基于一阶剪切变形理论FGM梁自由振动的改进型GDQ法求解  

Free vibration of FGM beams based on the first-order shear deformation theory by a modified generalized differential quadrature method

作　　者：蒲育 滕兆春[2] PU Yu;TENG Zhaochun(College of Civil Engineering,Lanzhou Institute of Technology,Lanzhou 730050,China;School of Science,Lanzhou University of Technology,Lanzhou 730050,China)

机构地区：[1]兰州工业学院土木工程学院,兰州730050 [2]兰州理工大学理学院,兰州730050

出　　处：《振动与冲击》2018年第16期212-218,共7页Journal of Vibration and Shock

基　　金：国家自然科学基金(11662008);兰州工业学院青年科技创新项目(17K-019)

摘　　要：基于一阶剪切变形梁理论(FSBT),建立了以轴向位移、横向位移及转角为未知函数的FGM梁自由振动的控制微分方程组。引入边界控制参数并采用改进型广义微分求积法(GDQ)数值研究了4种典型边界FGM梁自由振动的频率特性。结果表明该分析方法对FGM梁自由振动研究行之有效。刻画并分析了边界条件、梯度指标、跨厚比对FGM梁自振频率的影响规律。Based on the first-order shear deformation beam theory(FSBT),the governing differential equations for free vibration of functionally graded material(FGM)beams were obtained,in which the unknown functions are axial displacement,deflection and rotation angle.By introducing boundary condition coefficients and applying a modified generalized differential quadrature(GDQ)method,we investigated the natural frequencies for free vibration of FGM beams under four boundary conditions.The formulations’availability and accuracy were demonstrated by comparing them with results available in the existing literature.Then the effects of the boundary conditions,material graded index,and length-to-thickness ratio on the FGM beams’natural frequency parameters were analyzed.

关 键 词：一阶剪切变形理论 FGM梁 自由振动 固有频率 改进型广义微分求积法 

分 类 号：O343[理学—固体力学] O326[理学—力学]