Initially curved microplates under electrostatic actuation: Theory and experiment

Microplates are the building blocks of many micro-electro-mechanical systems. It is common for them to experience initial curvature imperfection due to residual stresses caused by the micro fabrication process. Such plates are essentially different from perfectly flat ones and cannot be modeled using flat plate models. In this paper, we adopt a dynamic analog of the von Karman governing equations of imperfect plates. These equations are then used to develop a reduced order model based on the Galerkin procedure, to simulate the static and dynamic behavior of the microplate under electrostatic actuation. To validate the simulation results, an initially curved imperfect microplate made of silicon nitride is fabricated and tested. The static behaviour of the microplate is investigated when applying a DC voltage V_dc. Then, the dynamic behaviour of the microplate is examined under the application of a harmonic AC voltage, V_ac, superimposed to V_dc. The simulation results show good agreement with the experimentally measured responses.