Static analysis for MEMS switch consisting of a fixed-fixed beam with the effect of temperature

Abstract

A two dimensional static model for analyzing the MEMS switch consisting of a fixed-fixed beam is presented,with which the effect of temperature is considered.This model is used to analyze the deflection of the fixed-fixed beam sub-jected to both the electrostatic forces and the temperature change.In the analysis the deflection of the beam is divided into three stages: A fixed-fixed beam subjected to both the elec-trostatic forces and temperature change without any constrain at the center;The second is the beam with another more constrain at the center,as a result,the beam is subjected to a concentrated force at the center besides the electrostatic force and tempera-ture change at this stage;The third is a beam subjected to the electrostatic forces,temperature change,and a concentrated force with a given deflection and a zero angle of rotation over the central part of the beam.The concentrated force at the sec-ond stage,and the concentrated force and its position at the third stage are related with the applied voltage and the tem-perature change.In addition,the governing equation for the bending of a beam with order four is converted into the four differential equations with order one and with partial unknown boundary conditions.In the examples,some results are given including the effect of temperature on the pull-in voltage,the deflection of the beam at different stages,the capacitance of the beam at the third stage,the effect of length and thickness of the beam on the pull-in voltage at different temperature changes,and so on,from which some beneficial conclusions can be drawn.