Transverse shear and normal deformation effects on vibration behaviors of functionally graded micro-beams  

作　　者：Zhu SU Lifeng WANG Kaipeng SUN Jie SUN 

机构地区：[1]State Key Laboratory of Mechanics and Control of Mechanical Structures,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China [2]Shanghai Institute of Satellite Engineering,Shanghai 201109,China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2020年第9期1303-1320,共18页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Nos.51805250 and 11602145);the Natural Science Foundation of Jiangsu Province of China(No.BK20180429);the China Postdoctoral Science Foundation(No.2019M660114);the Jiangsu Planned Projects for Postdoctoral Research Funds of China(No.2019K054)。

摘　　要：A quasi-three dimensional model is proposed for the vibration analysis of functionally graded(FG)micro-beams with general boundary conditions based on the modified strain gradient theory.To consider the effects of transverse shear and nor-mal deformations,a general displacement field is achieved by relaxing the assumption of the constant transverse displacement through the thickness.The conventional beam theories including the classical beam theory,the first-order beam theory,and the higher-order beam theory are regarded as the special cases of this model.The material proper-ties changing gradually along the thickness direction are calculated by the Mori-Tanaka scheme.The energy-based formulation is derived by a variational method integrated with the penalty function method,where the Chebyshev orthogonal polynomials are used as the basis function of the displacement variables.The formulation is validated by some comparative examples,and then the parametric studies are conducted to investigate the effects of transverse shear and normal deformations on vibration behaviors.

关 键 词：quasi-three dimensional theory modified strain gradient theory function-ally graded(FG)micro-beam size effect vibration general boundary condition 

分 类 号：O321[理学—一般力学与力学基础] O327[理学—力学]