Local nonlinear dynamics of MEMS arches actuated by fringing-field electrostatic actuation

The nonlinear dynamic behavior of a resonant MEMS arch microbeam actuated by fringing electric actuation is investigated in this paper. The arch microbeam is loaded with DC and AC harmonic electric load and the ground electrodes placed at either side of the beam. The curvature caused imbalance distribution of field lines and results in a resultant force. Euler–Bernoulli beam equation was used in accordance with the shallow beam theory to get the equation of motion. Method of multiple scales (MMS) perturbation technique was used to perturb the beam near the fundamental frequency of the microbeam to study its resonant behavior in the local vicinity of the considered frequency. Different midpoint elevations were investigated to study the effect of curvature on the resonance frequency of the beam. The MMS reveals that a beam with low initial midpoint elevation shows initially a softening behavior for small DC voltage excitation. Then, the beam undergoes a hardening when the DC voltage is increased. Finally, the beam returns back to softening behavior when the DC load is further increased to higher values with a curling in the frequency response graph. When the midpoint elevation is increased, the beam is known to undergo symmetry breaking when the DC load is increased before regaining symmetry at even further higher DC load. The MMS shows that there is softening behavior in the initial region prior to symmetry breaking. The effective nonlinearity even drops further to more negative values making the beam more softened in the region of symmetry breaking. After the beam regains symmetry, the effective nonlinearity experiences a more significant drop now causing the beam to be highly softened in this region of high DC load.