基于谱几何法构建了考虑温度场影响的功能梯度(functionally graded material，FGM)圆锥壳振动特性分析模型，在该模型中假设材料特性与温度相关并沿厚度方向变化。首先，采用人工弹簧技术来模拟圆锥壳的任意边界条件，并在一阶剪切变形理论框架下推导出温度场影响下FGM圆锥壳振动能量方程；然后应用高效、准确的谱几何法与周向傅里叶谐波函数乘积和的形式来描述壳体位移容许函数。在此基础上，将位移容许函数代入振动能量方程，并采用Rayleigh-Ritz法对位移容许函数未知级数展开系数进行变分操作即可获得热环境下FGM圆锥壳的振动求解方程。通过将文中构建模型求解结果与现有文献解和有限元分析结果对比分析，验证了所构建模型的正确性。最后，研究了边界条件、材料特性、几何结构参数以及温度场等因素对FGM圆锥壳瞬态振动特性的影响规律。
关键词：功能梯度圆锥壳；热环境；自由振动；瞬态振动；谱几何法
Abstract
Based on the spectro-geometric method, the prediction model for vibration characteristics of the functionally graded material (FGM) conical shell under thermal environment is established in this presentation. In the current model, temperature-dependent material characteristics, which change with the shell thickness direction is considered. Firstly, the boundary conditions for the shell is simulated with the artificial spring theory. The energy equation of the FGM conical shell under thermal environment is derived with the framework of the first-order shear deformation theory. Then, an efficient and accurate spectro-geometric method and the form of the sum of the products of the circumferential Fourier harmonic function are employed to express the displacement admissible function. On the basis, the displacement admissible functions are substituted into the energy equation. Also the Rayleigh-Ritz method is utilized to perform variational operations on the unknown coefficients of the displacement admissible function. The free and transient thermal vibration characteristics can be solved with the standard dynamic equation. By comparing the calculation results with those obtained from the existing literatures and finite element analysis, the accuracy and reliability of the current model is demonstrated. Finally, the effect of the boundary conditions, material properties, geometric properties and temperature field on the transient vibration characteristics of FGM conical shells are investigated.
Key words: functionally graded conical shell; thermal environment; free vibration; transient vibration; spectro-geometric method
关键词
功能梯度圆锥壳 /
热环境 /
自由振动 /
瞬态振动 /
谱几何法
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Key words
functionally graded conical shell /
thermal environment /
free vibration /
transient vibration /
spectro-geometric method
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