Nonlocal elasticity effect on column buckling of multiwalled carbon nanotubes under temperature field

Stochastic Resonance and Safe Basin of Single-Walled Carbon Nanotubes with Strongly Nonlinear Stiffness under Random Magnetic Field

“…The deformation and vibration of nanobeam have been studied by Lim [6][7] and Reddy [8], the assessment of nanotube structures has been investigated by Kiani K [9]. The studies on buckling of nanotubes have been reported in various references [10][11][12][13]. In addition, plenty of research results on nanotubes vibration have been reported recently [14][15][16][17][18][19][20][21][22][23][24][25].…”

“…Subsequently, much progress on nonlinear problems of nanostructures with the nonlocal elasticity theory has been reported [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. The deformation and vibration of nanobeam have been studied by Lim [6][7] and Reddy [8], the assessment of nanotube structures has been investigated by Kiani K [9].…”

Large amplitude free vibration of micro/nano beams based on nonlocal thermal elasticity theory

“…Firstly, for many micro/nano beams, both the physical (e.g., induced by van der Waals force) and geometrical (e.g., stem from large deflection) nonlinearities were observed by previous theoretical and experimental investigations (Yang et al, 2010;Ke et al, 2009), the nonlinearity causes the mechanical behaviors of the beams to be changed significantly (Setoodeh et al, 2011;Fang et al, 2013), so the linear beam theory is not appropriate in such situations. Moreover, some researches confirm that the thermal effects are effective on the mechanical behaviors of micro/nano beams (Amara et al, 2010;Ansari et al, 2011). Based on the theories of thermal elasticity and nonlocal elasticity, Chang (2012) developed an elastic Euler-Bernoulli beam model for the thermal-mechanical vibration and buckling instability of single-walled carbon nanotubes conveying fluid, numerical solutions obtained from the finite element method conclude that the effects of temperature change and nonlocal small scale are very significant on the fundamental natural frequency and critical flow velocity.…”

Flexural wave propagation in fluid-conveying carbon nanotubes with system uncertainties

“…Recently, the nonlocal continuum theory, which assumes that the stress tensor at any point is dependent on the whole strain field of the continuum, is widely used to characterize the small-scale effects of CNTs. This theory was firstly proposed by Eringen (1972) and was successfully used in solving the vibration (De Rosa and Lippiello 2017;Deng and Yang 2014;Ebrahimi and Nasirzadeh 2015;Hu et al 2012;Kiani 2013a, b;Xia and Wang 2010;Zhen et al 2011), wave propagation (Aydogdu 2014;Huang et al 2013;Narendar and Gopalakrishnan 2010;Narendar et al 2012;Wang et al 2006Wang et al , 2013Wang et al , 2015, and buckling (Adali 2008;Amara et al 2010;Khademolhosseini et al 2010;Robinson and Adali 2016;Setoodeh et al 2011) problems of CNTs. Several different nonlocal continuum theories, such as the nonlocal Euler-Bernoulli beam (Setoodeh et al 2011;Wang et al 2015;Zhen et al 2011), nonlocal Timoshenko beam (De Rosa and Lippiello 2017;Narendar and Gopalakrishnan 2010;Xia and Wang 2010), and nonlocal shell (Khademolhosseini et al 2010) theory, were adopted to study the mechanical behaviors of CNTs, in particular, because the CNT comprises a sheet of carbon atoms, which makes it perfect a candidate for nanocontainers to store gases and for nanotubes to convey fluids (Ansari et al 2016;Bahaadini and Hosseini 2016;SafarPour and Ghadiri 2017).…”