A MEMS Implementation of the Classic Meissner Parametric Resonator: Exploring High-Order Windows of Unbounded Response

In recent years, increasing attention is given to parametric resonators, in which an unbounded response may be induced by periodically modulating one of the system parameters. Parametric resonators with a single degree of freedom have many windows of unbounded response in which the response frequency is different from the modulation frequency. This difference between input and output frequencies may be relevant to sensing applications. In this paper, we explore the solution map of the Meissner parametric resonator, and we experimentally characterize odd-ordered windows of unbounded response, up to the 15th window. Another interesting feature of the Meissner resonator is discrete crossover points in which an unbounded response is possible at distinct modulation frequencies and distinct modulation amplitudes. In this paper, we experimentally characterize one such crossover point. Our parametric resonator is based on an electrostatic anti-spring, which allows to modulate stiffness that is otherwise unaffected by motion. This is in contrast to many previous experimental studies in which the modulated stiffness was affected by motion and thus included unwanted nonlinear effects.