Sensors & Transducers (Apr 2014)
Analysis to Effect of Non-linear Axial Force on the MEMS Clamped-clamped Switch Beam
Abstract
The effect of non-linear axial force, which is caused by both temperature change of environment and the length change of the beam, on the behavior of the switch is quite heavy because of the larger slenderness ratio of the MEMS clamped-clamped switch beams. By using the 1D beam model, the behaviors of electrostatic MEMS clamped-clamped switch beams with both the temperature change and the length change for three different stages were studied. In the paper, the governing equation of the elastic curve of the beam with the effect of non-linear axial force in the beam was given. A three-fold method of bisection was used to solve the unknown axial force in the governing equation, applied voltage and one boundary condition of the beam. On obtaining the axial force, the applied voltage and the boundary condition, the deflections at any cross-section could be obtained easily by using the numerical method to the ordinary differential equation. Incorporating the numerical method to the ordinary differential equation with some optimization method, pull-in voltage and the corresponding deflection could be distinguished and obtained automatically on a computer with the specifically designed program. In examples, the entire mechanical behavior of the MEMS clamped- clamped switch beam over the operational voltage ranges was investigated and the effects of the axial force on pull-in voltage at several temperature changes with different geometry dimensions of the beam were studied.
