The influence of various physical phenomena on the dynamic behavior of
nanostructures has been attracting more and more attention of the scientific
community. This paper discusses the effects of the axial magnetic field on the
externally excited double single-walled carbon nanotube (DSWCNT) coupled by a
Winkler elastic medium. It is assumed that both carbon nanotubes are identical and
under the influence of compressive axial load with simply supported ends.
Based on the Eringen nonlocal elasticity and Euler–Bernoulli beam theory,
the system of two coupled nonhomogeneous partial differential equations
of motion is derived, where the effects of the Lorentz magnetic force are
obtained via a Maxwell relation. The dynamic responses of the DSWCNT
system for four different cases of external transversal load are considered.
The closed form solutions for the transversal displacements are obtained by
applying the Bernoulli–Fourier method of particular integrals on the system of
nonhomogeneous partial differential equations of motion. Also, analytical
expressions of the amplitude ratio for forced vibration are derived and then
validated with existing results. Moreover, the obtained analytical results
for fundamental natural frequency are validated with results obtained by
molecular dynamics (MD) simulation and show fine agreements. The effects of
compressive axial load, nonlocal parameter, axial magnetic field and stiffness
coefficient of the elastic medium on the forced dynamic behavior of DSWCNT
are considered through numerical examples. From numerical results we can
conclude that the dynamical behavior of DSWCNT is greatly influenced by
the magnetic field and nonlocal parameter. Furthermore, by selecting the
intensity of the axial magnetic field in a certain range, it is possible to adjust
the stiffness of the system without changing the material and geometric
parameters. This effect implies a change in the natural frequencies of the
system.