摘要
由于功能梯度材料制备工艺的多样性与复杂性,造成其等效物性参数表现出明显的随机特征.考虑剪切变形,基于高阶剪切变形理论,建立了材料特性呈轴向连续变化分布的功能梯度材料梁的有限元模型,并在此基础上,利用随机变量函数的矩法,推导出动力特性统计数字特征的计算公式.综合考查材料热物参数的随机性在不同组分体积指数下对功能梯度材料梁动力特性的影响,并利用蒙特卡洛仿真进行了验证.结果表明,组分材料物性参数的随机性对动力特性分散性的贡献随体积组分指数的变化而变化;在体积组分指数确定的情况下,相比较仅考虑单一参数随机性的情况,同时考虑多个材料物性参数的随机性会明显造成模态频率分散性的提高,而模态振型的分散性主要来自材料密度的随机性,组分材料弹性模量的随机性及体积组分指数对其影响不大.
The uncertainty in effective physical properties is inherent since the manufacturing and fabrication processes of FGM （Functionally Graded Materials） are extremely complex. Based on the high- order shear deformation theory, the finite element model is developed for the FGM beam with material properties varying in the axial direction, taking into account the shear deformation. Using the moment method of the random function, the statistics of dynamic characteristics for the FGM beam is calculated, and the effect of random constituent material properties on the dynamic characteristics for the FGM beam is systemically investigated in the case of different volume fraction indexes. The Monte-Carlo method is used to verify the presented method. Numerical results show the dominant effect of the constituent volume fraction index on the dispersion in dynamic characteristics, and the dispersion in modal frequencies becomes higher when more material properties are considered random, and the dispersion in mode shapes depends mainly on the randomness of constituent material mass densities, while the volume fraction index and random elastic modulus of constituent materials have little influence on mode shapes.
出处
《西安电子科技大学学报》
EI
CAS
CSCD
北大核心
2015年第6期99-105,共7页
Journal of Xidian University
基金
中央高校基本科研业务费专项资金资助项目(JY10000904012)
国家863高技术研究发展计划资助项目(2006AA04Z402)
关键词
功能梯度材料
梁
轴向
随机性
动力特性
functionally graded material
beam
axial direction
randomness
dynamic characteristics
