沿板平面变异功能梯度板件的三维动力特性

3-D dynamic character of FGM plates with variation along the plane direction

功能梯度材料具有复杂的细部结构,其内部构造远比匀质材料复杂,因此其构件动力分析很难求得其解析解。文中建议一种新颖的功能梯度构件动力分析的细观元法。细观力学研究的目的在于建立材料的宏观性能同其组分材料性能及细观结构之间的定量关系,它可揭示不同的材料组合具有不同的宏观性能的内在机制。目前功能梯度板件分析只能处理材料特性沿厚度方向梯度变化,而细观元法则直接从制备时给定的材料组分分布出发计算构件宏观三维动力特性,并给出了沿板平面方向材料特性梯度变化的功能梯度板件三维固有频率及振型的三维分布。

Functionally graded materials possess complex microstructures,and its internal structure is more complex than the one of homogeneous material. Therefore, the analytic solution of functionally graded structure was difficult to obtain. A new microelement method for the dynamic analysis of functionally graded structures was suggested to establish quantitative relation between the macro-character and microstructures of functionally graded materials, and the mechanism, that different combination of materials have different macro-character, can be exposed. Up to now, the assumption that the material character changed only along the thickness direction is employed in the analyses of functionally graded plates. In this paper, the three dimensional dynamic character can be immediately calculated by the material component distribution determined in the process of material production, and then the three-dimensional dimensionless values of natural frequency and mode shape of the functionally graded plates with variant material character along the plate plane direction are given.