TY - JOUR
T1 - Nonlinear size-dependent longitudinal vibration of carbon nanotubes embedded in an elastic medium
AU - Fernandes, R.
AU - El-Borgi, S.
AU - Mousavi, S. M.
AU - Reddy, J. N.
AU - Mechmoum, A.
N1 - Publisher Copyright:
© 2016 Elsevier B.V.
PY - 2017/4/1
Y1 - 2017/4/1
N2 - In this paper, we study the longitudinal linear and nonlinear free vibration response of a single walled carbon nanotube (CNT) embedded in an elastic medium subjected to different boundary conditions. This formulation is based on a large deformation analysis in which the linear and nonlinear von Kármán strains and their gradient are included in the expression of the strain energy and the velocity and its gradient are taken into account in the expression of the kinetic energy. Therefore, static and kinetic length scales associated with both energies are introduced to model size effects. The governing motion equation along with the boundary conditions are derived using Hamilton's principle. Closed-form solutions for the linear free vibration problem of the embedded CNT rod are first obtained. Then, the nonlinear free vibration response is investigated for various values of length scales using the method of multiple scales.
AB - In this paper, we study the longitudinal linear and nonlinear free vibration response of a single walled carbon nanotube (CNT) embedded in an elastic medium subjected to different boundary conditions. This formulation is based on a large deformation analysis in which the linear and nonlinear von Kármán strains and their gradient are included in the expression of the strain energy and the velocity and its gradient are taken into account in the expression of the kinetic energy. Therefore, static and kinetic length scales associated with both energies are introduced to model size effects. The governing motion equation along with the boundary conditions are derived using Hamilton's principle. Closed-form solutions for the linear free vibration problem of the embedded CNT rod are first obtained. Then, the nonlinear free vibration response is investigated for various values of length scales using the method of multiple scales.
KW - Embedded carbon nanotube rod
KW - Linear and nonlinear free vibration
KW - Method of Multiple Scales
KW - Nonlinear von Kármán strain
KW - Strain and velocity gradient theory
UR - http://www.scopus.com/inward/record.url?scp=84999143111&partnerID=8YFLogxK
U2 - 10.1016/j.physe.2016.11.007
DO - 10.1016/j.physe.2016.11.007
M3 - Article
AN - SCOPUS:84999143111
SN - 1386-9477
VL - 88
SP - 18
EP - 25
JO - Physica E: Low-Dimensional Systems and Nanostructures
JF - Physica E: Low-Dimensional Systems and Nanostructures
ER -