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Forced Nonlinear Vibrational Analysis of Micro Rotating Shaft Based on Non Classical Continuum Theories

Beigzadeh, Sahar | 2019

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 51748 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Asghari, Mohsen
  7. Abstract:
  8. The analysis of nonlinear forced vibration of micro-rotors (rotating micro-shafts with disks) is carried out under loads of mass eccentricity distribution and in the presence of internal damping. For the analysis, the non-classical continuum theories of couple stress and strain gradient are employed. Vibrational behavior of micro-rotors is extremely sensitive due to the very high rotational speed, which is at the order of several millions per minute speed. The considered nonlinearity is of geometrical type due to the mid-plane stretching. First, the governing equations of motion of micro-rotors are derived by utilizing the Hamilton principle. In the next step, the Galerkin and multiple scale methods are employed to solve the non-linear differential equations and obtain the natural frequencies in both the backward and forward motions. The analytical expressions for natural frequencies in forward and backward whirl motions are obtained. In addition, the expressions for the vibrational amplitude of the micro-system due to mass eccentricity distribution and in the presence of internal damping are determined. Then, analytical results are presented for the system vibrational amplitude in the non-resonant response including subharmonic and superharmonic resonances. The effects of different parameters, including the high-order material parameters of non-classical theories, the rotational speed, eccentricity and the internal damping coefficient on the analytical results, are also investigated. In addition, the effects of the number of disks and their position on the system responses are studied. The results indicate that there is a correlation between the high-order material constants in the couple stress theory and strain gradient on the backward and forward natural frequencies, and the difference between prediction of classical and non-classical theories for the frequencies is more than ten percent. It is also observed that when the values of the high-order material constants tend to zero, the results approach to those of the classical continuum theory. Additionally, the increase in forces of mass eccentricity highlights the nonlinear behavior of the system
  9. Keywords:
  10. Non-Classical Continum Mechanics Theories ; Microrotating Shaft ; Nonlinear Forced Vibrations ; Couple Stress ; Strain Gradient Theory ; Microrotors

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