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Vibration Analysis of Micro-Engine Rotor on the Basis of Non-classical Theories of Continuum Mechanics

Hashemi, Mehdi | 2016

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 49191 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Asghari, Mohsen
  7. Abstract:
  8. Micro-rotating machinery with compact energy sources and high power density has been developed in the recent decade to run portable electronic devices. To achieve efficiency targets, these miniaturized turbo-machinery must spin at elevated rotational speeds which sometimes can reach up to one million revolutions per minute. At this relatively high spinning rate, the rotordynamic behavior of these systems plays an important role in the stage of design. On the other hand, the classical continuum theory has been proven not to be able to appropriately predict the mechanical behavior of the small-scale structures. To overcome overall mentioned weakness, in this thesis the rotor of micro-engines are modeled mathematically by using two non-classical continuum theories including the couple stress and strain gradient theories in order to determine vibration characteristics of the micro-system. The micro-rotor with internal damping consists of a micro-shaft with attached disks mounted on high speed hydrodynamic and hydrostatic pressurized gas bearings. To derive the governing equations for lateral motion, the total kinetic energy of the asymmetric micro-rotor with mass eccentricity is obtained. The strain energy of the micro-shaft on the basis of couple stress and strain gradient theories is also written under geometrical nonlinearity assumption, as well as the variation of the work done by external loads. Utilizing the Hamilton’s principle, nonlinear partial differential equations of motion are derived. Then, some analytical expressions are obtained for vibration characteristics of the micro-rotor on the basis of the Galerkin’s method. In addition, a Jeffcott and finite element based models are developed based on the couple stress and strain gradient theories. The effect of the nonlinear term is studied by solving nonlinear differential equations of motion with aid of the method of multiple scales. With utilization of the developed formulation, the natural frequencies, critical speeds, the threshold of instability rotational speed, and the response of the system under excitation of the mass eccentricity are obtained in some numerical examples. The numerical results show profound effects of length scale parameter of the couple stress theory and higher-order material constants of the strain gradient theory on the vibration characteristics of the micro-rotor
  9. Keywords:
  10. Rotor Dynamics ; Strain Gradient Theory ; Couple Stress ; Nonlinear Vibration ; Non-Classical Continum Mechanics Theories ; Microrotors ; Linear Vibration

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