This paper contends to be the first to report the experimental observation of up to 28 orders of parametric resonance, which has thus far only been envisioned in the theoretical realm. While theory has long predicted the onset of n orders of parametric resonance, previously reported experimental observations have been limited up to about the first 5 orders. This is due to the rapid narrowing nature of the frequency bandwidth of the higher instability intervals, making practical accessibility increasingly more difficult. Here, the authors have experimentally confirmed up to 28 orders of parametric resonance in a micromachined membrane resonator when electrically undamped. While the implication of this finding spans across the vibration dynamics and transducer application spectrum, the particular significance of this work is to broaden the accumulative operational frequency bandwidth of vibration energy harvesting for enabling self-powered microsystems. Up to 5 orders were recorded when driven at 1.0 g of acceleration across a matched load of 70 kΩ. With a natural frequency of 980 Hz, the fundamental mode direct resonance had a −3 dB bandwidth of 55 Hz, in contrast to the 314 Hz for the first order parametric resonance; furthermore, the half power bands of all 5 orders accumulated to 478 Hz.
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Jia, Y., Du, S., & Seshia, A. A. (2016). Twenty-Eight Orders of Parametric Resonance in a Microelectromechanical Device for Multi-band Vibration Energy Harvesting. Scientific Reports, 6, . https://doi.org/10.1038/srep30167