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

► 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.