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Coupled Flexural-Torsional Vibration Analysis of Micro-Rotors Based on The Non-Classical Theories of Continuum Mechanics

Jahangiri, Mostafa | 2018

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 51529 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Asghari, Mohsen
  7. Abstract:
  8. Todays, advances in manufacturing technologies have led to design and production of micro-scale elements, including the elements employed in micro-electro-mechanical systems (MEMS). Micro-rotating systems like the micro-turbines are that kind of systems at which the high rotational speeds and the complexity of design and analysis have led to a special attention in modeling and investigating of their dynamic-vibrational behavior. In addition, in small scales, using the non-classical continuum mechanics theories such as the couple stress theory and the strain gradient theory is required to obtain the high precise results. On the other hand, attention to the torsional deformation of rotors besides their flexural deformation is an important issue in evaluating their dynamic-vibrational behavior, since the flexural-torsional couplings due to mass-eccentricity and gyroscopic effect can excite the torsional mode that results in nonlinear behavior. According to these notes, the importance of researching and studying the nonlinear coupled vibrational behavior of the flexural-torsional of micro rotors is an evident matter which has been gained in this thesis utilizing the non-classical continuum mechanics theories. Using the Hamilton principle and the principles governing the variational calculous, three governing equations of the system motion are derived as coupled nonlinear partial differential equations of motion, and the boundary conditions are extracted in general form. To analyze the vibrational behavior of the system, the Galerkin and multiple scales perturbation methods are used. In some examples, by considering specific micro-rotor systems, the small-scale effects on the natural frequencies and the responses obtained by the analytical solution have been investigated. In order to evaluate the terms obtained from the analytic expressions resulted from the perturbation solution, the numerical solution of the governing equations has also been investigated besides the analytical solution where good agreement has been observed between them. As an example of torsional natural frequency obtained from the numerical results of a case study, the non-classical continuum theories predict more than fifty percents in comparison to the classical continuum theory
  9. Keywords:
  10. Microrotors ; Coupled Lateral-Torsional Vibration ; Non-Classical Continum Mechanics Theories ; Couple Stress ; Strain Gradient Theory ; Scale Effect ; Multiscale Method

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