Hindawi Publishing Corporation Advances in Mechanical Engineering Volume 2013, Article ID 634584, 10 pages http://dx.doi.org/10.1155/2013/634584 Research Article Free Vibration Analyses of FGM Thin Plates by Isogeometric Analysis Based on Classical Plate Theory and Physical Neutral Surface Shuohui Yin, Tiantang Yu, and Peng Liu Department of Engineering Mechanics, Hohai University, Nanjing 210098, China Correspondence should be addressed to Tiantang Yu; tiantangyu@hhu.edu.cn Received 2 January 2013; Revised 23 May 2013; Accepted 6 June 2013 Academic Editor: Indra Vir Singh Copyright © 2013 Shuohui Yin et al. his is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. he isogeometric analysis with nonuniform rational B-spline (NURBS) based on the classical plate theory (CPT) is developed for free vibration analyses of functionally graded material (FGM) thin plates. he objective of this work is to provide an eicient and accurate numerical simulation approach for the nonhomogeneous thin plates and shells. Higher order basis functions can be easily obtained in IGA, thus the formulation of CPT based on the IGA can be simpliied. For the FGM thin plates, material property gradient in the thickness direction is unsymmetrical about the midplane, so efects of midplane displacements cannot be ignored, whereas the CPT neglects midplane displacements. To eliminate the efects of midplane displacements without introducing new unknown variables, the physical neutral surface is introduced into the CPT. he approximation of the delection ield and the geometric description are performed by using the NURBS basis functions. Compared with the irst-order shear deformation theory, the present method has lower memory consumption and higher eiciency. Several numerical results show that the present method yields highly accurate solutions. 1. Introduction Although numerous plate theories have been developed since the late 19th century, the classical plate theory (CPT) [1] and the irst-order shear deformation theory (FSDT) [2] are the most widely accepted and applied theories in engineering. he CPT is the simplest theory with high computational eiciency that neglects transverse shear strains and midplane displacements. he efects of transverse shear strains and midplane displacements in homogeneous thin plates are small; hence, the CPT is widely used in homogeneous thin plates [3]. However, nonhomogeneous thin plates such as functionally graded material (FGM) plates have material property gradient in the thickness direction and this gradient is not symmetric about the midplane, so the results from the CPT may be incorrect. Our studies show that the natural frequencies of FGM thin plates based on the CPT and FSDT are close to each other for small or big gradient indices, while a signiicant diference exists for moderate gradient indices. As we all know, the transverse shear deformations have small efects in thin plates, so neglecting midplane displacements in the CPT causes diferences in the FSDT solution for FGM thin plates. he material appears relatively homogeneous for small or big gradient indices; in other words, the material property gradient in the thickness direc- tion is almost symmetric about the midplane, thus midplane displacements can be neglected, whereas the material is obvi- ously nonhomogeneous for moderate gradient indices; this means that the material property gradient in the thickness direction is apparently unsymmetrical about the midplane, so neglecting midplane displacements in the CPT causes signiicant diferences in the FSDT solution for FGM thin plates with moderate gradient indices. Abrate [4] indicated that stretching-bending couplings in constitutive equations of FGM plates do not exist if the proper reference surface is selected. Zhang and Zhou [5] recently proposed that the physical neutral surface is the proper reference surface and presented a theoretical analysis for FGM thin plates based on the physical neutral surface. To eliminate the efects of midplane displacements without introducing new unknown