Applicability and limitations of Donnell shell theory for vibration modelling of double-walled carbon nanotubes

Authors

• Matteo Strozzi, Università degli Studi di Modena e Reggio Emilia
• Isaac Elishakoff, Florida Atlantic University
• Leonid I. Manevitch, N.N. Semenov Federal Research Center for Chemical Physics, Russian Academy of Sciences
• Oleg V. Gendelman, Technion - Israel Institute of Technology

Author Type

Outside Researcher

Co-Author Type 1

Faculty

Co-Author Type 2

Outside Researcher

Co-Author Type 3

Outside Researcher

College

Engineering and Computer Science

Department

Ocean and Mechanical Engineering

Document Type

Article

Publication/Event/Conference Title

Thin Walled Structures

Publication Status

Version of Record

Abstract

In this paper, the comparison is conducted between two shell theories as applied to the vibrations of double-walled carbon nanotubes (DWCNTs); specifically, the evaluation of the natural frequencies is conducted via Donnell and Sanders shell theories. The discrete DWCNTs are modelled by means of couples of concentric continuous circular cylindrical shells, where van der Waals interaction forces between the two shells are modelled via He's formulation. In order to take into account the chirality of DWCNTs, an anisotropic elastic shell model is used. Simply supported, clamped and free boundary conditions are applied and Rayleigh–Ritz method is adopted to obtain approximate natural frequencies and mode shapes. At the beginning, comparisons with experimental and molecular dynamics data are made, from which it is confirmed that anisotropic elastic shell model is more accurate than isotropic one and it is obtained that Sanders shell theory is more accurate than Donnell one. Then, a parametric analysis considering different values of aspect ratio and numbers of waves along the longitudinal and circumferential directions is carried out in the framework of the anisotropic elastic shell model. From these simulations, it is found that Donnell shell theory yields unsatisfactory results for relatively low numbers of longitudinal and circumferential waves, and for relatively high values of aspect ratio, with respect to Sanders shell theory. Therefore Donnell shell theory cannot be used for vibration modelling of DWCNTs in a large range of longitudinal and circumferential wavenumbers and aspect ratios.

DOI

10.1016/j.tws.2022.109532

Publication Date

9-1-2022

Recommended Citation

Strozzi, Matteo; Elishakoff, Isaac; Manevitch, Leonid I.; and Gendelman, Oleg V., "Applicability and limitations of Donnell shell theory for vibration modelling of double-walled carbon nanotubes" (2022). Faculty Scholarship. 196.
https://digitalcommons.fau.edu/faculty_papers/196