The computation of bending eigenfrequencies of single-walled carbon nanotubes based on the nonlocal theory

Abstract

Abstract. In this work, a recently proposed nonlocal theory of bending is used in the analysis of eigenfrequencies of single-walled carbon nanotubes (SWCNTs). The nanotube vibration is analyzed in the form of a homogenized continuum. Classical treatment where a nanotube is approximated by standard beam theory, is replaced by the more sophisticated nonlocal method of material interactions where a nonlocal parameter is used. The eigenfrequencies are computed by the combination of analytical as well as numerical methods for four different carbon nanotube (CNT) supports. Various types of supports are considered for the analysis: fixed–simply supported, fixed–free, simply–simply supported and fixed–fixed. Due to the huge amount of computed data, only outcomes of eigenfrequency computations for the nanobeams of armchair type with fixed and simply supported ends, and different nonlocal parameters are represented in the form of graphs at the end of the article. The study shows how the nanotube eigenfrequencies depend on nonlocal parameters as well as on the length and diameter of CNTs. The obtained results are in good agreement with the results published in papers which were gained by different procedures.

Comparison of Structural Analysis of Thin-Walled Structures Accomplished by Isogeometric Analysis and the Finite Element Method

“…NURBS represents a special case of a B-spline curve where the nodal vector is “non-uniform”. “Non-uniformity” allows to plot curves with arbitrary degrees of continuity [ 9 ]. They are significant precisely for this ability, which allows them to represent every object quite accurately.…”

“…When comparing FEA with IGA, it is worth pointing out the works of [ 9 , 10 , 11 , 12 ], which represent a very rich source of information for understanding FEA. Only then can the capabilities and properties of NURBS elements be fully appreciated.…”

Experimental and Simulation Research on the Preparation of Carbon Nano-Materials by Chemical Vapor Deposition

“…First discovered in 1952, carbon nanotubes (CNTs) were not identified as single-walled carbon nanotubes until 1976 [34]. CNTs were later described as single-walled carbon nanotubes (SWCNTs) in 1993 [35], and multi-walled carbon nanotubes (MWCNTs) were first discovered in 1991 by Iijima, as shown in Figure 4 [36][37][38][39]. As a close relative of graphene, graphene-like materials have many properties similar to graphene, such as two-dimensional geometric properties with atomic thickness, good flexibility, excellent chemical stability, high thermal conductivity, and mechanical strength.…”

“…First discovered in 1952, carbon nanotubes (CNTs) were not identified as single-walled carbon nanotubes until 1976 [34]. CNTs were later described as single-walled carbon nanotubes (SWCNTs) in 1993 [35], and multi-walled carbon nanotubes (MWCNTs) were first discovered in 1991 by Iijima, as shown in Figure 4 [36][37][38][39]. Graphite sheets also have different curling angles, resulting in single-walled carbon nanotubes that can be categorized as zigzag, armchair, and chiral [40], as shown in Figure 5.…”

“…First discovered in 1952, carbon nanotubes (CNTs) were not identified as single-walled carbon nanotubes until 1976 [ 34 ]. CNTs were later described as single-walled carbon nanotubes (SWCNTs) in 1993 [ 35 ], and multi-walled carbon nanotubes (MWCNTs) were first discovered in 1991 by Iijima, as shown in Figure 4 [ 36 , 37 , 38 , 39 ].…”