6
1 Nanostructural Members in Various Fields: A Literature Review
Arefi et al. [40] investigated free vibration responses of piezoelectric sandwich
curved nanobeams resting on Winkler-Pasternak foundation in the framework of the
nonlocal elastic theory and higher order shear deformation theories. The Hamilton
principle yielded the governing equations of motion and boundary conditions. The
carried out numerical analysis allowed to study the influence of important parameters like nonlocal parameter, the volume fraction, different boundary conditions,
the external electric field and dimensionless geometric parameters of the dynamic
characterizes of the nanobeams.
Jasulaneca et al. [41] reviewed research devoted to switch architectures and structural elements in the field of electrostatically actuated nanobeam-based nanoelectromechanical structures. Experimental results overview was presented focused on
reliability issues and of the operating environment.
Arefi et al. [42] considered nonlocal magneto-electro-thermo-elastic behaviour of
the functionally graded nanobeams subjected to magneto-electro-elastic loads. The
governing equations were derived based on the third-order shear deformation theory
of beams, the principle of virtual work and the nonlocal magneto-electro-thermoelastic relations. The nanobeams were under transverse loads and electric/magnetic
potentials. They reported electric and magnetic potential distributions through the
nanobeam thickness as well as the influence of the chosen parameters including
inhomogeneous parameter, electric and magnetic potential, nonlocal parameter and
thermal load.
Arefi [43] analysed the thickness stretching effect in the framework on the shear
and normal deformation for magneto-electro-elastic vibrations of a three-layered
curved nanobeam with nanocore and two piezomagnetic layers. Eringen’s nonlocal
elasticity theory was utilized to emphasize the size dependency in the governing
PDEs. Both analytical and numerical studies were employed. In particular, the influence of the following parameters was investigated, electro-magneto-mechanical load,
size-dependent parameter, opening angle, Pasternak’s foundation parameter and core
thickness.
1.1.1.4 Magnetic Field
Firouz-Abadi and Hosseinian [44] analysed the resonance frequency and stability of
the nanobeams embedded into a longitudinal magnetic field with an account of the
small-scale effect. The study includes the Lorentz forces and thermal stress effects.
The governing equations were solved using the Galerkin method.
Karlici´ c et al. [45] studied vibration of a cracked nanobeam in an elastic Winklertype medium with an account of the effects of longitudinal magnetic field and temperature change. The considerations were based on the Euler-Bernoulli beam theory and
the nonlocal elasticity as well as on the Maxwell classical equation. The influence of
the nonlocal parameter, stiffness of rotational spring, temperature change and magnetic field on the vibration frequencies were investigated. The crack position versus
boundary conditions was also analysed.
1 Nanostructural Members in Various Fields: A Literature Review
Arefi et al. [40] investigated free vibration responses of piezoelectric sandwich
curved nanobeams resting on Winkler-Pasternak foundation in the framework of the
nonlocal elastic theory and higher order shear deformation theories. The Hamilton
principle yielded the governing equations of motion and boundary conditions. The
carried out numerical analysis allowed to study the influence of important parameters like nonlocal parameter, the volume fraction, different boundary conditions,
the external electric field and dimensionless geometric parameters of the dynamic
characterizes of the nanobeams.
Jasulaneca et al. [41] reviewed research devoted to switch architectures and structural elements in the field of electrostatically actuated nanobeam-based nanoelectromechanical structures. Experimental results overview was presented focused on
reliability issues and of the operating environment.
Arefi et al. [42] considered nonlocal magneto-electro-thermo-elastic behaviour of
the functionally graded nanobeams subjected to magneto-electro-elastic loads. The
governing equations were derived based on the third-order shear deformation theory
of beams, the principle of virtual work and the nonlocal magneto-electro-thermoelastic relations. The nanobeams were under transverse loads and electric/magnetic
potentials. They reported electric and magnetic potential distributions through the
nanobeam thickness as well as the influence of the chosen parameters including
inhomogeneous parameter, electric and magnetic potential, nonlocal parameter and
thermal load.
Arefi [43] analysed the thickness stretching effect in the framework on the shear
and normal deformation for magneto-electro-elastic vibrations of a three-layered
curved nanobeam with nanocore and two piezomagnetic layers. Eringen’s nonlocal
elasticity theory was utilized to emphasize the size dependency in the governing
PDEs. Both analytical and numerical studies were employed. In particular, the influence of the following parameters was investigated, electro-magneto-mechanical load,
size-dependent parameter, opening angle, Pasternak’s foundation parameter and core
thickness.
1.1.1.4 Magnetic Field
Firouz-Abadi and Hosseinian [44] analysed the resonance frequency and stability of
the nanobeams embedded into a longitudinal magnetic field with an account of the
small-scale effect. The study includes the Lorentz forces and thermal stress effects.
The governing equations were solved using the Galerkin method.
Karlici´ c et al. [45] studied vibration of a cracked nanobeam in an elastic Winklertype medium with an account of the effects of longitudinal magnetic field and temperature change. The considerations were based on the Euler-Bernoulli beam theory and
the nonlocal elasticity as well as on the Maxwell classical equation. The influence of
the nonlocal parameter, stiffness of rotational spring, temperature change and magnetic field on the vibration frequencies were investigated. The crack position versus
boundary conditions was also analysed.