热环境下功能梯度环板的谱几何法自由振动解

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振动与冲击 ›› 2022, Vol. 41 ›› Issue (10) : 1-7.

论文

石先杰1，左朋1,2

作者信息 +

Free vibration analysis of functionally graded annular plates under thermal environment by the spectro-geometric method

SHI Xianjie1，ZUO Peng1,2

Author information +

文章历史 +

摘要

建立了功能梯度环板在热环境作用下的谱几何法自由振动分析模型。首先，在该模型中假设材料特性与温度相关，且沿结构厚度方向呈现连续梯度变化；其次，通过在边界处设置不同类型的边界弹簧来模拟任意边界条件，并且基于一阶剪切变形理论推导出热环境下功能梯度环板结构的能量方程；然后，利用谱几何法和傅里叶正余弦函数来描述结构位移容许函数，进而采用Rayleigh-Ritz法获得功能梯度环板结构热振特性分析理论模型。通过热环境下功能梯度环板频率特性对比算例发现，文中模型具有良好的计算准确性，并且适用于多种边界条件。最后，文中给出了功能梯度环板结构的参数化研究，研究结果表明环境温度、边界条件、梯度指数的变化均会对结构的热振特性产生影响。

Abstract

A free vibration analysis model of functionally graded annular plates under thermal environment is established with the spectro-geometric method. Firstly, the model assumes that the material properties are temperature-dependent and show a continuous gradient along the thickness of the structure. Secondly, arbitrary boundary conditions are simulated by setting various type boundary restraining springs along boundary edge. Based on the first-order shear deformation theory, the vibration energy equation of the functionally graded annular plate is deduced. Thirdly, the displacement admissible functions are expressed with spectro-geometric method and Fourier series function. Then the Rayleigh-Ritz method is employed to derive the vibration analysis model for functionally graded annular plate under thermal environment. The numerical example gives a comparative analysis of the frequency characteristics of functionally graded annular plates considering thermal environment factors. The results show that the current model has good calculation accuracy. Also, it is suitable for analyzing the thermal vibration characteristics of functionally graded annular plates. Through the parameterization study of the FGM annular plate, it is found that the changes of the environmental temperature, boundary conditions, and gradient index will have an impact effect on the thermal vibration characteristics of the functionally graded annular plate.

导出引用

石先杰1，左朋1,2. 热环境下功能梯度环板的谱几何法自由振动解[J]. 振动与冲击, 2022, 41(10): 1-7

SHI Xianjie1，ZUO Peng1,2. Free vibration analysis of functionally graded annular plates under thermal environment by the spectro-geometric method[J]. Journal of Vibration and Shock, 2022, 41(10): 1-7

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