环扇形板的面内自由振动分析

摘要

Based on horizontal linear elastic theory,movement governing differential equation of annular sector plate inner free vibration is built.Non-dimensional movement governing differentia equation of annu-lar sector plate inner free vibration is dispersed with two dimensional differential quadrature method (DQM),non-dimensional nature frequency of annular sector plate inner free vibration under different boundary conditions was solved,comparing to calculated result with finite element ANSYS commercial software at sector angle of annular sector plate is,which verified our method is right.The result shows that under corresponded boundary condition,internal and external of annular sector plate and sector angle all have effect on non-dimensional nature frequency,its calculated results and analyzing methods can be as ref-erence for design and research.%基于平面线弹性理论,建立了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对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环扇形板面内自由振动的无量纲固有频率,并与环扇形板扇形角为π/4时有限元商用软件ANSYS的计算结果进行了对比,验证了新方法的正确性.结果表明:在相应边界条件下,环扇形板的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.