Vibrazioni di una Micro-Trave di Spessore Sottile Elettricamente Predeformata Immersa in un Fluido Viscoso: un’Analisi Multi-Fisica agli Elementi Finiti

Electrostatically-actuated microbeams are extensively being used in the design of microswitches, mass and force sensors, and microresonators. Despite considerable progress in modeling and understanding such systems, most of the literature has focused on in-vacuum vibrations. In this thesis, vibration of an electrically predeformed sharp-edged cantilever microbeam immersed in a viscous fluid is analyzed. We hypothesize that the beam is in close proximity with the ground rigid plate, such that the system exhibits pull-in instability at a critical voltage and vibrations are influenced by the squeeze fluid film. A one-dimensional structural model is proposed to understand the role of fluid-structure interactions and electrostatic forces on the vibrations of the cantilever. A multi-physics three-dimensional (3-D) finite element model is developed to provide both a robust benchmark for the 1-D model and a feasible pathway for further investigations. Pull-in instability is determined by solving an inverse problem using the displacement pull-in extraction method . Frequency response function and complex-valued eigenfrequencies are computed by perfoming a perturbation analysis around electrically-predeformed configurations. Our results demonstrate that the first damped natural frequency of the beam monotonically decreases with applied voltage, until pull-in occurs, with a trend that is strongly affected by the surrounding viscous fluid. Quality factors undergo a remarkable decay with increasing applied voltage, whereas the trend of the variation is slightly dependent on the fluid properties. The robustness of the solutions is assessed through convergence tests on both mesh and domain dimensions. Results from the 1-D model and the proposed multi-physics finite element model are in close agreement.