Resonant frequency analysis on an electrostatically actuated microplate under uniform hydrostatic pressure

The resonant frequency of a microplate is influenced by various physical parameters such as mass, surface stress, hydrostatic pressure and electrostatic force. In this paper, the effects of both electrostatic force and uniform hydrostatic pressure on the resonant frequency of a clamped circular microplate are investigated. An approximate solution is derived for the fundamental resonance frequency of the mciroplate under both types of loads using an energy equivalent method. It is found that both electrostatic force and uniform hydrostatic pressure decrease the resonant frequency of the microplate under small deflections. Additionally, the linearized expression of this solution shows that the resonant frequency varies linearly with pressure in the low and ultra-low range, and the corresponding pressure sensitivity depends on the voltage applied to the microplate. The analytical results are well validated by the finite element method. This study may be helpful for the design and optimization of electrostatically actuated resonance devices based on microplates, especially electrostatically actuated low- or ultra-low-pressure sensors.