Free vibration of cracked multilayer CNTRC plates with layer-wise CNT gradation using XFEM
摘要
The free vibration behavior of cracked multilayer carbon nanotube-reinforced composite (CNTRC) plates is investigated with emphasis on the interaction between layer-wise CNT gradation and structural discontinuities. A novel modeling framework is developed in which each lamina is independently reinforced using distinct functionally graded CNT distributions, enabling non-uniform stiffness tailoring through the plate thickness. The formulation is based on the First-Order Shear Deformation Theory (FSDT) and implemented within an Extended Finite Element Method (XFEM) framework to accurately capture crack-induced discontinuities without remeshing. Effective material properties are evaluated using the rule of mixtures, accounting for CNT distribution in each layer. A comprehensive parametric analysis is performed to examine the coupled effects of stacking sequence, number of layers, heterogeneous CNT distributions, and crack length on the natural frequencies. The results reveal that the interaction between crack presence and layer-wise CNT gradation leads to non-linear and configuration-dependent variations in the dynamic response, which cannot be predicted using conventional single-distribution or homogenized models. In particular, tailoring CNT distribution at the outer layers significantly enhances stiffness and vibration resistance, while alternative configurations may provide improved performance under severe crack conditions. The proposed approach provides new insights into the design of damaged CNTRC laminates and demonstrates that layer-wise CNT gradation offers an additional degree of freedom for optimizing vibration characteristics in advanced composite structures.