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1 Nanostructural Members in Various Fields: A Literature Review
Rouhi et al. [84] presented an analytical method to examine the geometrically
nonlinear free vibrations of cylindrical nanoshells. The Gurtin-Murdoch continuum
model was used to recreate the impact of surface stress. The equations governing the
shell’s nonlinear vibrations were derived applying energy-based technique, taking
into account the effect of surface stress. To get the frequency-amplitude curves of
nanoshells, a perturbation method was employed. In order to examine the vibrational
behaviour of nanoshells with various geometric and surface material properties, different numerical outcomes were afforded. When the surface stress was extremely
thin, it has been shown that the nonlinear free vibration behaviour of the nanoshells
was greatly impacted. It was also proved that if the surface residual stress is negative,
the impact of geometric nonlinearity is more apparent.
Razavi et al. [85] derived the electromechanical vibration equations of the cylindrical nanoshell produced of functionally graded piezoelectric material (FGPM) applying the consistent hypothesis of torque stress and the cylindrical shell model. By the
energy technique and the concept of Hamilton, the governing equations and boundary conditions were defined. The free vibration of a unique FGPM nanoshell model
under various boundary conditions was subsequently examined using Navier and
Galerkin theories. The length-to-radius, radius-to-thickness ratio and dimensionless
length scale parameter have been proved to play an important role in the vibration
behaviour of the FGPM cylindrical nanoshell build on the size-dependent principle.
Barati [86] studied the free vibrational behaviour of porous nanoshells graded
functionally applying the hypothesis of nonlocal strain gradient. A nonlocal parameter and a strain gradient parameter were used to define nanoshell stiffness reduction
and stiffness improvement. Porositics were allocated evenly and unevenly thoroughly
by nanoshell thickness. The power-law function was defined as the gradation of
material properties with porosities. The nanoshell was constructed by the hypothesis of first-order shear deformation, and the technique of Galerkin was used to
acquire vibration frequencies. In nonlocal strain gradient principle, shape functions
that achieved the available classical and nonclassical boundary conditions have been
presented. The vibrational behaviour of the nanoshell was influenced by the nonlocal and strain gradient coefficients, boundary conditions, fraction of the porosity
volume, porosity distribution and radius-to-thickness ratio.
Sahmani et al. [87] proposed, in the context of the surface elasticity hypothesis,
a size-dependent shell model that considered for geometrical imperfection sensitivity of the axial post-buckling characteristics of a cylindrical nanoshell created
of functionally graded material (FGM). On the basis of the theory of virtual work,
the nonclassical differential equations were derived and presumed from boundary
layer-type. A perturbation-based solving methodology was then used to deduce the
size dependence on the nonlinear instability of perfect and imperfect axially loaded
FGM nanoshells with different shell thickness values, index of material property gradients and different uniform variations in temperature. In the case of thicker FGM
nanoshells, in which the consequence of surface-free energy decrease, the impact of
the initial geometric imperfection on the critical buckling load was higher than its
impact on the minimum load in the post-buckling domain.
1 Nanostructural Members in Various Fields: A Literature Review
Rouhi et al. [84] presented an analytical method to examine the geometrically
nonlinear free vibrations of cylindrical nanoshells. The Gurtin-Murdoch continuum
model was used to recreate the impact of surface stress. The equations governing the
shell’s nonlinear vibrations were derived applying energy-based technique, taking
into account the effect of surface stress. To get the frequency-amplitude curves of
nanoshells, a perturbation method was employed. In order to examine the vibrational
behaviour of nanoshells with various geometric and surface material properties, different numerical outcomes were afforded. When the surface stress was extremely
thin, it has been shown that the nonlinear free vibration behaviour of the nanoshells
was greatly impacted. It was also proved that if the surface residual stress is negative,
the impact of geometric nonlinearity is more apparent.
Razavi et al. [85] derived the electromechanical vibration equations of the cylindrical nanoshell produced of functionally graded piezoelectric material (FGPM) applying the consistent hypothesis of torque stress and the cylindrical shell model. By the
energy technique and the concept of Hamilton, the governing equations and boundary conditions were defined. The free vibration of a unique FGPM nanoshell model
under various boundary conditions was subsequently examined using Navier and
Galerkin theories. The length-to-radius, radius-to-thickness ratio and dimensionless
length scale parameter have been proved to play an important role in the vibration
behaviour of the FGPM cylindrical nanoshell build on the size-dependent principle.
Barati [86] studied the free vibrational behaviour of porous nanoshells graded
functionally applying the hypothesis of nonlocal strain gradient. A nonlocal parameter and a strain gradient parameter were used to define nanoshell stiffness reduction
and stiffness improvement. Porositics were allocated evenly and unevenly thoroughly
by nanoshell thickness. The power-law function was defined as the gradation of
material properties with porosities. The nanoshell was constructed by the hypothesis of first-order shear deformation, and the technique of Galerkin was used to
acquire vibration frequencies. In nonlocal strain gradient principle, shape functions
that achieved the available classical and nonclassical boundary conditions have been
presented. The vibrational behaviour of the nanoshell was influenced by the nonlocal and strain gradient coefficients, boundary conditions, fraction of the porosity
volume, porosity distribution and radius-to-thickness ratio.
Sahmani et al. [87] proposed, in the context of the surface elasticity hypothesis,
a size-dependent shell model that considered for geometrical imperfection sensitivity of the axial post-buckling characteristics of a cylindrical nanoshell created
of functionally graded material (FGM). On the basis of the theory of virtual work,
the nonclassical differential equations were derived and presumed from boundary
layer-type. A perturbation-based solving methodology was then used to deduce the
size dependence on the nonlinear instability of perfect and imperfect axially loaded
FGM nanoshells with different shell thickness values, index of material property gradients and different uniform variations in temperature. In the case of thicker FGM
nanoshells, in which the consequence of surface-free energy decrease, the impact of
the initial geometric imperfection on the critical buckling load was higher than its
impact on the minimum load in the post-buckling domain.