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1 Nanostructural Members in Various Fields: A Literature Review
Youssef et al. [22] developed the model of vibration of gold nanobeam induced
by laser pulse heating in framework of two-temperature generalized thermoelasticity
and non-Fourier heat conduction. It was shown through numerical results the effects
of the two-temperature parameter and the laser pulse parameters on the damping of
energy accumulated inside the beams.
Leijssen and Verhagen [23] demonstrated experimentally optomechanical interactions in a sliced photonic crystal nanobeam. In particular, they showed how the
large interaction enables detection of the thermal motion with detection noise below
that associated with standard quantum limit.
Hoang [24] studied thermoelastic damping depending on vibration nanobeam
modes by using the finite element method. He showed that a properly carried out
optimization of the resonant beam dimensions may essentially increase its quality
factor.
Ebrahimi and Salari [25] studied the thermal action on buckling and free vibration
characteristics of functionally graded and size-dependent Timoshenko nanobeams
under in-plane thermal loading. The scale effect was studied based on Eringen’s nonlocal elasticity theory. The effects of a few parameters including thermal effect, material distribution profile, small size effects, beam thickness and mode number on the
critical buckling temperature and normalized natural frequencies of the temperaturedependent nanobeams were analysed.
Ebrahimi and Barati [26] derived an analytical model of inhomogeneous functionally graded nanobeam in thermal environment on a basis of nonlocal strain gradient
theory. The temperature across the nanobeam thickness was distributed in a nonlinear
way. The reported numerical examples allowed to observe how the characteristics
of the wave propagation of nanobeams depend on the nonlocality parameter length
scale parameter, gradient index and temperature changes.
Ghadiri et al. [27] derived the equation of motion for a rotating nanocantilever
based on the Euler-Bernoulli beam model. The effects of temperature, angular velocity and small scale were studied. Increase of the non-dimensional frequency of the
first mode was implied by an increase of the nonlocal parameter.
Ebrahimi and Barati [28] studied thermal effects on the buckling of functionally
graded nanobeams subjected to different types of thermal loading. The derived PDEs
were solved analytically. In particular, the effects of the power-law index, nonlocal
parameter slenderness ratio and thermal loading were illustrated and discussed.
Ebrahimi and Barati [29] carried out the analysis of surface and thermal effects on
the vibration characteristics of viscoelastic foundation by utilizing the nonlocal strain
gradient elasticity theory, the Euler-Bernoulli beam model and the Gurtin-Murdoch
elasticity theory. The Hamilton principle yielded the governing equations, which
were solved analytically for simple-simple and clamped-clamped boundary conditions. Effects of linear, shear and viscous layers of foundation, structural damping
coefficient, surface elasticity, length scale parameter, nonlocal parameter, temperature change, and slenderness ratio of the nanobeam frequencies were exhibited.
Abouelregal and Zenkour [30] studied the vibrational response of thermoelastic
nanobeam resonators subjected to ramp-type heating and exponential decaying timevarying load based on the Euler-Bernoulli beam theory. The small-scale effects were
1 Nanostructural Members in Various Fields: A Literature Review
Youssef et al. [22] developed the model of vibration of gold nanobeam induced
by laser pulse heating in framework of two-temperature generalized thermoelasticity
and non-Fourier heat conduction. It was shown through numerical results the effects
of the two-temperature parameter and the laser pulse parameters on the damping of
energy accumulated inside the beams.
Leijssen and Verhagen [23] demonstrated experimentally optomechanical interactions in a sliced photonic crystal nanobeam. In particular, they showed how the
large interaction enables detection of the thermal motion with detection noise below
that associated with standard quantum limit.
Hoang [24] studied thermoelastic damping depending on vibration nanobeam
modes by using the finite element method. He showed that a properly carried out
optimization of the resonant beam dimensions may essentially increase its quality
factor.
Ebrahimi and Salari [25] studied the thermal action on buckling and free vibration
characteristics of functionally graded and size-dependent Timoshenko nanobeams
under in-plane thermal loading. The scale effect was studied based on Eringen’s nonlocal elasticity theory. The effects of a few parameters including thermal effect, material distribution profile, small size effects, beam thickness and mode number on the
critical buckling temperature and normalized natural frequencies of the temperaturedependent nanobeams were analysed.
Ebrahimi and Barati [26] derived an analytical model of inhomogeneous functionally graded nanobeam in thermal environment on a basis of nonlocal strain gradient
theory. The temperature across the nanobeam thickness was distributed in a nonlinear
way. The reported numerical examples allowed to observe how the characteristics
of the wave propagation of nanobeams depend on the nonlocality parameter length
scale parameter, gradient index and temperature changes.
Ghadiri et al. [27] derived the equation of motion for a rotating nanocantilever
based on the Euler-Bernoulli beam model. The effects of temperature, angular velocity and small scale were studied. Increase of the non-dimensional frequency of the
first mode was implied by an increase of the nonlocal parameter.
Ebrahimi and Barati [28] studied thermal effects on the buckling of functionally
graded nanobeams subjected to different types of thermal loading. The derived PDEs
were solved analytically. In particular, the effects of the power-law index, nonlocal
parameter slenderness ratio and thermal loading were illustrated and discussed.
Ebrahimi and Barati [29] carried out the analysis of surface and thermal effects on
the vibration characteristics of viscoelastic foundation by utilizing the nonlocal strain
gradient elasticity theory, the Euler-Bernoulli beam model and the Gurtin-Murdoch
elasticity theory. The Hamilton principle yielded the governing equations, which
were solved analytically for simple-simple and clamped-clamped boundary conditions. Effects of linear, shear and viscous layers of foundation, structural damping
coefficient, surface elasticity, length scale parameter, nonlocal parameter, temperature change, and slenderness ratio of the nanobeam frequencies were exhibited.
Abouelregal and Zenkour [30] studied the vibrational response of thermoelastic
nanobeam resonators subjected to ramp-type heating and exponential decaying timevarying load based on the Euler-Bernoulli beam theory. The small-scale effects were