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1 Nanostructural Members in Various Fields: A Literature Review
Barati [66] proved that sort of vibration, temperature and moisture increase, strain
gradient and nonlocal parameter, elastic foundation, material graduation and proportion of side to thickness have a significant impact on the vibration behaviour
of double-layer nanoscale plates. A double-layered nanoplate was for the first time
constructed by means of nonlocal strain gradient theory, which matched both rigiditysoftening and rigidity-hardening effects. Consequences of magnetic and hydrothermal actions on double-layered nanoplates were also explored.
Barati [67] illustrated a nonlocal strain gradient plate framework for the vibration
assessment of double-layered nanoplates in hygrothermal areas with linearly variable
mechanical loads in the plane. The suggested hypothesis included two parameters of
scale connected to the effects of nonlocal and strain gradients. The Hamilton concept
was employed to derive governing equations of a nonlocal strain gradient nanoplate
on an elastic medium. The consequences of various factors such as load factor,
nonlocal and length scale parameters, increase in the percentage of moisture and
temperature or boundary conditions on vibration characteristics of a double-layered
nanoplate were illustrated.
1.1.2.3 Electric Fields
Pugno [68] analysed nanoelectromechanical (NEMS) three-dimensional systems. A
general formula based on free energy for the treatment of statics and dynamics of
three-dimensional NEMS was extracted and described in compliance with a classical/quantum mechanics. Nanoplates and nanowires were studied. The structural
destabilization, which would result from the so-called pull-in voltage, would pertain
to the device switch. The amplitude and frequency of the nanoplate thermal vibrations were assessed according to the voltage employed. The impact of the forces of
van der Waals on the dynamics of nanoelectromechanical three-dimensional systems
was presented. Based on the concept of uncertainty, the amplitude and frequency of
oscillations were estimated.
Wenjun Yang et al. [69] studied the influence of flexoelectricity on the electromechanical coupling behaviour of a piezoelectric nanoplate that was simply supported
by the Kirchhoff theory. The governing equations and the corresponding boundary
conditions were derived from the principle of Hamilton, and the analytical solutions for deflection and natural frequency were obtained. The results showed that
the deflections predicted by the current model were smaller than those calculated by
the classical model. For thinner plates, the flexoelectric effect was more prominent.
Differences in deflections or frequencies between the two models were gradually
decreasing with an increase of the plate thickness. This paper can help to understand
the mechanism of electromechanical higher order coupling.
Sobhy [70] described a functionally graded material (FGM) and its thermomechanical bending. Winkler springs with a variable modulus constituted one of the layers. Moreover, the plates were the other way round. By solving the one-dimensional
heat conduction equation, the temperature was estimated. The plate’s material features were established to be graded across the thickness of the panel. Numerous
1 Nanostructural Members in Various Fields: A Literature Review
Barati [66] proved that sort of vibration, temperature and moisture increase, strain
gradient and nonlocal parameter, elastic foundation, material graduation and proportion of side to thickness have a significant impact on the vibration behaviour
of double-layer nanoscale plates. A double-layered nanoplate was for the first time
constructed by means of nonlocal strain gradient theory, which matched both rigiditysoftening and rigidity-hardening effects. Consequences of magnetic and hydrothermal actions on double-layered nanoplates were also explored.
Barati [67] illustrated a nonlocal strain gradient plate framework for the vibration
assessment of double-layered nanoplates in hygrothermal areas with linearly variable
mechanical loads in the plane. The suggested hypothesis included two parameters of
scale connected to the effects of nonlocal and strain gradients. The Hamilton concept
was employed to derive governing equations of a nonlocal strain gradient nanoplate
on an elastic medium. The consequences of various factors such as load factor,
nonlocal and length scale parameters, increase in the percentage of moisture and
temperature or boundary conditions on vibration characteristics of a double-layered
nanoplate were illustrated.
1.1.2.3 Electric Fields
Pugno [68] analysed nanoelectromechanical (NEMS) three-dimensional systems. A
general formula based on free energy for the treatment of statics and dynamics of
three-dimensional NEMS was extracted and described in compliance with a classical/quantum mechanics. Nanoplates and nanowires were studied. The structural
destabilization, which would result from the so-called pull-in voltage, would pertain
to the device switch. The amplitude and frequency of the nanoplate thermal vibrations were assessed according to the voltage employed. The impact of the forces of
van der Waals on the dynamics of nanoelectromechanical three-dimensional systems
was presented. Based on the concept of uncertainty, the amplitude and frequency of
oscillations were estimated.
Wenjun Yang et al. [69] studied the influence of flexoelectricity on the electromechanical coupling behaviour of a piezoelectric nanoplate that was simply supported
by the Kirchhoff theory. The governing equations and the corresponding boundary
conditions were derived from the principle of Hamilton, and the analytical solutions for deflection and natural frequency were obtained. The results showed that
the deflections predicted by the current model were smaller than those calculated by
the classical model. For thinner plates, the flexoelectric effect was more prominent.
Differences in deflections or frequencies between the two models were gradually
decreasing with an increase of the plate thickness. This paper can help to understand
the mechanism of electromechanical higher order coupling.
Sobhy [70] described a functionally graded material (FGM) and its thermomechanical bending. Winkler springs with a variable modulus constituted one of the layers. Moreover, the plates were the other way round. By solving the one-dimensional
heat conduction equation, the temperature was estimated. The plate’s material features were established to be graded across the thickness of the panel. Numerous