Modal analysis of multi-walled carbon nanocones using molecular dynamics simulation Ali Narjabadifam ⇑ , Farid Vakili-Tahami, Mohammad Zehsaz Department of Mechanical Engineering, University of Tabriz, Tabriz, Iran article info Article history: Received 2 February 2017 Received in revised form 15 May 2017 Accepted 16 May 2017 Keywords: Multi-walled carbon nanocone Resonant frequency Mode shape Molecular dynamics simulation abstract To design carbon nanocone-based sensing and actuating nanodevices, it is necessary to study their vibra- tional behavior. For this purpose, modal analysis of multi-walled carbon nanocones are performed using molecular dynamics simulation. Initial closed-tip atomic structures of the carbon nanocones with differ- ent apex angles are modeled through a proposed method which is based on the molecular dynamics sim- ulation. The dependency of the resonant frequencies and their corresponding three-dimensional mode shapes on different geometric parameters of multi-walled carbon nanocones are investigated. The results indicate that the order of mode shapes is influenced by the number of layers and apex angle of the multi- walled carbon nanocones. The results also show that the variation of the resonant frequencies with the number of layers depends on the apex angle and shape of the modal displacement. The vibrational behav- ior of the multi-walled carbon nanocones is also compared with that of the multi-walled carbon nanotubes. Ó 2017 Elsevier B.V. All rights reserved. 1. Introduction In modern industry, carbon nanostructures are of great interest because of their potential for structural and electronic applications taking advantage of their novel properties. In particular, cylindrical and conical morphologies of carbon nanostructures are pioneer in this type of applications due to their large surface area and unique shape. Since the discovery of carbon nanotubes (CNTs) [1] and car- bon nanocones (CNCs) [2], there has been a great deal of experi- mental and theoretical researches that focused on their characterization. CNTs and CNCs are good candidates as sensing and actuating elements in nanoscale devices [3–9]. Among these applications, their usage as atomic force microscopy (AFM) tips [3,8] is of particular interest. The proper implementation of CNTs and CNCs as AFM tips, requires comprehensive understanding of their dynamic behavior and a remarkable amount of studies have been performed to investigate the vibrational behavior of these two nanostructures [10–32]. However, the reported works in this field for CNCs are relatively limited as compared with CNTs. Also, the inherent thermal vibration of CNT-based AFM tips, due to the high aspect ratio and small diameter of the nanostructure, reduces imaging quality, but, the sharp tip and less flexibility of CNCs, make them a better candidate to be used as AFM tips [8,33]. So, precise characterization of CNCs is of great importance considering all aspects of this nanostructure. Duo to the technical difficulties associated with the experimen- tal methods for investigating the structures at nanoscale, theoret- ical and numerical approaches are usually preferred. Continuum mechanics models, molecular mechanics method and molecular dynamics (MD) simulation have been widely used to study and approximate the behaviors of the nanostructures. In the first approach, which is usually based on the nonlocal elasticity theory, CNCs are modeled as beams with varying cross sections [21,30] or as shells [22–24]. The molecular mechanics method is a combina- tion of continuum mechanics models and atomistic approaches. In this method, the bonds between different atoms are represented by structural elements, whereas, the atoms are considered as mass elements and the material constants of the structural elements are obtained by equating the energies of the molecular and structural models. In this way, the nanostructure can be treated as a frame structure and its modal analysis can be performed using the stan- dard finite element method. The vibrational behavior of CNCs, based on this method, has been studied in Refs. [26–28,31]. In the third approach, i.e., MD simulation technique, the inter- action between different atoms is described by some potential energy functions and the displacement gradient of these functions results in the applied forces on each atom. Then, these forces are used in Newton’s second law to determine the movement of each atom. This method can provide a detailed understanding about dif- http://dx.doi.org/10.1016/j.commatsci.2017.05.031 0927-0256/Ó 2017 Elsevier B.V. All rights reserved. ⇑ Corresponding author. E-mail address: a.narjabadi@tabrizu.ac.ir (A. Narjabadifam). Computational Materials Science 137 (2017) 55–66 Contents lists available at ScienceDirect Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci