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On the Nonlinear Dynamics and Bifurcations in a New Class of MEMS Gyroscopes with Parametric Resonance

Pakniyat, Ali | 2010

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 41321 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Salarieh, Hassan; Alasti, Aria
  7. Abstract:
  8. In this thesis, implementing parametric resonance for the purpose of improvement in sensitivity of MEMS gyroscopes is studied. Based on a parametric study on effect of each factor on the sensor’s performance, the desired values for each parameter is determined. Stability of periodic orbits is studied using Floquet Theory. In addition, three expositions are defined and proved in order to make Floquet Theory applicable for stability analysis of origin. Based on this analysis, the relation between stabilities in the system and occurrence of parametric resonance is illustrated. Due to the complexity of dynamics of a parametrically excited MEMS gyroscope, bifurcations are observed in performance of the sensor. These bifurcations include both Hopf bifurcation, and behavioral bifurcations. The study shows that although there is evidence for occurrence of chaos, in the considered domain for parameters, the topological dimension of chaos is zero and hence, chaotic behavior for the gyroscope is not observed. Bifurcation trend in the system reveals that changing nonlinear term of parametric excitation beyond the designed scope, in negative values increases instabilities and in positive values decreases the amplitude of gyroscope’s output together with emergence of new non-resonant orbits which alters system’s performance. In conclusion, behavioral bifurcations should be avoided as much as possible
  9. Keywords:
  10. Gyroscope ; Resonance ; Design ; Stability ; Bifurcation ; Parametric Excitation

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