Dynamics of MEMS Arches of Flexible Supports

We present an investigation into the dynamics of microelectromechanical systems (MEMS) arches when actuated electrically including the effect of their flexible supports. Using a shallow-arch model with rotational and transversal springs at its boundaries, a reduced-order model is developed. Shooting technique is utilized to find periodic motions. The stability of the captured periodic motion is examined using the Floquet theory. Simulation results are shown for the forced-vibration response of an arch when excited by a dc electrostatic force superimposed to an ac harmonic load. The results show softening behavior and several jumps in the response during snap-through motion and pull-in. It is demonstrated that nonideal boundary conditions can have significant effect on the qualitative dynamical behavior of the MEMS arch. This may include lowering its natural frequencies from the expected range of operation and causing unpredictable snap through or dynamic pull-in. Simulation results are compared to experimental data obtained for an imperfect microfabricated clamped-clamped beam with initial curvature actuated electrically for the cases of primary and superharmonic resonances.