The Effect of Startup Parameters on the Operation of Microelectromechanical Systems

The study results of the operation features of two-electrode microelectromechanical systems (MEMS) with changing of in-terelectrode gap during startup, taking into account the constant force and electromechanical coupling in a nonlinear approximation for the elastic and electrostatic forces, are presented. It is shown that the operation of such MEMS is significantly affected not only by the initial state and parameters of the system, but also by the rate of the supplied electrical voltage changing. Analytical expressions have been found which make it possible to determine the range of parameters of the normalized stiffness в and the normalized force F, for which, in the case of a quasi-static change of the applied potential difference, unstable equilibrium points will be observed on the dependences of the movable electrode relative displacement z versus the normalized voltage λ. For the case when the MEMS is excited by a voltage surge in the form of a step, analytical expressions have been derived that allow, for arbitrary system parameters, to obtain separatrices limiting the areas of initial conditions, for which periodic self-oscillations will be established in the system. Analytical expressions are obtained for calculating the magnitude of such self-oscillations. For zero initial conditions, it is shown that at F > -0,5 the self-oscillations will be concentrated at positive displacements of the movable electrode. It was found that with a decrease of F from F > 0 to F = -0,5, the range of self-oscillations will decrease, and with a further decrease of F, the range of self-oscillations will begin to increase, but already in the region of negative displacements of the movable electrode.