基于孔洞分布理论的多孔材料板振动分析

主要研究了不规则几何结构多孔材料制备的板材的振动分析．基于Gibson-Ashby等效模量计算，引入了分布因子加以改进原有的理论．对于材料的孔洞分布情况，提出了Burr分布的概率密度拟合，获得了Burr分布的3个自变量参数并用实际的孔洞几何参数进行了比对与描述．基于平板振动理论和等效模量理论，计算出了随着孔洞分布情况变化下的平板固有振动频率，并分析了孔洞尺寸与频率间的关系．之后引入了尺度因子来量化描述平均孔洞尺寸对多孔平板的频率影响．结论证明了改进的等效理论能够有效地体现孔洞的分布对平板力学性能的改变，论述了孔洞尺寸范围，孔洞离散度以及平均孔洞尺寸对多孔方板结构固有频率的影响．这种影响将会对多孔材料结构的优化设计起指导作用．

Vibration Analysis of Foam Plates Based on Cell Volume Distribution

In this paper, vibration analysis of irregular-closed-cell foam plates is per-formed. A cell volume distribution coefficient is introduced to modify the original Gibson-Ashby equations of effective Young’s modulus of foam materials. A Burr distribution is imported to describe the cell volume distribution situation. Three Burr distribution pa-rameters are obtained and related to the cell volume range and the diversity. Based on the plate theory and the effective modulus theory, the natural frequency of foam plates is calculated with the change of the cell volume distribution parameters. The relationship between the frequencies and the cell volumes are derived. The scale factor of the average cell size is introduced and proved to be an important factor to the performance of the foam plate. The result is shown by the existing theory of size effects. It is determined that the cell volume distribution has an impact on the natural frequency of the plate structure based on the cell volume range, the diversity, and the average size, and the impact can lead to optimization of the synthesis procedure