Nonlinear behavior for nanoscale electrostatic actuators with Casimir force

The influence of Casimir force on the nonlinear behavior of nanoscale electrostatic actuators is studied in this paper. A one degree of freedom mass-spring model is adopted and the bifurcation properties of the actuators are obtained. With the change of the geometrical dimensions, the number of equilibrium point varies from zero to two. Stability analysis shows that one equilibrium point is Hopf point and the other is unstable saddle point when there are two equilibrium points. We also obtain the phase portraits, in which the periodic orbits exist around the Hopf point, and a homoclinic orbit passes through the unstable saddle point.