Parametric resonance threshold regulation based on electrothermal effect

Parametric resonance, with its remarkable signal amplification capabilities, holds great potential in areas such as sensing, warning detection, and energy harvesting. However, its practical applications are limited by the high excitation threshold required to trigger parametric resonance and the narrow instability region in which it occurs. To address this limitation, this paper presents a method for tuning the parametric resonance threshold in micro-resonators based on the electrothermal effect. The nonlinear dynamic model for a parametric excited micro-resonator is established. Theoretical analysis is conducted to reveal the influence of frequency and damping on the parametric instability region, which indicates that reducing the vibration frequency can decrease the parametric instability threshold while expanding the parametric instability region. Subsequently, the electrothermal current is applied to the body of the micro-resonator. The influence of the electrothermal effect on the dynamic behavior of the resonator is investigated. It is observed that the vibration frequency could be reduced from 125 kHz to 25 kHz, and the rate of frequency change accelerates under high current condition. Finally, the electrothermal effect is used to regulate both the threshold and bandwidth of the parametric instability region. Experimental results demonstrate that, under frequency-sensitive conditions, the electrothermal effect effectively reduces the threshold by 71% and broadens the instability region's bandwidth. This study is expected to provide technical support for the practical applications of parametric resonance.