材料属性温度相关变厚度FGM圆板自由振动DQM求解

摘要

Based on the first order shear deformation theory and Hamilton's principle,the free vibration of functionally graded material (FGM) circular plates with variable thickness in thermal environment was investigated.The material properties of the functionally graded plates were assumed to vary along their thickness as a power function and be temperature-dependent.The differential motion equations of the axisymmetric FGM circular plates were derived in terms of the middle surface angles of rotation and the lateral displacements.By using the differential quadrature method (DQM),the natural frequencies of the transverse free vibration of FGM annular plates with variable thickness subjected to thermal environment were obtained,and the formulations were validated by comparing the results with those available in literatures.The influences of different temperature field,thickness variation coefficient,volume fraction index and boundary conditions on the natural frequencies were discussed in detail.%基于一阶剪切理论和哈密顿原理,研究了功能梯度材料(FGM)变厚度圆板在热环境中的自由振动问题.假设材料性质沿厚度幂指数连续变化且材料属性与温度相关,推导了问题的运动微分方程.用微分求积法(DQM)计算了变厚度FGM圆板横向振动的无量纲频率,并与各向同性等厚度圆板的固有频率进行了比较.讨论不同均匀和非均匀温度场、材料梯度变化、厚度系数变化以及不同边界条件对FGM圆板固有频率的影响.