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Modeling and Statical, Vibrational and Dynamical Analysis of Electrically actuated Microplates Using the Extended Kantorovich Method

Moeinfard, Hamid | 2008

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 39052 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Ahmadiyan, Mohammad Taghi
  7. Abstract:
  8. Nano/Microelectromechanical systems have generated a great impact on industry and technology. There are many applications for these systems in micropumps, airbag accelerometers and inkjet printer heads. In theses systems mechanical and electrical fields are involved with each other, and complexities due to this involvement has prevented the scientific society from an effective tool for analysis of this systems in computational point of view. So the objective of this project is to use the Extended Kantorovich method to solve the equations of microplate deformation due to electrostatic actuation. This method is based on variational principals and it uses an initial guess function which doesn’t need to satisfy the geometric, nor the force boundary conditions. That is because of the repetitive solution’s procedure, which is highly convergent and will force the response to satisfy all boundary conditions. Furthermore this method reduces the solution of a partial differential equation, to a set of non-coupled ordinary differential equations which in most cases can be solved exactly. So this method can solve the equations governing the microelectromechanical systems behavior in coupled energy fields with lower computational efforts and with high precision. To achieve this goal, in this project, first, a model for the static behavior of microplate under electrostatic actuation was implemented. Then this model is solved using the Extended Kantorovich method. The relevant results show that increasing the microplate aspect ratio and applying tensile in-plane loads, would increase the pull-in instability limits. Afterwards, a model for the vibrational behavior of the microplate due to electrostatic actuation was presented and the corresponding eigenvalues-eigenfunction equations are solved using the Extended Kantorovich method. Results show that increasing the applied bias voltage, would decrease the fundamental natural frequency of the microplate. It was also seen that increasing the microplate aspect ratio and applying in-plane tensile loads, would decrease the fundamental natural frequency of the microplate and hence increasing the pull-in instability limits. Finally the micro plate’s equation of vibration is solved using the Galerkin approach and modeshapes obtained in the Extended Kantorovich procedure. It was observed that the only dominant mode in the micro plate’s dynamics is the first mode. It is shown that for specific cases, results obtained for the statical and vibrational behavior of the microplate is in close agreement with theoretical and experimental data available in the literature and so validating the proposed model
  9. Keywords:
  10. Microplate ; Static ; Vibration ; Dynamics ; Pull-in Phenomenon ; Extended Kantorovich Method ; Electrostatic Actuation

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