12
1 Nanostructural Members in Various Fields: A Literature Review
of the MEE material on the natural frequencies of the nanoplate with regard to small
scale, thickness and radius.
In order to analyse the mechanical behaviour of a single-layer graphene sheet as an
orthotropic nanoplate, Karlici´ c et al. [76] applied the nonlocal theory of KirchhoffLove. Using the classical equations of Maxwell, the equation of motion of a simply supported nanoplate was derived. The analysis suggested that the sensitivity of
nanomechanical detectors can be enhanced with the help of magnetic field.
Arani et al. [77] used for the first time a control feedback system to analyse
the free vibration response of magnetic material (MsM). Due to the consideration
of both normal and shear modulus, the Pasternak foundation was chosen to model
the elastic medium. Nonlocal equations of motion were derived using the Hamilton
principle and resolved using a differential quadrature method (DQM) taking into
account various boundary conditions. The outcomes showed the impact of different
parameters of MsNP’s vibration behaviour, in particular, the control effect of velocity
feedback gains to minimize the frequency.
Karami et al. [78] focused on the assessment of nanoplate propagation, made of
functionally graded porous (FG) temperature-reliant materials based on the WinklerPasternak foundation in the magnetic in-plate field. The porosity distribution of
nanoplates was regarded in accordance with the power-law rule as an even pattern.
The Hamilton principle was used in connecting to the theory of nonlocal strain
gradients to derive the governing equations based on the hypothesis of second-order
shear deformation.
1.1.3 Nanoshells
1.1.3.1 Vibration
Arman et al. [79] studied the spectrum of vibrational radial modes in composite
metal nanostructures. Metal nanoshells with dielectric core in an environment and
bimetallic core-shell particles were investigated. For all of these nanostructures, the
frequencies and damping rates of essential (breathing) modes with those of two
higher order modes were measured together. For metal nanoshells, the frequency
of breathing mode was invariably lower than the frequency of solid molecules of
equal dimension, while damping was higher and enhanced with a reduction in the
thickness of the shell. Two regimes that can be defined in the appearance of an external
medium as weakly damped and overdamped vibrations were classified. For bimetallic
particles, the frequency and damping rate depended periodically on the thickness of
the shell with the period defined by the number of the mode. The frequency of higher
modes was almost independent of the environment for both forms of nanostructures,
while the damping rate demonstrated a powerful sensitivity to the external excitation.
Zaera et al. [80] analysed the free axisymmetric vibrations of a closed spherical
nanoshell applying the hypothesis of nonlocal elasticity of Eringen. Bearing in mind
the theories of thin shells, the motion equations were adequately derived, and the
1 Nanostructural Members in Various Fields: A Literature Review
of the MEE material on the natural frequencies of the nanoplate with regard to small
scale, thickness and radius.
In order to analyse the mechanical behaviour of a single-layer graphene sheet as an
orthotropic nanoplate, Karlici´ c et al. [76] applied the nonlocal theory of KirchhoffLove. Using the classical equations of Maxwell, the equation of motion of a simply supported nanoplate was derived. The analysis suggested that the sensitivity of
nanomechanical detectors can be enhanced with the help of magnetic field.
Arani et al. [77] used for the first time a control feedback system to analyse
the free vibration response of magnetic material (MsM). Due to the consideration
of both normal and shear modulus, the Pasternak foundation was chosen to model
the elastic medium. Nonlocal equations of motion were derived using the Hamilton
principle and resolved using a differential quadrature method (DQM) taking into
account various boundary conditions. The outcomes showed the impact of different
parameters of MsNP’s vibration behaviour, in particular, the control effect of velocity
feedback gains to minimize the frequency.
Karami et al. [78] focused on the assessment of nanoplate propagation, made of
functionally graded porous (FG) temperature-reliant materials based on the WinklerPasternak foundation in the magnetic in-plate field. The porosity distribution of
nanoplates was regarded in accordance with the power-law rule as an even pattern.
The Hamilton principle was used in connecting to the theory of nonlocal strain
gradients to derive the governing equations based on the hypothesis of second-order
shear deformation.
1.1.3 Nanoshells
1.1.3.1 Vibration
Arman et al. [79] studied the spectrum of vibrational radial modes in composite
metal nanostructures. Metal nanoshells with dielectric core in an environment and
bimetallic core-shell particles were investigated. For all of these nanostructures, the
frequencies and damping rates of essential (breathing) modes with those of two
higher order modes were measured together. For metal nanoshells, the frequency
of breathing mode was invariably lower than the frequency of solid molecules of
equal dimension, while damping was higher and enhanced with a reduction in the
thickness of the shell. Two regimes that can be defined in the appearance of an external
medium as weakly damped and overdamped vibrations were classified. For bimetallic
particles, the frequency and damping rate depended periodically on the thickness of
the shell with the period defined by the number of the mode. The frequency of higher
modes was almost independent of the environment for both forms of nanostructures,
while the damping rate demonstrated a powerful sensitivity to the external excitation.
Zaera et al. [80] analysed the free axisymmetric vibrations of a closed spherical
nanoshell applying the hypothesis of nonlocal elasticity of Eringen. Bearing in mind
the theories of thin shells, the motion equations were adequately derived, and the