Surface and Thermal Effects on the Pull-In Behavior of Doubly-Clamped Graphene Nanoribbons Under Electrostatic and Casimir Loads

Abstract

In this study, a comprehensive analytical model is established based on Euler–Bernoulli beam theory with von Kármán geometric nonlinearity to investigate the effect of residual surface tension, surface elasticity, and temperature on the static pull-in voltages of multilayer graphene nanoribbon (MLGNR) doubly-clamped beams under electrostatic and Casimir forces and axial residual stress. An explicit closed-form analytical solution to the governing fourth-order nonlinear differential equation of variable coefficients is presented for the static pull-in behavior of electrostatic nanoactuators using a Fredholm integral equation of the first kind. The high accuracy of the present analytical model is validated for some special cases through comparison with other existing numerical, analytical, and experimental models. The effects of the number of graphene nanoribbons (GNRs), temperature, surface tension, and surface elasticity on the pull-in voltage and displacement of MLGNR electrostatic nanoactuaotrs are investigated. Results indicate that the thermal effect on the pull-in voltage is significant especially when a smaller number of GNRs are used. It is found that the surface effects become more dominant as the number of GNRs decreases. It is also demonstrated that the residual surface tension exerts a greater influence on the pull-in voltage in comparison with the surface elasticity.