The influence of the intermolecular surface forces on the static deflection and pull-in instability of the micro/nano cantilever gyroscopes

In this paper, the effects of van der Waals and Casimir forces on the static deflection and pull-in instability of a micro/nano cantilever gyroscope with proof mass at its end are investigated. The micro/nano gyroscope is subjected to coupled bending motions which are related by base rotation and nonlinearities due to the geometry and the inertial terms. It is actuated and detected by capacitance plates which are placed on the proof mass. The extended Hamilton principle is used to find the equations governing the static behavior of the clamp-free micro/nano gyroscopes under electrostatic, Casimir and van der Waals forces. The equations of static motion are discritized by Galerkin’s decomposition method. The nonlinear equilibrium equations are solved analytically using homotopy perturbation method (HPM). The static response of the micro/nano gyroscopes to variations in the DC voltage across the drive and sense electrodes is obtained and the effects of different parameters on pull-in instability are investigated. The presented results can be used for accurate estimations of the instability and performance of the micro/nano gyroscopes.