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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e-mail: snarendar@aero.iisc.ernet.in/nanduslns07@gmail.com
e-mail: krishnan@aero.iisc.ernet.in
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November 2011
Research Papers
Spectral Finite Element Formulation for Nanorods via Nonlocal Continuum Mechanics
S. Narendar,
e-mail: snarendar@aero.iisc.ernet.in/nanduslns07@gmail.com
S. Narendar
Defence Research and Development Laboratory
, Kanchanbagh, Hyderabad-500 058, Andhra Pradesh, India
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S. Gopalakrishnan
e-mail: krishnan@aero.iisc.ernet.in
S. Gopalakrishnan
Structures Laboratory
, Department of Aerospace Engineering, Indian Institute of Science, Bangalore-560 012, Karnataka, India
Search for other works by this author on:
S. Narendar
Defence Research and Development Laboratory
, Kanchanbagh, Hyderabad-500 058, Andhra Pradesh, India
e-mail: snarendar@aero.iisc.ernet.in/nanduslns07@gmail.com
S. Gopalakrishnan
Structures Laboratory
, Department of Aerospace Engineering, Indian Institute of Science, Bangalore-560 012, Karnataka, India
e-mail: krishnan@aero.iisc.ernet.in
J. Appl. Mech. Nov 2011, 78(6): 061018 (9 pages)
Published Online: August 26, 2011
Article history
Received:
May 23, 2010
Revised:
February 14, 2011
Online:
August 26, 2011
Published:
August 26, 2011
Citation
Narendar, S., and Gopalakrishnan, S. (August 26, 2011). "Spectral Finite Element Formulation for Nanorods via Nonlocal Continuum Mechanics." ASME. J. Appl. Mech. November 2011; 78(6): 061018. https://doi.org/10.1115/1.4003909
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