微细观碳纳米管增强型功能梯度板的弯曲及振动分析

发布时间：2018-03-09 04:34

本文选题：修正偶应力理论　切入点：功能梯度材料　出处：《沈阳航空航天大学》2017年硕士论文　论文类型：学位论文

【摘要】：本文基于一种新的各向异性修正偶应力理论建立了碳纳米管增强复合材料功能梯度板的自由振动以及静力模型。模型能够描述尺度效应,且仅包含一个尺度参数,因而非常便于工程应用。基于三阶剪切变形理论和哈密顿原理推演了板的运动微分方程和相应的边界条件,并给出了板的平衡微分方程。以四边简支板为例给出了方板自振频率和板中心挠度的解析解。讨论了板的几何尺寸、碳纳米管体分比含量和分布方式等因素对板的自振频率和板中心挠度的影响。分析结果表明本文模型所预测的板的自振基频总是高于经典模型预测的结果,二者间的差异在板的几何尺寸接近于尺度参数的值时非常明显,且会随着板的几何尺寸的增大而逐渐消失。进一步研究发现,随着碳纳米管体积分数的增加,板中心挠度减小,振动频率增加。表明碳纳米管能够提高结构的刚度。另外,碳纳米管的分布形式对板挠度和基频有显著影响。
[Abstract]:Based on a new anisotropic modified couple stress theory, the free vibration and static models of functionally gradient plates of carbon nanotube reinforced composites are established in this paper. The model can describe the scale effect and contain only one scale parameter. Based on the third-order shear deformation theory and Hamiltonian principle, the differential equations of motion of plates and the corresponding boundary conditions are derived. The equilibrium differential equation of the plate is given. The analytical solutions of the natural vibration frequency and the central deflection of the square plate are given by taking the simply supported plate with four sides as an example. The geometric dimensions of the plate are discussed. The effect of the content and distribution of carbon nanotubes on the frequency of the plate and the deflection of the plate center is studied. The results show that the base frequency of the plate predicted by this model is always higher than that predicted by the classical model. The difference between the two is very obvious when the geometric dimension of the plate is close to the value of the scale parameter, and will gradually disappear with the increase of the geometric size of the plate. Further study shows that with the increase of the volume fraction of carbon nanotubes, the central deflection of the plate decreases. The increase of vibration frequency shows that carbon nanotubes can improve the stiffness of the structure. In addition, the distribution of carbon nanotubes has a significant effect on the deflection and fundamental frequency of the plate.
【学位授予单位】：沈阳航空航天大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TB33

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