Reduction of settling time by multi-frequency pulsed parametric excitation

Introducing a time-periodicity into a system parameter leads to parametric excitation, which in general, may cause a parametric resonance with exponentially increased vibration. Applying a parametric excitation but carefully tuning its frequencies to multiple parametric anti-resonance frequencies is investigated here. The parametric excitation here is realized by an open-loop control at the system boundary that allows for an energy flow into or from the system. A parametric anti-resonance successfully triggers an energy transfer between specific vibration modes of the system and occurs in systems with at least two degrees of freedom. Such an energy transfer increases the overall dissipation of kinetic energy of a lightly damped system. This contribution presents an approach to accelerate the mitigation of transient vibrations by applying a multi-frequency parametric excitation with two or more parametric anti-resonance frequencies. The potential application in a MEMS sensor arrangement consisting of two and more coupled flexible beams exemplifies the method. Starting from the minimum system with two degrees of freedom, the averaging method is applied to analyze the transient slow flow, leading to an analytical approximation of the transition time response of a pulsed multi-frequency parametric excitation system. For a specific example, a reduction of 96.7% of the transient vibrations is achievable.