Nonlinear dynamics of mems arches

In this paper, the dynamic response of electrostatically actuated clamped-clamped arch microbeam is investigated when excited by a DC load superimposed to an AC harmonic load. The dynamic analysis is carried out using a Galerkin-based reduced order model along with a shooting technique to find periodic motions and analyzing its stability using a Floquet theory. Results are presented for the cases of primary and super harmonic resonances. We found several nonlinear dynamic phenomena due to the inherent nonlinear electrostatic force and geometric nonlinearity of the arch. These include frequency-amplitude dependence, jumps, tangent bifurcations, coexistence of solutions, and softening and hardening behaviors. The shooting technique showed high robustness in capturing both the stable and unstable states of the system. Hence, it helped clarify vague behaviors that were previously reported using longtime integration of the equations of motion.