Study On the Size Dependent Behavior of a Micro-beam Subjected to a Nonlinear Electrostatic Pressure

Size dependent behavior of materials appears for a structure when the characteristic size such as thickness or diameter is close to its internal length-scale parameter. In these cases, ignoring this behavior in modeling may leads to incorrect results. In this paper, strong effects of the size dependence on the static and dynamic behavior of the electrostatically actuated micro-beams have been studied. The equilibrium positions or fixed points of the gold and nickel micro-beams have been determined and shown that for a given DC voltage, there is a considerable difference between the fixed points gained using the classic beam theory and the modified couple stress theory. In addition, it has been shown that the static and dynamic pull-in voltages gained using the couple stress theory are several times higher than those gained using the classic beam theory. Some previous studies have applied the classic beam theory in their models and introduced a considerable hypothetical value of residual stress to match their experimental and incorrect theoretical results. It has been shown that using the modified couple stress theory decreases considerably the difference with the experimental results.