A closed-form solution for critical buckling temperature of a single-walled carbon nanotube

Thermal effects on vibration properties of double-layered nanoplates at small scales

“…a = À1.6 Â 10 À6 K À1 ) and high temperature (i.e. a = 1.1 Â 10 À6 K À1 ) used for the nanotubes are considered [22][23][24]. The temperature change T = 60 K, the width l a = 2l b = 20 nm and the half wave number n = 1.…”

“…In their research, it is concluded that the thermal expansion coefficient is negative for the low or room temperature but positive for the high temperature. Then some works on the mechanical characteristics of the carbon nanotubes with thermal effects are reported [21][22][23][24][25].…”

Thermal Vibration of a Single-Walled Carbon Nanotube Including Small Scale and Quantum Effects

“…In order to know the effect of relative parameters on the RMS amplitude distribution of thermal vibration of mode 1 of an armchair (10, 10) SWCNT, we considered the geometric and material parameters as follows: 12 E = 1 TPa, L = 9 8 nm, t = 0 34 nm, = 2237 kg/m 3 , and = 1 1 × 10 −6 / C. 18 Figure 2 depicts the comparison of present work with earlier reported work on RMS amplitude distribution of thermal vibration of an armchair (10, 10) SWCNT considered as a simply supported beam for the case of P = 0, K = 0, e 0 a = 0, and T = 300 K. The RMS amplitude distribution is symmetric with respect to the center of the SWCNT length due to boundary condition effects. It can be seen that the RMS amplitude distribution obtained in this study is consistent with previously reported work 12 for the same conditions.…”

Vibration and instability of a single-walled carbon nanotube in a three-dimensional magnetic field

“…In the framework of local and nonlocal continuum theories, free longitudinal vibration [19][20][21], free transverse vibration [22][23][24][25][26][27], lateral buckling analysis [28][29][30][31][32], fluid flow-induced vibration [33][34][35], and moving nanoparticle caused excitation [36,37] of such nanostructures were of concern to applied mechanics researchers during the past decade. However, in the context of the nonlocal continuum mechanics, the effect of applied magnetic fields on the dynamical characteristics of SWCNTs has not been thoroughly covered.…”