Symmetry Breaking and Multistability of Electrostatically Actuated Annular Microplates

The article investigates the nonlinear problem of statics of a hollow circular microplate in the electrostatic field of two electrodes. Using the assumptions of the geometrically nonlinear Karman model, partial differential equilibrium equations for the system are obtained. The branch points of nontrivial axisymmetric and skew-symmetric forms of equilibrium are analytically rigorously found. It is noted that at certain ratios between the internal and external radii of the plate, the lowest form of buckling is the skew-symmetric form with the lowest circumferential variability. Using the Galerkin projection method and numerical methods of the theory of bifurcations, branching diagrams of both axisymmetric and skew-symmetric equilibrium positions of the plate in the space of key parameters of the system are found. It is shown that at certain relationships between the thickness of the plate and the interelectrode gap, multistability is observed in the system—the existence of two or more non-trivial stable forms of equilibrium that are symmetrical relative to the plane of the plate. A qualitative (parametric) analysis of the found areas of multistability is performed. The possibility of a plate jumping from one stable equilibrium position to another, controlled by an electrostatic field, is indicated. The discovered effect can be used to develop high-precision microelectromechanical sensors of limiting values of various physical quantities, the output signal of which is an abrupt change in the amplitude of the static deflection of the sensitive element of the proposed configuration measured by a capacitive sensor.