Free vibration analysis of dissimilar connected CNTs with atomic imperfections and different locations of connecting region

In this paper, the vibrational characteristics of hetero-junction carbon nanotubes (HJCNTs) are investigated using the well-known molecular mechanics approach. The paper contains two main novel parts. In the first part, the influence of connecting region location on the first five natural frequencies of perfect HJCNTs is investigated. In the second part, the effects of some common defects on fundamental frequencies are studied. The study is performed for different boundary conditions and different structures of HJCNTs. The results show that the frequencies and mode shapes are effectively influenced by changing the location of connecting region. Interestingly, it is found that the frequencies of HJCNTs can be even higher than those of their constituent CNTs for a specific location of connecting region. In the second part, it is shown that the fundamental frequency of HJCNTs decreases with introducing the defects. Furthermore, the frequency shift of defective structures with lower aspect ratios is more affected by the level of imperfections. Finally, the obtained numerical results are adopted to develop a predictive equation for calculating the fundamental frequency shift of defective straight HJCNTs based on the kind and level of defect, aspect ratio as well as the type of boundary conditions.