1.1 Introduction
11
numerical outcomes were described, such as the impact of boundary conditions,
power factor, plate aspect ratio and side-to-thickness bending ratio of FGM plates.
Park and Han [71] presented buckling of nonlocal magneto-electro-elastic
nanoplates, which was examined on the basis of the theory of higher order shear
deformation. The variation of the magneto-electro-elastic plate was established in
compliance with the Maxwell equation and the magneto-electric boundary condition. Furthermore, Eringen’s nonlocal differential theory was employed. The governing equations of nonlocal principle were derived by using the variation principle.
Numerical results revealed the relationship between local and nonlocal hypotheses.
The consequences of aspect ratio, nonlocal parameters and in-plate load directions
on the reaction to buckling were analysed.
1.1.2.4 Magnetic Fields
Fujiwara et al. [72] investigated magnetic orientation of carbon nanotubes, which can
be used in the engineering of nanometers. Nanotube alignment is essential for their
anisotropic behaviour. The orientation of paramagnetic and diamagnetic substances
and proteins in magnetic fields was examined. The exposure emerges from the energy
of magnetic anisotropy and obeys the thermal equilibrium distribution of Boltzmann.
The method could be applied for nanotubes in an isolated condition and therefore
can be used to position gas and liquid phases in production and process.
Kiani [73] investigated behaviour of free in-plane and out-of-plane vibration of
rectangular nanoplates, which were submitted to unidirectional in-plane magnetic
fields of concern. The body forces on the nanoplate were acquired based on the theories of Kirchhoff, Mindlin and higher order plate. The couching described demonstrated the magnetic field’s small scale. The frequencies of the nanoplates were
assessed for the suggested models. The role of dimensional relations and magnetic
field strength in both in-plane and out-of-plane frequencies was discussed.
Karlici´ c et al. [74] developed nanostructure of the graphene sheet. The impact
of in-plane magnetic field on the viscoelastic orthotropic multi-nanoplate system
(VOMNPS) inserted in a viscoelastic medium using nonlocal principle was investigated. The system of partial differential equations characterizing the free transverse
vibration of VOMNPS under the uniaxial in-plane magnetic field applying the nonlocal elasticity of Eringen principle and the plate hypothesis of Kirchhoff taking into
account the viscoelastic and orthotropic properties of nanoplates was derived and
studied.
Amiri et al. [75] analysed the free vibration of circular magneto-electro-elastic
(MEE) nanoplates. Those nanoplates were modelled using Kirchhoff’s assumption in
the context of the theory of nonlocal elasticity, in order to take into account the smallscale effect. The MEE nanoplate explored here was deemed to be completely clamped
under external electrical end magnetic potentials. The influence of the magnetoelectric potential on the system’s destabilization was examined, and critical values
of the potential employed were measured. A comprehensive numerical investigation
was carried out to study the effects of the nanoplate and piezoelectric volume fraction
11
numerical outcomes were described, such as the impact of boundary conditions,
power factor, plate aspect ratio and side-to-thickness bending ratio of FGM plates.
Park and Han [71] presented buckling of nonlocal magneto-electro-elastic
nanoplates, which was examined on the basis of the theory of higher order shear
deformation. The variation of the magneto-electro-elastic plate was established in
compliance with the Maxwell equation and the magneto-electric boundary condition. Furthermore, Eringen’s nonlocal differential theory was employed. The governing equations of nonlocal principle were derived by using the variation principle.
Numerical results revealed the relationship between local and nonlocal hypotheses.
The consequences of aspect ratio, nonlocal parameters and in-plate load directions
on the reaction to buckling were analysed.
1.1.2.4 Magnetic Fields
Fujiwara et al. [72] investigated magnetic orientation of carbon nanotubes, which can
be used in the engineering of nanometers. Nanotube alignment is essential for their
anisotropic behaviour. The orientation of paramagnetic and diamagnetic substances
and proteins in magnetic fields was examined. The exposure emerges from the energy
of magnetic anisotropy and obeys the thermal equilibrium distribution of Boltzmann.
The method could be applied for nanotubes in an isolated condition and therefore
can be used to position gas and liquid phases in production and process.
Kiani [73] investigated behaviour of free in-plane and out-of-plane vibration of
rectangular nanoplates, which were submitted to unidirectional in-plane magnetic
fields of concern. The body forces on the nanoplate were acquired based on the theories of Kirchhoff, Mindlin and higher order plate. The couching described demonstrated the magnetic field’s small scale. The frequencies of the nanoplates were
assessed for the suggested models. The role of dimensional relations and magnetic
field strength in both in-plane and out-of-plane frequencies was discussed.
Karlici´ c et al. [74] developed nanostructure of the graphene sheet. The impact
of in-plane magnetic field on the viscoelastic orthotropic multi-nanoplate system
(VOMNPS) inserted in a viscoelastic medium using nonlocal principle was investigated. The system of partial differential equations characterizing the free transverse
vibration of VOMNPS under the uniaxial in-plane magnetic field applying the nonlocal elasticity of Eringen principle and the plate hypothesis of Kirchhoff taking into
account the viscoelastic and orthotropic properties of nanoplates was derived and
studied.
Amiri et al. [75] analysed the free vibration of circular magneto-electro-elastic
(MEE) nanoplates. Those nanoplates were modelled using Kirchhoff’s assumption in
the context of the theory of nonlocal elasticity, in order to take into account the smallscale effect. The MEE nanoplate explored here was deemed to be completely clamped
under external electrical end magnetic potentials. The influence of the magnetoelectric potential on the system’s destabilization was examined, and critical values
of the potential employed were measured. A comprehensive numerical investigation
was carried out to study the effects of the nanoplate and piezoelectric volume fraction