The static and dynamic behavior of MEMS arches under electrostatic actuation

In this paper, we investigate the static and dynamic behavior of electrostatically actuated clamped-clamped micromachined arches. The Galerkin method is used to discretize the distributed-parameter model of the considered shallow arch, and thus approximate it by a set of nonlinear algebraic equations and ordinary-differential equations describing its statics and dynamics. Five symmetric mode shapes of either a straight beam or a deformed arch is found to be sufficient to simulate the static and dynamic behavior of the arch. The natural frequencies and mode shapes of the arch are calculated for various values of DC voltages and initial rises of the arch. The forced vibration response of the arch to a combined DC and AC harmonic load is determined when excited near its fundamental natural frequency. The results show various nonlinear behaviors, such as hysteresis, softening behavior, and dynamic pull-in. Several scenarios of snap-through and pull-in are shown, which found depend on the initial rise of the arch.