Aplication of the generalized differential quadrature method to the study of pull-in phenomena of MEMS switches

Abstract

This paper reports on the pull-in behavior of nonlinear microelectromechanical coupled systems. The generalized differential quadrature method has been used as a high-order approximation to discretize the governing nonlinear integro-differential equation, yielding more accurate results with a considerably smaller number of grid points. Various electrostatically actuated microstructures such as cantilever beam-type and fixed-fixed beam-type microelectromechanical systems (MEMS) switches are studied. The proposed models capture the following effects: 1) the intrinsic residual stress from fabrication processes; 2) the fringing effects of the electrical field; and 3) the nonlinear stiffening or axial stress due to beam stretching. The effects of important parameters on the mechanical performance have been studied in detail. These results are expected to be useful in the optimum design of MEMS switches or other actuators. Further, the results obtained are summarized and compared with other existing empirical and analytical models.

Index Terms-Electromechanical coupled system, generalized differential quadrature method (GDQM), microelectromechanical systems (MEMS) switch, pull-in voltage.