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.
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页数:9
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