Transient Vibrations Suppression in Parametrically Excited Resonators

Micromechanical resonators with a high-quality factor have been studied in recent years due to their excellent performance and potential applications. Some of these micromechanical resonators describe a long settling time, which can be disabled for fast switching applications. A novel design reduces the settling time by coupling two micromechanical resonators with parametric excitation; the parametric excitation tuned at the anti-resonant frequency increases the damping into the system; thus, the responses vibrations are attenuated, and the settling time is minimized. The scheme can be classified as open-loop control and belongs to the vibrational control field. Through a mathematical approach, this article describes this phenomenon in detail; by the averaging technique, the parametric excitation effects are analyzed. Moreover, we give new analytic conditions and formulas to minimize the settling time; these formulas might be helpful for future experimentation. Finally, using the current analysis, this contribution proposes a methodology to suppress the transient vibrations in this class of systems.