Analytical and numerical modeling of higher order free vibration characteristics of single-walled carbon nanotubes

被引：14

作者：

Azrar, Abdellhadi ^{[1
]}

Azrar, Lahcen ^{[1
,2
,3
]}

Aljinaidi, Adbulmalik A. ^{[3
]}

机构：

[1] Abdelmalek Essaadi Univ, Fac Sci & Tech Tangier, Dept Math, MMC, Tangier, Morocco

[2] Mohammed V Univ, Higher Sch Tech Educ Rabat ENSET, Lab LaMIPI, Rabat, Morocco

[3] King Abdulaziz Univ, Dept Mech Engn, Fac Engn, Jeddah, Saudi Arabia

来源：

MECHANICS OF ADVANCED MATERIALS AND STRUCTURES | 2016年 / 23卷 / 11期

关键词：

carbon nanotubes; nonlocal elasticity; small-scale effect; higher order modes; eigenfrequencies; analytical formulations; differential quadrature method; well conditioned modes; Timoshenko; Euler-Bernoulli; FLAPWISE BENDING VIBRATION; NONLOCAL ELASTICITY; VARIATIONAL-PRINCIPLES;

D O I：

10.1080/15376494.2015.1068405

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In this article, analytical and numerical investigations of small, higher, and asymptotic order vibration eigenmodes and natural eigenfrequencies of single-walled carbon nanotubes (CNT) are elaborated. The nonlocal elasticity theory is used and the numerical simulation is based on the differential quadrature method. Due to numerical instability, the common analytical forms of eigenmodes can be only used for the first 12 modes or so. New mathematical models for higher eigenmodes and associated eigenfrequencies of CNT are developed. The obtained eigenmodes are well conditioned and numerically stable and may be used as modal bases at any required frequency range.

引用

页码：1245 / 1262

页数：18

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