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In-plane free vibration analysis of FGM annular sector plates[J].计算力学学报,2018,35(5):560~566
FGM环扇形板的面内自由振动分析
In-plane free vibration analysis of FGM annular sector plates
In-plane free vibration analysis of FGM annular sector plates

DOI：10.7511/jslx20170703001

 作者 单位 E-mail 滕兆春 兰州理工大学 理学院, 兰州 730050 tengzc@lut.cn 朱亚文 兰州理工大学 理学院, 兰州 730050 蒲育 兰州工业学院 土木工程学院, 兰州 730050

假定功能梯度材料（FGM）的物性参数沿环扇形板径向按照幂律梯度变化，基于平面线弹性理论，建立了FGM环扇形板面内自由振动的运动控制微分方程。采用二维微分求积法（DQM）对FGM环扇形板面内自由振动的无量纲运动控制微分方程进行离散，数值求解了不同边界条件下FGM环扇形板面内自由振动的无量纲固有频率，同时也给出了FGM环扇形板扇形角为π/4时有限元商用软件ANSYS的部分计算结果，验证了本文方法的正确性。结果表明，在相应边界条件下，FGM环扇形板的梯度指标、内外半径比以及扇形角对无量纲固有频率均有影响，其计算结果和分析方法可供设计和研究参考。

Assuming that the material physical parameters of the annular sector plates follows a power law distribution along the radius and based on plane linear theory of elasticity,the governing differential equations of motion for in-plane free vibration of a functionally graded material (FGM) annular sector plate are established.Then using two-dimensional differential quadrature method (DQM),the dimensionless governing differential equations of motion of in-plane free vibration of FGM annular sector plates are discretized and the dimensionless natural frequencies of the in-plane free vibration of FGM annular sector plates under the corresponding boundary conditions are solved numerically.Some results of dimensionless natural frequencies of FGM annular sector plate with π/4 angle of the sector are computed by the finite element commercial software ANSYS.They show that the current method is effective and accurate.When the plates are under the corresponding boundary conditions,the results indicate that the gradient index of FGM,the internal and external radius ratio and the angle of the sector all affect the dimensionless natural frequencies,the calculation results and the analysis method can be used in design and research.