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 Kأ،rmأ،n geometric nonlinearity to investigate the effect of residual surface tension, surface elasticity, and temperature on the static pullin voltages of multilayer graphene nanoribbon (MLGNR) doublyclamped beams under electrostatic and Casimir forces and axial residual stress. An explicit closedform analytical solution to the governing fourthorder nonlinear differential equation of variable coefficients is presented for the static pullin 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 pullin voltage and displacement of MLGNR electrostatic nanoactuaotrs are investigated. Results indicate that the thermal effect on the pullin 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 pullin voltage in comparison with the surface elasticity.