1.1 Introduction
7
Baghani et al. [46] illustrated and discussed the effects of magnetic field, surface
energy and compressive axial load on the nanobeam dynamics and stability. The
vibration frequencies and critical buckling loads of the nanobeam were estimated
using the differential quadrature method. It was demonstrated that the magnetic
field, surface energy and angular velocity play an important role in the dynamic and
stability analysis of the nanobeams.
Du et al. [47] reported the design, fabrication and characterization of a resonant Lorentz force magnetic field sensor based on dual-coupled photonic crystal
nanobeam cavities. The resonance wavelength shift of a selected supermode of the
coupled cavities caused by the Lorentz force-induced displacement was employed
to achieve the optical transmission variation.
Alibeigi et al. [48] investigated the buckling response of nanobeams based on the
Euler-Bernoulli model, the von Kármán geometric nonlinearity, and the modified
couple stress theory under action of thermal, electric and magnetic loadings. The
governing equation and boundary conditions were obtained by using the minimum
potential energy principle. The problem was solved using the Galerkin approach
with an account of size effect as well as length and thickness influence on the critical
buckling temperature.
Kerid et al. [49] investigated the magnetic field, thermal loads and small-scale
effects on vibrations of a nanobeam structure using the Euler-Bernoulli and Timoshenko beam theories. The resonance frequency change, the magnetic field intensity,
the thermal load and small-scale effects were presented and discussed.
1.1.2 Nanoplates
1.1.2.1 Natural Environment
Alibeigloo [50] analysed dynamics of a nanoplate by employing 3D theory of elasticity and nonlocal continuum mechanics. A closed-form solution was proposed
based on the state-space method in the thickness direction and Fourier series in the
nanoplate directions. In particular, the effects of the nonlocal parameter, aspect ratio,
thickness-to-length ratio and half wavenumbers on the frequencies were illustrated
and discussed.
Yan and Jiang [51] investigated the surface effects on the vibration and buckling
of a simply supported piezoelectric nanoplate employing a modified Kirchhoff plate
model. The effects of the applied electric potential, the mode number, the plate aspect
ratio and the plate thickness on the vibration frequencies were illustrated numerically.
The authors detected a critical transition point where the combined surface effects
on the critical electric voltage may disappear.
The vibration response of a double-piezoelectric-nanoplate system subjected
to external electric voltage was studied by Asemi and Farajpour [52] where two
nanoplates were coupled by a polymer matrix. The governing PDEs were derived
7
Baghani et al. [46] illustrated and discussed the effects of magnetic field, surface
energy and compressive axial load on the nanobeam dynamics and stability. The
vibration frequencies and critical buckling loads of the nanobeam were estimated
using the differential quadrature method. It was demonstrated that the magnetic
field, surface energy and angular velocity play an important role in the dynamic and
stability analysis of the nanobeams.
Du et al. [47] reported the design, fabrication and characterization of a resonant Lorentz force magnetic field sensor based on dual-coupled photonic crystal
nanobeam cavities. The resonance wavelength shift of a selected supermode of the
coupled cavities caused by the Lorentz force-induced displacement was employed
to achieve the optical transmission variation.
Alibeigi et al. [48] investigated the buckling response of nanobeams based on the
Euler-Bernoulli model, the von Kármán geometric nonlinearity, and the modified
couple stress theory under action of thermal, electric and magnetic loadings. The
governing equation and boundary conditions were obtained by using the minimum
potential energy principle. The problem was solved using the Galerkin approach
with an account of size effect as well as length and thickness influence on the critical
buckling temperature.
Kerid et al. [49] investigated the magnetic field, thermal loads and small-scale
effects on vibrations of a nanobeam structure using the Euler-Bernoulli and Timoshenko beam theories. The resonance frequency change, the magnetic field intensity,
the thermal load and small-scale effects were presented and discussed.
1.1.2 Nanoplates
1.1.2.1 Natural Environment
Alibeigloo [50] analysed dynamics of a nanoplate by employing 3D theory of elasticity and nonlocal continuum mechanics. A closed-form solution was proposed
based on the state-space method in the thickness direction and Fourier series in the
nanoplate directions. In particular, the effects of the nonlocal parameter, aspect ratio,
thickness-to-length ratio and half wavenumbers on the frequencies were illustrated
and discussed.
Yan and Jiang [51] investigated the surface effects on the vibration and buckling
of a simply supported piezoelectric nanoplate employing a modified Kirchhoff plate
model. The effects of the applied electric potential, the mode number, the plate aspect
ratio and the plate thickness on the vibration frequencies were illustrated numerically.
The authors detected a critical transition point where the combined surface effects
on the critical electric voltage may disappear.
The vibration response of a double-piezoelectric-nanoplate system subjected
to external electric voltage was studied by Asemi and Farajpour [52] where two
nanoplates were coupled by a polymer matrix. The governing PDEs were derived