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Download nonlinear dynamics of electrostatically actuated mems and nems
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NONLINEAR DYNAMICS OF ELECTROSTATICALLY ACTUATED MEMS AND NEMS Dumitru I. Caruntu, PhD, PE Mechanical Engineering Department, The University of Texas Pan American May 2011 Abstract Microelectromechanical (MEMS) and nanoelectromechanical (NEMS) resonator systems such as beams and plates are used in many applications. As nonlinearities play a significant role at small scales, a better understanding of the nonlinear dynamics of MEMS/NEMS is essential. Nonlinearities arise from a number of sources such as large deflections, squeeze-film damping, electrostatic actuation (to include fringe effect), and intermolecular surface forces present at micron and submicron scales such as Casimir and/or van der Waals. Electrostatic actuation is produced by a DC voltage and/or AC voltage between a flexible MEMS/NEMS structure, such as a cantilever, and a rigid ground plate. This actuation creates a variety of nonlinear parametric resonances depending on system parameters, excitation frequency, and excitation voltage. These resonances can be used to design mass sensors, microscopy probes, filters, and resonators. This research deals with nonlinear parametric resonances of cantilever MEMS/NEMS beams and plates, and Single Wall Carbon NanoTubes (SWCNTs), due to soft AC electrostatic excitation (nonlinear parametric force) and Casimir and/or van der Waals forces, for mass sensing applications. MEMS/NEMS beam model includes electrostatic, fringe and Casimir forces. NEMS circular plate model includes besides the electrostatic force, both Casimir and van der Waals forces. However, these two intermolecular forces describe the same type of interaction at different scales. Van der Waals forces are present at values less than fifty nanometers of the gap between the flexible plate and ground plate. Casimir forces are significant for gap values less than one micrometer. SWCNT model includes electrostatic and van der Waals forces. The methods used in this research are the Method of Multiple Scales (MMS) and the Reduced Order Method (ROM). Numerical simulations conducted in this research show a softening effect in all nonlinear parametric resonances. Influences of damping, voltage, frequency, fringe, Casimir, and van der Waals parameters on the resonances are showed as well.
