TY - JOUR
T1 - Variational Principles for Vibrating Carbon Nanotubes Conveying Fluid, Based on the Nonlocal Beam Model
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 - <p style="text-align: justify;">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.</p>