Effects of the molecular forces on the free vibration of electromechanical integrated electrostatic harmonic actuator

Abstract

► The dynamic equations of an electrostatic actuator under three situations are deduced. ► Effects of van der Waals force or Casimir force on the natural frequencies are investigated. ► Effects of van der Waals force or Casimir force on vibrating modes are studied. ► When the molecular forces are considered, the natural frequency drops. ► Molecular forces have obvious effects on the modes under certain condition. The electromechanical integrated electrostatic harmonic actuator is favorable for miniaturization of the electromechanical devices. As the dimensions of the actuator decreases, the effects of the Casimir or van der Waals forces should be considered. Here, effects of the molecular forces on the free vibration of the actuator are investigated. The dynamic equations of the flexible ring for the actuator for three different situations are deduced. The three situations are: (i) only considering electrostatic force; (ii) considering electrostatic force and van der Waals force simultaneously; (iii) considering electrostatic force and the Casimir force simultaneously. Using these equations, the effects of the van der Waals force or the Casimir force on the natural frequencies and the vibrating modes of the flexible ring for the actuator are investigated. Results show: for high order modes, the effects of the van der Waals force and the Casimir force on the actuator are relatively large for mode one. The effects are more obvious and should be considered for small clearance, and large operating voltage. For clearance = 0.2 μm, the relative errors between natural frequencies with and without van der Waals force gets to 9.9%, and the relative errors with and without the Casimir force is 13.1%. Besides it, the vibrating amplitudes of the flexible ring become larger when the molecular forces are considered. The results are useful in theory and technique studies on further miniaturization of the actuator.