Initially Imperfect MEMS Microplates Under Electrostatic Actuation: Theory and Experiment

Microplates are building blocks of many Micro-Electro-Mechanical Systems (MEMS). It is common for them to undergo imperfections due to residual stresses caused by the micro fabrication process. Such plates are essentially different from perfectly flat plates and cannot be modeled using the governing equations of flat plates. In this article, we adopt the governing equations of imperfect plates employing the modified von-Karman strains. These equations then are used to develop a Reduced Order Model based on the Galerkin procedure to simulate the static and dynamic behavior of an electrostatically actuated microplate. Also, microplates made of silicon nitride are fabricated and tested. First, the static behaviour of the microplate is investigated when applying a static voltage V_dc. To study the dynamic behaviour we apply a harmonic voltage, V_ac, superimposed to V_dc. Simulation results show good agreement with the experimentally measured responses.