Size-dependent vibration analysis of carbon nanotubes
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Size-dependent vibration analysis of carbon nanotubes Wu-Rong Jian1, Xiaohu Yao1,a)
, Yugang Sun1, Zhuocheng Xie1, Xiaoqing Zhang1
1
Department of Engineering Mechanics, South China University of Technology, Guangzhou, Guangdong 510640, People’s Republic of China Address all correspondence to this author. e-mail: [email protected]
a)
Received: 5 September 2018; accepted: 29 October 2018
Considering the nonlocal small-scale effect and surface effect, we perform the size-dependent vibration analysis of carbon nanotube (CNT). The modified governing equations for CNT’s vibration behaviors are derived by using the nonlocal Euler–Bernoulli and Timoshenko beam models, together with the consideration of surface tension and surface elasticity. According to the numerical experiments, both small-scale effect and surface effect make a substantial difference. For flexural vibration, size effect for CNT’s vibration behaviors weakens with the increase of its diameter, but strengthens with the increase of the length–diameter ratio; for shear vibration with constant length–diameter ratio, a nonlinear correlation between size effect and CNT’s diameter exists, suggesting that there is a typical diameter for CNTs, which corresponds to the “strongest” size effect. In addition, the effects of elastic substrate modulus, temperature change, and axial preloading on the vibration behaviors and their size-dependence are analyzed, respectively.
Introduction As a unique one-dimension material, carbon nanotube (CNT) has exceptional mechanical and physical properties, including high tensile strength [1, 2], strength-to-weight ratio [3], and Young’s modulus [4]. In addition, their excellent thermal, electronic, gas-storage, and fluid-conveying properties [5] are attracting more and more attention and also bear potential applications in the nanoelectromechanical systems, such as nanoresonators [6, 7], nanomotor [8], nanogear [9], and nanoactuator [10]. All of these applications are closely connected with the vibration behaviors of CNTs. To better design novel nanodevices, CNT’s vibration analysis is inevitable and plays an important role in the practical application. Currently, CNT’s vibration analysis is mainly carried out by molecular dynamics (MD) simulations [11, 12, 13, 14, 15, 16] and nonlocal continuum mechanical models [17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27]. Because of the difficulties associated with probing atomic-level structures via laboratory apparatuses in some cases, the former can be a good supplement to the experiments. Using MD simulations, CNT’s vibration behaviors can be simulated accurately by calculating the positions of all the carbon atoms, given the utilization of proper potentials, e.g., the interatomic potential developed by Tersoff [28], the reactive empirical bond order potential [29], or the adaptive
ª Materials Research Society 2019
intermolecular reactive empirical bond order potential [30]. However, fully MD simulations in the engineering cases would be extremely difficult and computationally expensive. T
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