Size-dependent behavior of slacked carbon nanotube actuator based on the higher-order strain gradient theory
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Size-dependent behavior of slacked carbon nanotube actuator based on the higher-order strain gradient theory Iswan Pradiptya . Hassen M. Ouakad
Received: 20 May 2017 / Accepted: 5 July 2017 Springer Science+Business Media B.V. 2017
Abstract This paper proposes to investigate the nonlinear size dependent behavior of electrically actuated carbon nanotube (CNT) based nano-actuator while including the higher-order strain gradient deformation, the geometric nonlinearity due to the von Karman nonlinear strain as well as the slack effect, and the temperature gradient effects. The assumed non-classical beam model adopts some internal material size scale parameters related to the material nanostructures and is capable of interpreting the size effect that the classical continuum beam model is unable to pronounce. The higher-order governing equations of motion and boundary conditions are derived using the so-called extended Hamilton principle. A Galerkin based reduced-order model (ROM) modal decomposition is developed to prescribe the non-classical nanotube mode shape as well as its static behavior under any applied DC actuation load. Results of the static analysis is compared with those obtained by both classical elasticity continuum and strain gradient theories. A Jacobian method is utilized to determine the variation of the natural frequencies of the nanobeam with the DC load as well as the slack level. A thorough parametric study is conducted to study the influences of the size scale
I. Pradiptya H. M. Ouakad (&) Mechanical Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Kingdom of Saudi Arabia e-mail: [email protected]
dependent parameters, the geometric nonlinearity, the initial curvature, the gate voltage, and the temperature gradient effect on structural behavior of the CNTbased nano-actuator. It is found that the size effect based on the strain gradient deformation has significant influence on the fundamental nanotube natural frequency dispersion. Also, varying this size effect have revealed the offering of numerous possibilities of modes veering and crossing, all shown to be dependent of the strain gradient parameters as well as the CNT slack level. Keywords Carbon nanotube Higher-order strain gradient theory Electrostatic Slack Temperature gradient
1 Introduction Carbon nanotubes (CNTs) have been studied extensively since their discovery back in the earlier 1990s (Iijima 1991). These tiny structures represent the most promising contenders in various nano-based applications in numerous fields such as: physical, biological and electromechanical devices, etc. This is mainly due to their favorable mechanical and electrical properties. To be able to possibly overcome the difficulties of conducting conscientious experimental investigations on these nano based structures, researchers have been competing, in the past few decades, to improve
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analytical/numerical modeling tools capable of predicting the structural behaviors of the C
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