A method for constructing reduced-order models (ROM) of an electrostatically actuated clamped silicon diaphragm is presented. This reduced-order model is constructed by using basis the spatially dependent eigen-functions. A commercial finite element package is firstly used to form the system mass and stiffness matrices representing the model. These matrices are then manipulated in MATLAB™ and reduced using modal type dynamic condensation. The eigen-value problem is then solved for the reduced mass and stiffness matrices and subset of the modes are used to producing low-order but highly accurate models of electrostatically actuated diaphragm. The reduced-order model can accounts for general residual stress and strain hardening and allows for any other electric driving signal simulations. Once the ROM has been generated, it can be reused to simulate the quasi-state and dynamics behaviors of the device over a range of different electric driving waveforms. The calculated results show that the resulting ROM can capture the static/dynamic behaviors of the device very well. The simulation results also show good agreement with the fully meshed dynamic models simulation results, thus the efficiency and accuracy of the modeling technology are valid.
Model Reduction for the Electrostatically Actuated Silicon Diaphragm Based on Modal-Type Dynamic Condensation
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Lin, XZ, Hu, ZM, & Huang, JM. "Model Reduction for the Electrostatically Actuated Silicon Diaphragm Based on Modal-Type Dynamic Condensation." Proceedings of the ASME 2014 International Mechanical Engineering Congress and Exposition. Volume 10: Micro- and Nano-Systems Engineering and Packaging. Montreal, Quebec, Canada. November 14–20, 2014. V010T13A027. ASME. https://doi.org/10.1115/IMECE2014-37800
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