Loading...

Static and Dynamic Analysis of Micro-structures in Electric Field Using Newly Developed Strain Gradient Finite Elements

Kahrobaiyan, Mohammad Hossein | 2014

539 Viewed
  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 46150 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Ahmadian, Mohammad Taghi; Asghari, Mohsen
  7. Abstract:
  8. Due to importance of micro electromechanical systems (MEMS), inability of the classical continuum theory to predict the mechanical behavior of micro-scale structures accurately, and vast applications of finite element method (FEM) in modeling of the MEMS, in this dissertation, the static and dynamic mechanical behavior of electrostatically actuated micro structures has been investigated using newly developed finite elements based on strain gradient continuum theory. The governing equations and boundary conditions have been developed for longitudinal and torsional behavior of microbars as well as flexural behavior of Euler-Bernoulli and Timoshenko microbeams based on strain gradient elasticity theory. The results indicate that the strain gradient theory predicts stiffer models for micro-scale structures than the classical theory. In addition, it is observed that the difference between the classical and strain gradient results is significant when the size of the structure is comparable to its length scale parameter but it diminishes as the size increases. Using the aforementioned governing equations and boundary conditions, new finite elements are developed for microbars and microbeams based on the strain gradient elasticity. The new elements degrees of freedom are more than those of their respective classical elements and their shape functions are more complicated. The outcomes reveal that the results of the new elements are in better agreement with the experimental findings compared to the results of the classical FEM. A new yield criterion is developed based on the strain gradient theory which can be considered as the generalized von-Mises yield criterion for micro-scale structures. Comparing the results of the new criterion with the experimental data indicates that the new criterion is able to capture the experimental data successfully while the difference between the results of the classical von-Mises yield criterion and experimental outcomes is substantial (more than 100% relative error) when the size of the structures is in micron and sub-micron scales. Moreover, three standards tests are proposed in order to determine the three length scale parameters appeared in strain gradient theory. Afterward, the new beam elements are employed in order to investigate the static and dynamic behavior of electrostatically actuated microbeams considering squeeze film damping and Casimir force. Utilizing the new beam elements, the static and dynamic pull-in voltages, resonance frequencies and time response to the suddenly applied voltage (step voltage) are evaluated for the electrostatically actuated microbeams. The results are compared to the experimental data in which good agreements have been observed. Furthermore, the results reveal that the Casimir effect is considerable only if the gap is less than a few nanometers. A finite element model has been developed based on the strain gradient theory in order to account for the charge migration effects during oscillations of the microbeam. The results indicate that considering the charge migration (considering the dynamics of voltage) results in frequency shift and appearance of damping in vibration of microbeams
  9. Keywords:
  10. Strain Gradient Theory ; Yield Criterion ; Size Effect ; Microelectromechanical Systems (MEMS) ; Finite Element Method ; Charge Migration Effect

 Digital Object List

 Bookmark

No TOC