Finite Element Modeling of Timoshenko Micro-beam Based MEMS Sensor Behavior against Variation in Poisson’s Ratio

Abstract

Epoxy Micro-beams are used in microelectromechanical systems (MEMS) for sensoring applications in two operating mode of deflection and resonant frequency shift. One of the main questions in micro-beam based MEMS sensors behavior is effect of Poisson’s ratio on the deflection and resonant frequency of the micro-beam. In this study, two epoxy Timoshenko microbeams with different dimensions were modeled based on the finite element method considering the effects of variation in Poisson’s ratio. The results of this analysis indicated that change in the Poisson’s ratio of the microbeams does not significantly affect the deflection and resonant frequency. Therefore, in the design of the microbeam based microelectromechanical systems where Poisson’s ratio is one of the system variables, the FEM analysis ensures that changes in the environmental conditions affecting Poisson’s ratio would not affect the system outputs. There was a good agreement between the results of this study and those obtained based on the strain gradient elasticity theory, classical theory, and the couple stress theory.