The analysis and model formulation of a coupled micro-probe and elastic thin plate subjected to electrostatic force

• Analytical solution of coupled probe-plate system subjected to the ac and dc voltages is presented.
• The coupled mechanism of system depends significantly on the interacting position and the dc voltage but slightly on ac voltage.
• For small interaction distance or large dc voltage, the coupled frequencies are significantly different to those of independent probe and plate.
• The higher the ratio of beam-plate bending rigidities is, the smaller the pull-in voltage is.

The mathematical model of coupled probe-plate system subjected to the ac and dc voltages is constructed. Among that, the coupled interacting force between probe and plate is the electrostatic force due to the ac and dc voltages, and the coupled displacements of beam and plate occur simultaneously. It is different to the conventional micro-/nano-actuator which is constructed by two independent fixed/mobile conducting electrodes. It is worth noting that the pull-in phenomenon of the coupled system subjected to the dc voltage only is discovered as a significant difference with respect to the conventional one. In this study, the analytical method for the coupled vibration is presented; the suitability of the conventional perturbation method is investigated; the relationship between the coupled frequencies of the system and the frequencies of the probe and plate is also found. This relationship is defined as the coupled characteristic phenomenon here.