2015 # Refined 2D and Exact 3D Shell Models for the Free Vibration Analysis of Single- and Double-Walled Carbon Nanotubes

**Abstract:** The present paper talks about the free vibration analysis of simply supported Single-and Double-Walled Carbon Nanotubes (SWCNTs and DWCNTs). Refined 2D Generalized Differential Quadrature (GDQ) shell methods and an exact 3D shell model are compared. A continuum approach (based on an elastic three-dimensional shell model) is used for natural frequency investigation of SWCNTs and DWCNTs. SWCNTs are defined as isotropic cylinders with an equivalent thickness and Young modulus. DWCNTs are defined as two concentric…

Help me understand this report

Search citation statements

Paper Sections

Select...

3

1

1

Citation Types

0

17

0

Year Published

2016

2017

Publication Types

Select...

7

Relationship

2

5

Authors

Journals

(17 citation statements)

0

17

0

“…This number of frequencies depends on the order used in each exponential matrix A * * and the number of mathematical layers employed for the shell curvature and/or the FGM law approximations. The results shown in [32][33][34][35][36][37][38][39][40] confirm that = 3 for the exponential matrix and = 100 for the mathematical layers are appropriate to always calculate the correct free frequencies for each structure, lamination sequence, number of layers, material, FGM law, and thickness value.…”

confidence: 98%

“…This number of frequencies depends on the order used in each exponential matrix A * * and the number of mathematical layers employed for the shell curvature and/or the FGM law approximations. The results shown in [32][33][34][35][36][37][38][39][40] confirm that = 3 for the exponential matrix and = 100 for the mathematical layers are appropriate to always calculate the correct free frequencies for each structure, lamination sequence, number of layers, material, FGM law, and thickness value.…”

confidence: 98%

“…The three-dimensional exact shell model employed for the comparisons proposed in Section 4 has been elaborated in [32][33][34][35][36][37][38][39][40] for the free frequency analyses of single-layered and multilayered isotropic, orthotropic, composite, FGM, and sandwich plates and shells with constant radii of curvature and for the free vibrations of single-and double-walled carbon nanotubes including van der Waals interactions. The equilibrium equations proposed in the general orthogonal curvilinear coordinate system ( , , ) are valid for both plates and shells with constant radii of curvature.…”

confidence: 99%

“…The governing di erential equation of curved singlewalled carbon nanotube on a Pasternak elastic foundation under harmonic excitation (see Figure 3) is: d 2 T (t) dt 2 + 1 T (t) + 2 T (t) 2 + 3 T (t) 3 = F cos( t):…”

confidence: 99%

“…Carbon nanotubes (CNTs) are perfect materials for a wide range of applications [3][4][5]. Carbon nanotubes possess excellent mechanical properties such as extremely high strength, sti ness, and resilience.…”

confidence: 99%