Bistability and simultaneous mode actuation in electrostatically actuated initially curved coupled micro beams

Abstract

The symmetric snap-through response of a bistable structure, composed from two beams, coupled via a rigid truss at their midpoint, is studied when subjected to a distributed electrostatic load. Both beams are double clamped and initially curved. The analysis is based on a reduced order (RO) model, resulting from Galerkin’s decomposition. For the base functions, symmetric buckling modes are used for either beam. The results of the RO model are compared with results obtained via finite differences (FD) solutions, to validate the approximation to the original differential formulation, and a finite element (FE) model. Specifically, FE analysis was used as a reference under “mechanical” displacement-independent load, facilitating the usage of solutions extracted via FD for validation of the model under electrostatic, displacement-dependent, load. All solutions employed the usage of the arc-length “Riks” method to accommodate swerving equilibrium paths. To enable a broader approach, the two beams may have different initial elevations. The study indicates that a model with at least three degrees of freedom (DOF) is needed to depict an equilibrium path, for either load. For reliably quantitative equilibrium curves, a model with a minimum of five DOF was found to be necessary. The presented results also indicate that a double curved beam structure can attain actuation of several modes simultaneously, while demonstrating snap-through at reasonable voltages. In so doing, the model suggests that such a construct can be feasible for usage in various applications.