Spectral Finite Element Formulation for Nanorods via Nonlocal Continuum Mechanics

被引：21

作者：

Narendar, S. ^{[1
]}

Gopalakrishnan, S. ^{[2
]}

机构：

[1] Def Res & Dev Lab, Hyderabad 500058, Andhra Pradesh, India

[2] Indian Inst Sci, Struct Lab, Dept Aerosp Engn, Bangalore 560012, Karnataka, India

来源：

JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME | 2011年 / 78卷 / 06期

关键词：

spectral finite element; nonlocal elasticity; nanorod; wavenumber; dynamic stiffness; escape frequency; small scale; WAVE-PROPAGATION ANALYSIS; FREE TRANSVERSE VIBRATIONS; CARBON NANOTUBES; ELASTICITY; SINGLE; MODEL;

D O I：

10.1115/1.4003909

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

In this article, the Eringen's nonlocal elasticity theory has been incorporated into classical/local Bernoulli-Euler rod model to capture unique properties of the nanorods under the umbrella of continuum mechanics theory. The spectral finite element (SFE) formulation of nanorods is performed. SFE formulation is carried out and the exact shape functions (frequency dependent) and dynamic stiffness matrix are obtained as function of nonlocal scale parameter. It has been found that the small scale affects the exact shape functions and the elements of the dynamic stiffness matrix. The results presented in this paper can provide useful guidance for the study and design of the next generation of nanodevices that make use of the wave dispersion properties of carbon nanotubes.

引用

页数：9

共 42 条

[11] NONLOCAL ELASTICITY [J].

ERINGEN, AC ;

EDELEN, DGB .

INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE, 1972, 10 (03) :233-&

[12]

ERINGEN AC, 1987, RES MECH, V21, P313

[13]

Eringen AC., 1996, Nonlocal polar field models

[14] Low-frequency vibrational modes of viruses used for nanoelectronic self-assemblies [J].

Fonoberov, VA ;

Balandin, AA .

PHYSICA STATUS SOLIDI B-BASIC SOLID STATE PHYSICS, 2004, 241 (12) :R67-R69

[15] WAVE-PROPAGATION IN CONNECTED WAVE-GUIDES OF VARYING CROSS-SECTION [J].

GOPALAKRISHNAN, S ;

DOYLE, JF .

JOURNAL OF SOUND AND VIBRATION, 1994, 175 (03) :347-363

[16]

Gopalakrishnan S, 2008, COMPUT FLUID SOLID M, P1

[17] SPECTRAL SUPER-ELEMENTS FOR WAVE-PROPAGATION IN STRUCTURES WITH LOCAL NONUNIFORMITIES [J].

GOPALAKRISHNAN, S ;

DOYLE, JF .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1995, 121 (1-4) :77-90

[18] Nonlocal shell model for elastic wave propagation in single- and double-walled carbon nanotubes [J].

Hu, Yan-Gao ;

Liew, K. M. ;

Wang, Q. ;

He, X. Q. ;

Yakobson, B. I. .

JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, 2008, 56 (12) :3475-3485

[19] C-60 - BUCKMINSTERFULLERENE [J].

KROTO, HW ;

HEATH, JR ;

OBRIEN, SC ;

CURL, RF ;

SMALLEY, RE .

NATURE, 1985, 318 (6042) :162-163

[20] On a theory of nonlocal elasticity of bi-Helmholtz type and some applications [J].

Lazar, M ;

Maugin, GA ;

Aifantis, EC .

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, 2006, 43 (06) :1404-1421

← 1 2 3 4 5 →