Non-linear behaviors of carbon nanotubes under electrostatic actuation based on strain gradient theory

The paper deals with studying the deflection and pull-in voltages of the carbon nanotubes under electrostatic actuation with various dimensions and boundary conditions. The size-dependent behaviors of the carbon nanotubes (CNTs) are considered via application of the strain gradient theory. The results obtained from the strain gradient theory are compared to those estimated using the classical elasticity. The outcomes reveal that the classical elasticity theory underestimates the pull-in voltages of the carbon nanotubes and strain gradient theorem results in stiffer nano-structures with higher pull-in voltages. Increasing of the deflection due to the higher voltages increases the differences between the results of the strain gradient theory and classical elasticity. Thus, in order to design CNT-based nano-electromechanical systems, researchers should consider the size-dependent theories such as the theorem used in this paper. In addition, the influences of different dimensions on the pull-in voltages are studied in detail. The results proved that longer CNTs with smaller diameters possess lower pull-in voltages than shorter ones with larger diameters.