compscitech.2004.11.012 Ying, 2008, Two-dimensional elasticity solutions for functionally graded beams resting on elastic foundations, Compos. Struct., 84, 209, 10.1016/j.compstruct.2007.07.004 Huang, 2008, Benchmark solutions for functionally graded thick plates resting on Winkler–Pasternak elastic foundations, Compos. Struct., 85, 95, 10.1016/j.compstruct.2007.10.010