STATIC INSTABILITY ANALYSIS OF A NONLINEAR MICROSWITCH CONSIDERING MODIFIED COUPLE STRESS THEORY

Microelectromechanical systems (MEMS) are used in many elds of industry like automotive, aerospace and medical instruments. Among the various ways to operate the MEMS devices, the electrostatic actuator is the common mechanism, due to simplicity and fast response. Previous experiments have shown that the mechanical behavior of devices, which their sizes are in order of micron and submicron, are dependent to size dependency. They also have illustrated that by decreasing the dimension of structures, the size dependent eect is highlighted. In this case, the classical theories are not capable to predict the size dependent eects and mechanical behavior of the microstructures properly. Therefore, nonclassical theories such as modied couple stress and strain gradient theories have been introduced. It was shown that the modied couple stress theory can accurately predict the size dependent behavior of microstructures. There are some in uences observed in the MEMS, that they have notable eects on the mechanical behavior of microswitches, such as fringing elds and large de- ection. When the air gap is larger than the electrode's width of microswitches, the impacts of fringing elds and geometric nonlinearity signicantly aect the mechanical behavior of the system. Therefore, neglecting the abovementioned eects leads to errors in the instability prediction of microswitches. Most of microswitches consist of a microcantilever with a proof mass and a xed substrate which there is an air gap between them. By applying voltage to the system, the microcantilever starts to de ect into the xed substrate. In this paper, pull-in instability and de ection of MEMS switches are investigated based on the size dependent model. The nonlinear model is introduced by considering modied couple stress theory and fringing eld eects as well as geometric nonlinearity. Utilizing the minimum total potential energy principle, the static equation of motion is derived in framework of the nonclassical theory. The eects of various parameters on static pull-in instability are studied and errors of considering the linear model or classical theories is calculated. The results show that the presented model is capable to predict the displacement and pull-in instability of the microswitches.