Closed-form solutions for free vibration of rectangular FGM thin plates resting on elastic foundation

作     者：T. F. Xu Y. F. Xing 

作者机构：Institute of Solid Mechanics Beihang UniversityBeijing 100191 China China Academy of Launch Vehicle Technology R&D Center Beijing 100076 China 

出 版 物：《Acta Mechanica Sinica》 (力学学报（英文版）)

年 卷 期：2016年第32卷第6期

页      面：1088-1103页

核心收录：

学科分类：08[工学] 0805[工学-材料科学与工程（可授工学、理学学位）] 0802[工学-机械工程] 080101[工学-一般力学与力学基础] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 0702[理学-物理学] 

基　　金：supported by the National Natural Science Foundation of China (Grants 11172028, 1372021) Research Fund for the Doctoral Program of Higher Education of China (Grant 20131102110039) the Innovation Foundation of Beihang University for PhD graduates 

主　　题：Functionally graded material Free vibration Rectangular plate Close form solutions Neutral surface 

摘      要：This article presents closed-form solutions for the frequency analysis of rectangular functionally graded material (FGM) thin plates subjected to initially in-plane loads and with an elastic foundation. Based on classical thin plate theory, the governing differential equations are derived using Hamilton s principle. A neutral surface is used to eliminate stretching-bending coupling in FGM plates on the basis of the assumption of constant Poisson s ratio. The resulting governing equation of FGM thin plates has the same form as homogeneous thin plates. The separation-of-variables method is adopted to obtain solutions for the free vibration problems of rectangular FGM thin plates with separable boundary conditions, including, for example, clamped plates. The obtained normal modes and frequencies are in elegant closed forms, and present formulations and solutions are validated by comparing present results with those in the literature and finite element method results obtained by the authors. A parameter study reveals the effects of the power law index n and aspect ratio a/b on frequencies.