The dynamic response of electrostatically driven resonators under mechanical shock

This paper presents a theoretical and experimental investigation of the response of electrostatically actuated parallel-plate resonators when subjected to mechanical shock. Resonators are commonly employed in resonant sensors, where they are operated at low pressure for enhanced sensitivity making their response to external disturbances such as shock a critical issue. A single-degree-of-freedom system is used to model a resonator, which is electrostatically driven by a dc load superimposed to an ac harmonic load. Simulation results are demonstrated in a series of shock spectra that help indicate the combined influence of shock, dc and ac loads. The effect of the shock duration coinciding with the ac harmonic frequency is investigated. It is concluded that accounting for electrostatic forces, especially the ac load, is crucial when addressing the reliability and performance of resonators against shock. It is found that for specific shock and ac excitation conditions, a resonator may experience early dynamic pull-in instability. Experimental work has been conducted on a capacitive sensor to verify the obtained theoretical results. The sensor is mounted on top of a small shaker and then both are placed inside a vacuum chamber. Acceleration pulses were applied on the sensor while powered by dc and ac loads. The response of the device was monitored using a laser-Doppler vibrometer. The experimental data were compared to the theoretical results and were found to be in good agreement.