Size Dependent Pull-in Phenomena in Electro-statically Actuated Micro-beam Based on the Modified Couple Stress Theory

A modified continuum model of electro-statically actuated micro-beam is presented based on the modified couple stress theory. The new model contains a material length scale parameter and can capture the size effect, unlike the classical Bernoulli-Euler beam theory. The governing equation of the micro-beam is derived based on the Hamilton's principle, which accounts for the effects of the moderately large deflection, the residual stress and the fringing electrostatic field. The numerical analysis of mechanical characterization is performed by the Analog Equation Method (AEM). The effects of the couple stress on the static and dynamic responses, pull-in voltage and pull-in time are discussed.