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 integrodifferential 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.[ 2006-0101]Index Terms-Electromechanical coupled system, generalized differential quadrature method (GDQM), microelectromechanical systems (MEMS) switch, pull-in voltage.

In this paper, a novel method has been developed to control the pull-in voltage of the fixedfixed and cantilever MEM actuators and measure the residual stress in the fixed-fixed model using of the piezoelectric layers that have been located on the upper and lower surfaces of actuator. In the developed model, the tensile or compressive residual stresses, fringingfield and axial stress effects in the fixed-fixed end type micro-electro-mechanical systems actuator have been considered. The non-linear governing differential equations of the MEM actuators have been derived by considering the piezoelectric layers and mentioned effects. The results show that due to different applied voltage to the piezoelectric layers, the pull-in voltage can be controlled and in the fixed-fixed type the unknown value of the residual stress can be obtained.

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