Pull-in behavior of electrostatically actuated stepped microbeams

The stepped microbeams are typical low stiffness structures widely used in MEMS devices. Approximated solutions of the natural frequency and the pull-in voltage of stepped microbeams, including clamped-free (CF) and clamped clamped (CC) boundary conditions are developed, and the unique pull-in behavior of the stepped microbeams is investigated. The stepped microbeam is viewed as a beam with a rectangular electrode pad at its tip for CF beam and at its center for CC beam. The motion equations are deduced based on the Euler Bernoulli beam and the modified couple stress theory. The natural frequency and the pull-in voltage are extracted with a one-degree-of-freedom model. The present model correctness is validated by comparing with the finite element results, and the effect of the length ratio of the electrode pad to the beam and the width ratio of the beam to the electrode pad are discussed. The results show that both the natural frequency and the pull-in voltage monotonously increase with the increase of the width ratio, and first decrease and then increase with the increase of the length ratio. The minimum value of them does not appear at the same time, but is determined by the width ratio. The results can be used to design and improve the performance of MEMS devices.