On Finite Element Vibration Analysis of Carbon Nanotubes

Seyed M. Hashemi and Ishan Ali Khan

A chapter in Perusal of the Finite Element Method from IntechOpen

Abstract: In this chapter, a finite element formulation is proposed to study the natural frequencies of double-walled carbon nanotubes modeled as, both, local and nonlocal Euler-Bernoulli beams, coupled with van der Waals interaction forces. The formulation uses Galerkin-weighted residual approach and employs Hermite cubic polynomial function to derive the linear eigenvalue problem. Natural frequencies are found for clamped-free, clamped-clamped and simply supported-simply supported boundary conditions. The results are in good agreement with the formulations found in the literature. The effect of nonlocal factor on the natural frequencies of the system is found out by comparing local and nonlocal results. Additionally, the universality of the proposed model is proven by application to a double-elastic Euler-Bernoulli beam. This formulation paves way for Finite Element Method (FEM) analysis of multi-walled CNTs--either locally or nonlocally.

Keywords: carbon nanotubes; Euler-Bernoulli beam; DWCNTs; finite element analysis; nonlocal continuum mechanics; vibrations (search for similar items in EconPapers)
JEL-codes: C60 (search for similar items in EconPapers)
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Persistent link: https://EconPapers.repec.org/RePEc:ito:pchaps:106428

DOI: 10.5772/65358

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