Nonlinear vibrations and chaos in electrostatic torsional actuators

Electrostatic torsional micro-mirrors have wide spread use in different industries for diverse purposes. This paper investigates the development of superharmonics and chaotic responses in electrostatic torsional micro-mirrors near the pull-in condition. Appearance of nonlinear phenomena is investigated in models accounting for and disregarding the coupling of torsional and flexural deflections. Analysis of the system response to step and harmonic excitation reveals the appearance of DC and AC symmetry breaking. Increasing the amplitude of harmonic excitation, the response in the form of distinct superharmonics changes to a broad band response, where there is loss of periodicity and the response becomes chaotic. Accounting for flexural deflections in coupled model reduces the voltage thresholds corresponding to symmetry breaking and chaotic responses. It is also shown that damping has a regularizing effect and introduction of damping changes the chaotic undamped response into quasi-periodic one.