Bi-stability of pressurized electrically actuated flat micro-plates

Despite the usual belief that only curved micro-structures can behave bi-stably, recently, it has been substantiated that flat micro-structure can also experience this type of behavior. In this way, the present paper aims to investigate snapping behavior in pressurized 2-D flat micro-electro-mechanical plates with a rectangular shape. To this end, a size-dependent and geometric non-linear thin plate model based on the modified couple stress theory is employed. The governing equilibrium equations as well as their corresponding boundary conditions are obtained using the principle of the minimum total potential energy. Employing an efficient Galerkin's discretization procedure, the instability thresholds of the system are determined by vanishing the first and the second variations of the total potential energy expression of the system. The present findings for non-pressurized systems are verified by those published in previous studies. Furthermore, the results concerning the cases under the differential pressures are validated through direct comparison with those extracted from 3-D finite element simulations carried out in COMSOL Multiphysics commercial software. Results reveal that flat micro-plates may experience snap-through instability when they are subjected to some certain values of the differential pressure in the opposite direction of the electrical field. To find the conditions in which a flat micro-plate may face with the snapping behavior, a large number of systems with different material and geometric properties are analyzed. Employing this detailed parametric study, snapping criteria which provide the combination of the system properties and the level of the applied pressure required for prompting snap-through instability are then introduced.