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Non-Linear Vibration and Stability Analysis of a Rotor with Rubbing and NonLinear Support

Eisvand Chenari, Ashkan | 2021

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 53927 (45)
  4. University: Sharif University of Technology
  5. Department: Aerospace Engineering
  6. Advisor(s): Mohammad Navazi, Hossein
  7. Abstract:
  8. The present study aims to achieve two major objectives in the field of Rotordynamics. The first one is to investigate the frequency response function by considering rubbing between fixed and rotating components of the system and also the presence of nonlinear support such as tiling-pad bearings using analytical approach and the second one is to study the stability of the system using both analytical and numerical methods. In first step, by using assumptions and laws of physics, a model for dealing with the rubbing phenomenon and the friction force between fixed and rotating components of the system is presented. In the next step, the rubbing force is modeled. Then using the Jeffcott rotor model and also adding related linear and nonlinear stiffness and damping to the nonlinear bearing, the vibrational nonlinear governing equations of the rotor were extracted in both directions. To obtain the frequency response of these equations, the multiple scales method has been used and the rotor response to forced vibrations has been obtained analytically. The third order approximation of perturbations has been obtained in multiple scales method. In calculating the frequency response of the rotor, external resonance and in particular the primary resonance was investigated. In the last step, the stability of the rotor was investigated using the analytical method near the equilibrium points of the system and finally verified using numerical methods. The results show that the system may behave hardening or softening. In both cases, the jump phenomena can be observed, and the amplitude of the system is dependent not only on the excitation frequency but also on the increasing or decreasing manner of the excitation frequency. The change of the response amplitude versus the excitation force amplitude studied too. The jump phenomena can be observed in these results also. It means that in some excitation forces, the system may have more than one stable response. In the study of stability by analytical method, it was found that this method is in the small neighborhood of points Equilibrium has an acceptable consistency with numerical methods and by moving away from equilibrium points, the accuracy of this method decreases. Finally, it was found that the system tends to move towards stable equilibrium points and away from unstable equilibrium points, and the initial condition of the system will determine that The system around which of the equilibrium points will be destination.

  9. Keywords:
  10. Nonlinear Vibration ; Perturbation Theory ; Multiple Scales Method (MMS) ; Rotor Dynamics ; Nonlinear Tilting Pad Journal Bearing (TPJB) ; Jeffcott Rotor ; Nonlinear Support

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