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Analysis of Micro Rotating Disk Based on the Strain Gradient Elestisity

Danesh Kaftroody, Vahid | 2013

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 45491 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Asghari, Mohsen
  7. Abstract:
  8. In the present study, we analyzed the mechanical behavior of micro rotating disk based on the most general form of strain gradient elasticity. According to the fact that micro rotating disks have an important role in MEMS, it is necessary to present an exact analysis of their mechanical behavior. It is noticed experimentally that materials behave stronger in deformation as they get smaller. The classical continuum theory is not capable to predict such behavior; therefore, it is essential to use one of the non-classical continuum theories to analyze the material in micro scales, which can capture this phenomenon. In this work, the strain gradient theory is utilized to derive the governing equation and corresponding boundary conditions. By using variational calculus in Hamilton’s principle, the governing equation and the boundary conditions are derived. Further, we make these equations non-dimensional and then present the analytical solution of displacement field. By using the obtained solution, we will present some numerical solution in a case study. Presenting the graphs of different variables helps up to understand the physical aspects of the solution. As the most important result, we can see as the disk becomes smaller it behaves stronger in deformation, the famous phenomenon in the micro scale so-called size effect. Also, it can be seen that the trend of non-classical variables in the graphs converge to classical ones as the size of the disk increases
  9. Keywords:
  10. Continuum Mechanics ; Spinning Disk ; Strain Gradient Elasticity ; Size Effect ; Microelectromechanical Systems (MEMS) ; Micro-Scales

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