Dynamics of MEMS resonators under superharmonic and subharmonic excitations

We present an analysis and simulations for the dynamics of electrically actuated microbeams under secondary resonance excitations. The presented model and methodology enable simulation of the transient and steady-state dynamics of microbeams undergoing small or large motions. The microbeams are excited by a dc electrostatic force and an ac harmonic force with a frequency tuned near twice their fundamental natural frequencies (subharmonic excitation of order one-half) or half their fundamental natural frequencies (superharmonic excitation of order two). In the case of superharmonic excitation, we present results showing the effect of varying the dc bias, the damping and the ac excitation amplitude on the frequency-response curves. In the case of subharmonic excitation, we show that, once the subharmonic resonance is activated, all frequency-response curves reach pull-in, regardless of the magnitude of the ac forcing. We conclude that the quality factor has a limited influence on the frequency response in this case. This result and the fact that the frequency-response curves have very steep passband-to-stopband transitions make the combination of a dc voltage and a subharmonic excitation of order one-half a promising candidate for designing improved high-sensitive RF MEMS filters. For both excitation methods, we show that the dynamic pull-in instability can occur at an electric load much lower than a purely dc voltage and of the same order of magnitude as that in the case of primary-resonance excitation.