Mechanical response of the isolated cantilever with a floating potential in steady electrostatic field

Isolated micro structure, which is not directly connected to the electric circuit, can be excited into sustainable oscillation in steady electrostatic field. However, the underlying mechanism of the electrostatically self-excited oscillation is still unclear. In this work, the mechanical response of an isolated cantilever with a floating potential in steady electrostatic field is investigated. The electrically neutral cantilever is fixed to an insulating base and placed between positive and negative parallel electrodes. When a DC bias voltage is applied to the electrodes, the cantilever is observed to bend towards the positive electrode to initiate sustainable oscillation. Considering the electrostatic force applied on the cantilever is determined by the polarity and amount of electric charge, the mechanical response of the cantilever is investigated by analyzing the charge distribution on the cantilever. To explain the starting direction of the oscillation, an indirectly grounded theory is proposed with experimental validations. The free end of the cantilever carries initial negative charge due to the equivalent capacitor between the earth and the fixed end of the cantilever. Based on the oscillation mechanism, a theoretical model is developed by analyzing the equivalent capacitance of the system. The amount of charge carried by the cantilever and the corresponding electrostatic force are quantitatively analyzed to characterize of the onset DC bias voltage. Besides, the dynamic response of the cantilever during oscillation is also investigated by looking into the transferred charge by the cantilever. The modeling and test results lead to a comprehensive understanding of the electrostatic oscillator for the application in the field of micro actuation system.