Dynamic response of single-walled carbon nanotubes based on various shell theories

Abstract

Carbon nanotubes are used in several engineering applications because of their superior mechanical properties. Scientific works still need to be carried out, especially on their dynamic response. These studies mainly focus on modal analysis, considering zigzag and armchair nanotubes, and sometimes, varying chirality. However, these works do not present any results on the steady-state responses. Therefore, the objective of this paper is to perform different studies, in terms of the stiffness response, modal analysis and steady-state response of single-walled carbon nanotubes by using a 3D finite-element model of the single-walled carbon nanotube, under different types of boundary conditions, to provide more results in this field. The single-walled carbon nanotube is modeled as a space frame structure by using the Morse potential and as a thin shell model based on various shell theories. A static analysis is performed to compare the stress–strain behavior between the Morse potential and the thin shell model. A parametric study on chirality effects and aspect ratio is also conducted to determine which shell theory is more suitable to model the mechanical behavior of single-walled carbon nanotubes. Finally, the analysis of harmonic response is conducted to describe the steady-state response between both the models.

Determination of fundamental coupled torsional—radial frequency of single-walled carbon nanotubes

“…Since being discovered in 1993 by Iijima and Ichihashi (1993), carbon nanotubes (CNTs) are becoming increasingly popular nanomaterial because of their extremely high thermal and electrical conductivity, high mechanical strength (>150 GPa) (Hashemnia et al, 2009), and low density (2267 kg/m3) (Lee and Lee, 2012; Palacios and Ganesan, 2019; Wu et al, 2009), which gives them extremely high specific strength (≈150×109/2267≈6.6×107 Nm/kg), that is, 200 times that of steel. They are being widely used to reinforce concrete beam composites (Bourada et al, 2020; Bousahla et al, 2020; Mohammadimehr et al, 2020) where they are shown to improve resistance to buckling and vibration.…”

“…CNTs are also being used for three-phase CNT/polymer/fiber laminated truncated conical shells (Yousefi et al, 2020). Such CNT-based composites have application as lightweight, high strength, vibration resilient materials in automotive, aerospace, space research, and nuclear industries (Palacios and Ganesan, 2019). Further, CNTs are used as high-frequency oscillators in nano-electromechanical systems (NEMS) such as nano-sensors, nano-resonators, charge detectors, field emitters, and nano-actuators (Gibson et al, 2007; Gupta et al, 2018; Wang and Arash, 2014; Zaporotskova et al, 2016).…”

“…Thus, in this condition, SWCNTs behave as thin shells, instead of hollow beams as is the case with transverse vibration. Existing research on torsional vibrations of SWCNTs includes the study of its equations of motion using modified couple stress theory (Ansari et al, 2013; Yayli, 2018), strain gradient theory (Ansari et al, 2013; Guo et al, 2016), Eringen’s nonlocal elasticity theory (Khosravi et al, 2020; Li, 2014), thin shell theory (Palacios and Ganesan, 2019; Selim, 2010), and molecular dynamic simulations (Chang, 2013; Georgantzinos et al, 2009). Calculation of torsional vibration frequency using these methods is time consuming because it requires heavy computation.…”