Natural dynamic characteristics of a circular cylindrical Timoshenko tube made of three-directional functionally graded material  

作　　者：Ye TANG Jiye XU Tianzhi YANG 

机构地区：[1]School of Mechanical Engineering,Anhui Polytechnic University,Wuhu 241000,Anhui Province,China [2]Department of Mechanics,Tianjin University,Tianjin 300350,China [3]School of Mechanical Engineering and Automation,Northeastern University,Shenyang 110819,China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2022年第4期479-496,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.11902001 and12072221);the China Postdoctoral Science Foundation(No.2018M641643);the Anhui Provincial Natural Science Foundation of China(Nos.1908085QA13 and 1808085ME128)。

摘　　要：The natural dynamic characteristics of a circular cylindrical tube made of three-directional(3 D)functional graded material(FGM)based on the Timoshenko beam theory are investigated.Hamilton’s principle is utilized to derive the novel motion equations of the tube,considering the interactions among the longitudinal,transverse,and rotation deformations.By dint of the differential quadrature method(DQM),the governing equations are discretized to conduct the analysis of natural dynamic characteristics.The Ritz method,in conjunction with the finite element method(FEM),is introduced to verify the present results.It is found that the asymmetric modes in the tube are controlled by the 3 D FGM,which exhibit more complicated shapes compared with the unidirectional(1 D)and bi-directional(2 D)FGM cases.Numerical examples illustrate the effects of the axial,radial,and circumferential FGM indexes as well as the supported edges on the natural dynamic characteristics in detail.It is notable that the obtained results are beneficial for accurate design of smart structures composed from multi-directional FGM.

关 键 词：circular cylindrical tube three-directional(3D)functionally graded material(FGM) asymmetric mode natural dynamic characteristic differential quadrature method(DQM) 

分 类 号：O343.6[理学—固体力学]