随机FG-CNTRC结构的动力特性分析

Analysis of dynamic characteristics of random FG-CNTRC structures

为考查功能梯度碳纳米管增强复合材料结构中组分材料物理参数及组分分布随机性对结构固有频率的影响,采用高阶剪切变形理论及广义混合律建立了碳纳米管在不同排布方式下梁结构的有限元动力学模型;运用一阶摄动法引入随机变量参数,建立了随机有限元模型,确定了结构固有频率数字特征与随机组分材料物理参数及组分分布数字特征之间的关系。结果表明,组分材料物理参数随机性对结构固有频率分散性的贡献远大于组分分布随机性的贡献;随着碳纳米管体积分数的增加,碳纳米管X型功能梯度排布下结构固有频率的分散性由衰减转为迅速增加,O型功能梯度排布下结构固有频率分散性仍处于衰减状态。

In order to investigate the influences of the randomness of physical parameters of constituent materials and constituent distribution on natural frequencies of a functionally graded carbon nanotube reinforced composite structure,a finite element dynamics model is developed for a beam structure with different arrangements of carbon nanotube by using the high-order shear deformation theory and generalized mixture law.The first-order perturbation method is used to introduce the random variables and the stochastic finite element model is established.The numerical characteristics relationships between natural frequencies and the randomness of physical parameters of constituent materials as well as constituent distribution are derived.The results show that the contribution of the randomness of physical parameters of constituent materials to the scattering of natural frequencies is much greater than the constituent distribution.The dispersion of natural frequencies for the carbon nanotube X-type decreases with the increase in volume fraction at the very beginning,and then turns to increase rapidly.However,O-type natural frequencies dispersion is still in the attenuated state.