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Nonlinear Analysis of an Electrostatically Actuated Microbeam Considering Coupled Vibrations Due to Rotation

Mojahedi, Mahdi | 2014

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 45301 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Ahmadian, Mohammad Taghi; Firoozbakhsh, Keikhosrow
  7. Abstract:
  8. This research is concerned with the study of the static, dynamic, vibration and instability of an electrostatically actuated microbeam gyroscope considering geometric nonlinearities and electrostatic fringing fields. A vibrating microbeam gyroscope consists of a beam with a rigid (proof) mass attached to it and undergoes coupled flexural-flexural vibrations coupled with base rotation. The primary oscillation is generated in drive direction of the microbeam gyroscope by a pair of DC and AC voltages on the mass. The secondary oscillation occurring in the sense direction is induced by the Coriolis coupling caused by the input angular rate of the beam along its axis. In this case gyroscope acts like an actuator in the derive direction and a sensor in sense direction. The input angular rotation can be measured by sensing the oscillation tuned to another DC voltage of the proof mass. In the vibratory microgyroscopes, pull-in instability is undesirable and determination of the pull-in voltage is critical in the design process of microgyroscopes to determine the sensitivity, instability and the dynamics of Devices. So static and dynamic pull-in instability are investigated considering nonlinear phenomena, intermolecular forces and squeeze film damping. Vibrating gyroscopes should have close natural frequencies for the drive and sense modes. When the two natural frequencies are mismatched, the Coriolis force yields a small displacement for the sense direction, thereby decreasing the sensitivity. The frequency mismatch is erased by means of electrostatic frequency tuning with a DC voltage. Investigation of the oscillatory behavior is studied in order to determine the tuned natural frequencies. The primary and secondary vibrations of the system subjected to AC voltage are then analytically studied. Nonlinear resonance, jump phenomenon, bifurcation points and coupling effect are investigated along with the vibrational analysis. When the angular rotation is zero, the effect of nonlinear factors including nonlinear curvature and mid-plane stretching on the secondary vibration produced in sense direction are assessed. The results show that consideration of the geometric nonlinearity and fringing field are important for accurate prediction of the static, dynamic and instability behaviors of the microbeams and these effects substantially change the stability region. In the presence of air pressures, the squeeze air film damping greatly reduces the amplitude of oscillations and increase the time to reach equilibrium. The displacement and instability behavior of the NEMS beam gyroscope are different from the microbeam gyroscope, in that they may be significantly affected by the intermolecular surface force. Even in the absence of electrostatic actuation, instability can occur due to the intermolecular forces. Bifurcation phenomena jump and frequencies islands are strongly dependent on nonlinear effects and amplitude of vibration. In order to enhance the sensitivity of the system, the appropriate voltage is determined from the amplitude vs. AC voltage curves with greatest sensing amplitude
  9. Keywords:
  10. Voltages ; Pull-in Phenomenon ; Nonlinear Vibration ; Electrostatic Actuation ; Electrostatic Detection ; Natural Frequency ; Casimir Force ; Nonlinear Resonance ; Squeeze Film Damping ; Van Der Waals Model

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