Effect of Initial Conditions on the Behavior of Two-Electrode MEMS with Variable

The influence of initial conditions on the behavior of two-electrode microelectromechanical systems (MEMS) having parallel-plate and comb structures with variable interelectrode gap is studied and analyzed here within a nonlinear approach. It has been revealed that the two-electrode MEMS operation is considerably influenced not only by the initial conditions and the system characteristics, but also the speed of the applied electrical voltage change. It has been established that during slow change of the applied voltage the constant force along with the nonlinear restoring force can lead to emergence of the second unstable equilibrium point on the dependences of the movable electrode displacement versus the applied voltage. As a result, when the applied voltage reverses a hysteresis can occur in the system. It is shown that due to the optimal use of the constant force in MEMS with the nonlinear dependence of the restoring force versus the movable electrode displacement, the capacitance modulation depth and the relative range of the controlled capacitance change can be increased by several times in comparison with MEMS having the linear dependence of the restoring force. Analytical formulas have been obtained to get separatrices defining the set of initial conditions for which periodic oscillations are observed in case of MEMS excitation using a voltage step. It is demonstrated that for MEMS with the comb structure of electrodes where not only the fixed, but also the movable electrode is split, the pull-in voltage decreases when the number of the split electrode components increases.