Pull-in instability of electrostatic doubly clamped nano actuators: Introduction of a balanced liquid layer (BLL)

In this paper, the effect of a liquid layer, water, underneath an electrostatic nano actuator on the pull-in instability of actuator is investigated. A continuum model is employed to obtain the non-linear constitutive equation of the nano actuator and the applied forces. The governing differential equation of the actuator is forth order and highly non-linear. Hence, the modified Adomian decomposition method (MADM) is utilized to obtain an analytical solution for bucking and pull-in instability of the actuator. The results of analytical solution were compared with results of a numerical method, and they were found in good agreement. It is found that the voltage, Casimir and liquid layer parameters are the most significant parameters which affect the pull-in instability of the actuator. Interestingly, the outcomes show that there is a distinct liquid layer parameter in which the variation of the Casimir parameter does not have a significant influence on the values of maximum deflection, internal stress and bending moment of the nano actuators at the onset of pull-in instability. We introduced this value of liquid layer parameters as Balance Liquid Layer (BLL) value because of its unique effect on the maximum deflection, internal stress and bending moment of the nano actuators. The BLL value is of interest for design of NEMS actuators.