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Volume 5, Issue 3
Variational Principles for Vibrating Carbon Nanotubes Conveying Fluid, Based on the Nonlocal Beam Model

Sarp Adali

DOI: 10.4208/eajam.130814.250515a

East Asian J. Appl. Math., 5 (2015), pp. 209-221.

Published online: 2018-02

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  • Abstract

Variational principles are derived in order to facilitate the investigation of the vibrations and stability of single and double-walled carbon nanotubes conveying a fluid, from a linear time-dependent partial differential equation governing their displacements. The nonlocal elastic theory of Euler-Bernoulli beams takes small-scale effects into account. Hamilton’s principle is obtained for double-walled nano-tubes conveying a fluid. The natural and geometric boundary conditions identified are seen to be coupled and time-dependent due to nonlocal effects.

  • Keywords

Variational principles, carbon nanotube, fluid flow, nonlocal beam, vibration.

  • AMS Subject Headings

58E30, 74H45, 82D80

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-5-209, author = {Sarp Adali}, title = {Variational Principles for Vibrating Carbon Nanotubes Conveying Fluid, Based on the Nonlocal Beam Model}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {5}, number = {3}, pages = {209--221}, abstract = {

Variational principles are derived in order to facilitate the investigation of the vibrations and stability of single and double-walled carbon nanotubes conveying a fluid, from a linear time-dependent partial differential equation governing their displacements. The nonlocal elastic theory of Euler-Bernoulli beams takes small-scale effects into account. Hamilton’s principle is obtained for double-walled nano-tubes conveying a fluid. The natural and geometric boundary conditions identified are seen to be coupled and time-dependent due to nonlocal effects.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.130814.250515a}, url = {http://global-sci.org/intro/article_detail/eajam/10797.html} }
TY - JOUR T1 - Variational Principles for Vibrating Carbon Nanotubes Conveying Fluid, Based on the Nonlocal Beam Model AU - Sarp Adali JO - East Asian Journal on Applied Mathematics VL - 3 SP - 209 EP - 221 PY - 2018 DA - 2018/02 SN - 5 DO - http://doi.org/10.4208/eajam.130814.250515a UR - https://global-sci.org/intro/article_detail/eajam/10797.html KW - Variational principles, carbon nanotube, fluid flow, nonlocal beam, vibration. AB -

Variational principles are derived in order to facilitate the investigation of the vibrations and stability of single and double-walled carbon nanotubes conveying a fluid, from a linear time-dependent partial differential equation governing their displacements. The nonlocal elastic theory of Euler-Bernoulli beams takes small-scale effects into account. Hamilton’s principle is obtained for double-walled nano-tubes conveying a fluid. The natural and geometric boundary conditions identified are seen to be coupled and time-dependent due to nonlocal effects.

Sarp Adali. (2018). Variational Principles for Vibrating Carbon Nanotubes Conveying Fluid, Based on the Nonlocal Beam Model. East Asian Journal on Applied Mathematics. 5 (3). 209-221. doi:10.4208/eajam.130814.250515a
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