The Effects of Van der Waals Interactions on the Vibrational Behavior of Single-Walled Carbon Nanotube Using Hammer Impact Test: A Molecular Dynamics Study
Hammer impact test is a conventional modal analysis technique in large-scale structures. Possessing efficient capability in the excitation of any structure within a wide range of frequency, this technique can be a good mean to identify the dynamics of any structure. Here we implement this method on nano-scale structures in using molecular dynamics simulations. For convenience, we use a carbon nanotube (CNT) which shows complicated behavior due to van der Waals (vdW) interactions with a graphene sheet. Graphene sheet represents the vdW interactions of the CNT with its surroundings, which is an important distinction between the phenomena in the nano-scale. The variations in fundamental natural frequency and quality factor of the CNT with different strength of vdW interactions are explored. For this purpose, the distance between the CNT and graphene is used as the tuning parameter. The results of the hammer impact tests are compared and matched to those obtained with a well-established method in the nano-scale, thermomechanical noise. Having the natural frequencies of CNT and graphene sheet at their isolated state, it can be noted that the vdW effects bring both the structures into a common intermediary natural frequency when they are close enough. However, as the distance between the graphene sheet and the CNT increases, while the fundamental natural frequency of the CNT experiences a constant value at the beginning, after passing a certain distance, tends to the natural frequency of isolated graphene sheet. Up to this certain limit, the fundamental frequency of the graphene sheet is completely equal to that of the CNT. This shows a full coupling of the two structures at closer distances, which transforms into decoupling at higher distances. The frequencies corresponding to the two structures deviate in a way that the CNT vibrates faster than the graphene sheet. At far enough distance, the natural frequencies meet the values of the isolated state of the structures. As an aside, the quality factor of the CNT shows an inverse relation with the fundamental frequencies. These results can be used as concerns in the design of novel experimental procedures for evaluation of vibrational properties of nanostructures.