On pull-in instabilities of microcantilevers

In this paper the static deflection and pull-in instability of electrostatically actuated microcantilevers is investigated based on the strain gradient theory. The equation of motion and boundary conditions are derived using Hamilton’s principle and solved numerically. It is shown that the strain gradient theory predicts size dependent normalized static deflection and pull-in voltage for the microbeam while according to the classical theory the normalized behavior of the microbeam is independent of its size. The results of strain gradient theory are compared with those of classical and modified couple stress theories and also experimental observations. According to this comparison, the classical theory underestimates the stiffness of the microbeam and there is a gap between the results predicted by the classical theory and those observed in experiment. It is demonstrated that this gap can be reduced when utilizing the strain gradient theory.