Dynamic Characteristics of Functionally Graded Timoshenko Beams by Improved Differential Quadrature Method  

作　　者：Xiaojun Huang Liaojun Zhang Hanbo Cui Gaoxing Hu 

机构地区：[1]School of Architecture and Civil Engineering,Anhui Polytechnic University,Wuhu,241000,China [2]College of Water Conservancy and Hydropower Engineering,Hohai University,Nanjing,210098,China

出　　处：《Computer Modeling in Engineering & Sciences》2024年第8期1647-1668,共22页工程与科学中的计算机建模（英文）

基　　金：Anhui Provincial Natural Science Foundation(2308085QD124);Anhui Province University Natural Science Research Project(GrantNo.2023AH050918);The University Outstanding Youth Talent Support Program of Anhui Province.

摘　　要：This study proposes an effective method to enhance the accuracy of the Differential Quadrature Method(DQM)for calculating the dynamic characteristics of functionally graded beams by improving the form of discrete node distribution.Firstly,based on the first-order shear deformation theory,the governing equation of free vibration of a functionally graded beam is transformed into the eigenvalue problem of ordinary differential equations with respect to beam axial displacement,transverse displacement,and cross-sectional rotation angle by considering the effects of shear deformation and rotational inertia of the beam cross-section.Then,ignoring the shear deformation of the beam section and only considering the effect of the rotational inertia of the section,the governing equation of the beam is transformed into the eigenvalue problem of ordinary differential equations with respect to beam transverse displacement.Based on the differential quadrature method theory,the eigenvalue problem of ordinary differential equations is transformed into the eigenvalue problem of standard generalized algebraic equations.Finally,the first several natural frequencies of the beam can be calculated.The feasibility and accuracy of the improved DQM are verified using the finite element method(FEM)and combined with the results of relevant literature.

关 键 词：Timoshenko beams functionally graded materials dynamic characteristics natural frequency improved differential quadrature method 

分 类 号：O17[理学—数学]