Resonators
Nonlinearity issues
Resonating beams can exhibit hardening due to large displacements and/or softening due to parallel plate actuation.
Electrostatically actuated beam resonator
We developed analytical and numerical methods to predict such behaviours.
Frequency curves of a beam resonator exhibiting hard spring, soft spring and linear behaviours
Non linear softening behavior due to electrostatic actuation can also appear in torsional resonators. The following figure shows the comparison between experimental results and numerical simulations for a torsional resonator constituted by a square mass suspended by folded springs which tilts out-of-plane; the soft spring effect increases with voltage.
(a) Torsional resonator (b) frequency curves for increasing actuation voltage, experimental data (solid lines) and model prediction (dotted lines).