Numerical analysis on snapping induced by electromechanical interaction of shuffling actuator with nonlinear plate

摘要

When a voltage is applied between two electrodes consisting of a rigid ground and a deformable rectangular plate that has two parallel free edges, and one movable edge and one fixed edge, the plate bends under the electrostatic force generated in it. Accompanying to the bending deformation, the movable edge of the plate results in some displacement along the movable direction, which is the main clue of the MEMS actuator of shuffling movement. As the control voltage is applied up to a critical value, the phenomenon of snapping occurs at the plate electrode under the interaction of electromechanical coupling such that the shuffling displacement is obtained as possibly as large. Based on the nonlinear theory of plates with the von Karman's type deformation and the electrostatic theory, a theoretical analysis for the snapping behavior is quantitatively displayed in this paper. For this purpose, a numerical code is proposed by associating the increment finite element methods for deformation with the moment method for electrostatic fields as well as the arc-length control approach in the quantitative calculations. The numerical results for some case studies show that the path of bending deformation from stability into instability passing through the snapping criterion can be tracked well by this numerical code, while the characteristic curves of the maximum deflection in the plate and the shuffling displacement versus the control voltage, which are mainly concerned in the design of the MEMS shuffling actuator, are obtained additionally.