考虑温度效应的两端固支微机电开关梁静力分析

STATIC ANALYSIS FOR MEMS SWITCH CONSISTING OF A FIXED-FIXED BEAM WITH THE EFFECT OF TEMPERATURE

建立考虑温度效应的二维两端固支微机电开关梁静力变形分析模型,利用该模型分析温度变化引起的失稳问题,并利用该模型对两端固支微开关梁受电场力和温度作用下的受力变形进行分析。分析过程分为三个阶段:梁受电场力和温度变化作用,而在梁中点不受任何约束的变形阶段;除受电场力和温度变化作用外,梁中点变形受约束,因而梁中点受支反力作用的变形阶段;梁受电场力、温度变化以及支反力作用,并且在梁的中间一段具有指定挠度和转角的变形阶段。第二阶段中支反力的大小以及第三阶段中支反力的大小和位置都同驱动电压和温度变化有关。在实例中,给出部分计算结果,包括:温度变化对不同阶段梁受力变形的影响、对吸合电压的影响、对微开关电容的影响,以及不同温度变化下梁长对吸合电压的影响和不同温度变化下梁高对吸合电压的影响等,从中可以看出温度变化的作用及考虑温度效应的必要性。

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 subjected 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 electrostatic 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 temperature 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 second stage, and the concentrated force and its position at the third stage are related with the applied voltage and the temperature 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.