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Application of the R‐functions in free vibration analysis of FGM plates and shallow shells with temperature dependent properties
ZAMM - Journal of Applied Mathematics and Mechanics ( IF 2.3 ) Pub Date : 2020-09-16 , DOI: 10.1002/zamm.202000080 Jan Awrejcewicz 1 , Lidiya Kurpa 2 , Tetyana Shmatko 2
ZAMM - Journal of Applied Mathematics and Mechanics ( IF 2.3 ) Pub Date : 2020-09-16 , DOI: 10.1002/zamm.202000080 Jan Awrejcewicz 1 , Lidiya Kurpa 2 , Tetyana Shmatko 2
Affiliation
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The free vibration of plates and shallow shells with/without cutouts made of functionally graded materials (FGM) is investigated using variational FG shallow shells with temperature dependent mechanical characteristics of the constituent materials. First‐order shear deformation theory of shallow shells is employed. It is supposed that material properties vary through thickness according to a power‐law distribution of the constituent's volume fraction. They depend on both the temperature and the thickness. Temperature field is modeled by one‐dimensional heat transfer equation, since the temperature is varied only in thickness direction. Solution of this equation is determined by a polynomial power series expansion. Corresponding software was developed to implement the proposed approach. The vibration analysis was carried out for FG plates and shallow shells with cutout and various boundary conditions.
中文翻译：
R函数在温度依赖特性的FGM板和浅壳自由振动分析中的应用
使用变化的FG浅壳，并根据成分材料的机械特性，研究了具有/不具有由功能梯度材料（FGM）制成的切口的板和浅壳的自由振动。采用了浅壳的一阶剪切变形理论。据推测，材料特性会根据成分体积分数的幂律分布而随厚度而变化。它们取决于温度和厚度。由于温度仅在厚度方向上发生变化，因此温度场通过一维热传递方程建模。该方程的解由多项式幂级数展开确定。开发了相应的软件来实施所提出的方法。
更新日期：2020-09-16
中文翻译：
R函数在温度依赖特性的FGM板和浅壳自由振动分析中的应用
使用变化的FG浅壳，并根据成分材料的机械特性，研究了具有/不具有由功能梯度材料（FGM）制成的切口的板和浅壳的自由振动。采用了浅壳的一阶剪切变形理论。据推测，材料特性会根据成分体积分数的幂律分布而随厚度而变化。它们取决于温度和厚度。由于温度仅在厚度方向上发生变化，因此温度场通过一维热传递方程建模。该方程的解由多项式幂级数展开确定。开发了相应的软件来实施所提出的方法。
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