Estimation of the effective homogenized properties is an essential step in the application of carbon nanotube (CNT)-reinforced composites. The difference between the experimental results and continuum-based homogenization schemes has motivated this work to present a modified Mori–Tanaka homogenization approach for CNT-reinforced nanocomposites. The agglomeration of CNT fibres in the matrix phase and slight weakening of the CNT–matrix interface are considered, which are incorporated in the effective homogenized properties of the nanocomposites using a two-parameter agglomeration model and interface spring-layer model, respectively. The nanotube fibres in the well-dispersed form are considered as cylindrical inclusions in the isotropic polymeric matrix. The bundled structure of CNTs is first modelled as cylindrical inclusions in the matrix and later as cumulative spherical inclusions in the hybrid matrix. Further, the effective material properties of nanocomposites are used to study the free vibration response of cylindrical panels reinforced with CNT fibres. Efficient higher-order shear and normal deformation theory is adopted, and fundamental natural frequencies are evaluated for a different set of agglomeration and interface weakening parameters using an analytical approach. The results show a significant reduction in the material stiffness as well as the natural frequency with increasing degree of agglomeration. At the same time, a slightly weakened interface is found less severe for stiffness reduction. An analysis of straight aligned CNTs highlighted their larger vulnerability to agglomeration than randomly distributed CNTs in the matrix.

有效均质性能的评估是碳纳米管（CNT）增强复合材料应用中必不可少的步骤。实验结果和基于连续体的均质化方案之间的差异促使这项工作提出了一种改进的Mori-Tanaka均质化方法，用于CNT增强的纳米复合材料。考虑了CNT纤维在基体相中的团聚和CNT-基体界面的轻微减弱，分别使用两参数团聚模型和界面弹簧层模型将其纳入纳米复合材料的有效均质性能。均匀分散形式的纳米管纤维被认为是各向同性聚合物基体中的圆柱形夹杂物。碳纳米管的束缚结构首先被建模为基质中的圆柱形夹杂物，随后被建模为杂化基质中的累积球形夹杂物。此外，纳米复合材料的有效材料性能用于研究用CNT纤维增强的圆柱形面板的自由振动响应。采用有效的高阶剪切和法向变形理论，并使用分析方法针对一组不同的团聚和界面弱化参数评估基本固有频率。结果表明，随着团聚程度的增加，材料刚度以及固有频率显着降低。同时，发现稍微减弱的界面对于降低刚度而言不那么严重。