应用数学和力学2023，Vol.44Issue(11)：1354-1365,12.DOI:10.21656/1000-0887.440050
弹性地基上多孔二维功能梯度材料微梁自由振动研究
Free Vibration Analysis of Porous 2D Functionally Graded Material Microbeams on Winkler's Foundation
摘要
Abstract
Based on the modified couple stress theory and the Timoshenko beam theory,the governing equa-tions for free vibration of porous 2D functional graded material(FGM)on Winkler's foundation were derived under Hamilton's principle.The differential quadrature method was used to obtain the numerical solutions of the vibration frequencies and fundamental mode shapes of microbeams with both ends clamped(C-C)and sim-ply supported(S-S).The improved stiffness matrix was used to greatly improve the calculation efficiency.The proposed model was degenerated to the macro and micro 2D-FGM models,which were compared with those in previous literatures for validation.The results show that,the present mathematical model is suitable for differ-ent types of 2D material distributions.The dimensionless frequencies increase with the dimensionless elastic modulus of Winkler's foundation.Under a certain dimensionless elastic foundation modulus,the dimensionless frequencies decrease with the functionally graded index,the axial functionally graded index and the porosity.The effect of the material variation on the mode shape increases with the mode number.For the same parame-ter,the dimensionless frequencies of the beam with uniform porosity distribution are slightly lower than those with linear porosity distribution.关键词
修正偶应力理论/孔隙率/Winkler弹性地基/二维功能梯度材料/微分求积法Key words
modified couple stress theory/porosity/Winkler's foundation/2D functionally graded material/differential quadrature method分类
数理科学引用本文复制引用
赵英治,唐怀平,赖泽东,章家杰..弹性地基上多孔二维功能梯度材料微梁自由振动研究[J].应用数学和力学,2023,44(11):1354-1365,12.基金项目
国家自然科学基金项目(51778548) （51778548）
