温度影响下FGM圆环板的面内自由振动分析

In-plane free vibration of FGM annular plates considering temperature effect

基于二维弹性理论和Hamilton原理,假设材料物理性质随温度变化且沿圆环板径向按照幂律梯度分布,导出了温度影响下FGM薄圆环板面内自由振动的运动微分方程。用微分求积法(DQM)计算了温度影响下FGM圆环板面内自由振动的无量纲频率,并与各向同性材料圆环板面内自由振动的无量纲频率进行了比较,说明该分析方法的有效性。同时考虑了沿圆环板径向均匀升温和非均匀升温两种情况下,几何参数、材料性质和温度变化对面内自由振动频率的影响。

Based on the two-dimensional elastic theory and the Hamilton＇s principle,the differential motion equations for in-plane free vibration of the functionally graded material thin annular plate in thermal environment were derived. In the equations,the material properties were assumed to be temperature-dependent and graded in the radial direction of annular plates according to power law distributions. By using differential quadrature method（ DQM）,the dimensionless frequency parameters of in-plane free vibration of FGM annular plates under thermal environment were obtained. The formulations were validated by comparing the results with those available in literatures. Considering the cases of uniform and variable temperature rise distribution in the radial direction of annular plate respectively,the effects of geometrical parameters,material graded index and temperature rise on the natural frequencies of in-plane free vibration of annular plates were investigated.