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Forced Vibration Analysis of Rotating Micro-Shaft Based on the Non-local Strain Gradient Theory

Panahi Dorcheh, Ramin | 2022

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 54883 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Asghari, Mohsen
  7. Abstract:
  8. Nowadays, with progresses made in manufacturing technologies, it is possible to produce micro-scale products such as micro-electromechanical systems. Micro-motors are one type of these systems that can be used in such applications as power supply of electronic devices. To achieve a better performance, these systems must rotate at high rotational speeds (about one million revolutions per minute). At such a high rotational speed, vibrational analysis is highly crucial. The results of recent studies indicate the inability of classical theories of continuum mechanics to analyze the behavior of these micro systems. Therefore, in this research, the rotor of micro-motors are modeled using the non-classical theory of non-local strain gradient in order to study the vibration behavior of the micro-system. To do so, first, the micro-rotor is considered as a micro-shaft with internal damping and its attached disks mounted on high speed pressurized gas bearings. Then, the governing equations of the lateral motion of this micro-rotor are obtained and dimensioned based on the calculus of variations and Hamilton's principles. To do so, the kinetic energy of the system—assumed by mass eccentricity in the micro-shaft and disks—is obtained. The strain energy of the micro-shaft on the basis of non-local strain gradient theory is also written under geometrical nonlinearity assumption as well as the variation of the work done by external forces. In the next step, the Galerkin and Multiple time scales methods are applied to solve the nonlinear ODEs and obtain the vibrational amplitude of the micro-system as well as its natural frequencies in both the backward and forward whirling. These expressions are obtained considering external loads—due to the mass eccentricity distribution—and the internal damping. Then, the effects of various system parameters, including the length scale parameter of strain gradient, nonlocal material constant, the rotational speed, the amount of eccentricity, and the internal damping coefficient, are investigated. To sum up, the results show the significant effects of the length scale parameter of the strain gradient and the nonlocal material constant on the motion amplitude and natural frequencies such that increasing the length scale parameter of the strain gradient and nonlocal material constant will result in the increase and decrease of the system rigidity, respectively
  9. Keywords:
  10. Forced Vibration ; Microelectromechanical Systems (MEMS) ; Non-Classical Continum Mechanics Theories ; Strain Gradient Theory ; Non-Local Strain Gradient Theory ; Rotating Micro-Shaft

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