热环境下功能梯度环板的谱几何法自由振动解  

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

作　　者：石先杰[1] 左朋 SHI Xianjie;ZUO Peng(Institute of Systems Engineering,China Academy of Engineering Physics,Mianyang 621999,China;Department of Modern Mechanics,University of Science and Technology of China,Hefei 230026,China)

机构地区：[1]中国工程物理研究院总体工程研究所,四川绵阳621999 [2]中国科学技术大学近代力学系,合肥230026

出　　处：《振动与冲击》2022年第10期1-7,22,共8页Journal of Vibration and Shock

基　　金：国家自然科学基金面上项目(51975547);中国工程物理研究院院长基金(YZJJLX2018008)。

摘　　要：采用谱几何法建立了热环境下功能梯度环板自由振动分析模型。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,该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,给出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。A free vibration analysis model for functionally graded annular plates under thermal environment was established by the spectro-geometric method.In the model,it was assumed that the material properties are temperature-dependent with a continuous gradient variation along the thickness of the structure.Arbitrary boundary conditions were simulated by setting various type boundary restraining springs along boundary edges.Based on the first-order shear deformation theory,the vibration energy equation of the functionally graded annular plate was deduced.The displacement admissible functions were expressed by virtue of the spectro-geometric method and Fourier series function.Then the Rayleigh-Ritz method was employed to derive the vibration solutions.A numerical example was given to carry out a comparative analysis of the frequency characteristics of the functionally graded annular plate 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 the functionally graded annular plate.Through the parameterization study on the functionally graded annular plate,it is found that the changes of the environmental temperature,boundary conditions,and gradient index will have an obvious impact on its thermal vibration characteristics.

关 键 词：功能梯度环板 热环境 自由振动 谱几何法 

分 类 号：TH212[机械工程—机械制造及自动化] TH213.3