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Nonlinear Vibrations of a Circular Plate Using Perturbation and Experimental Methods

Mohammadi Farani, Mohammad Hossein | 2020

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 53253 (45)
  4. University: Sharif University of Technology
  5. Department: Aerospace Engineering
  6. Advisor(s): Navazi, Hossein Mohammad
  7. Abstract:
  8. In this thesis, the nonlinear vibrations of the circular plate is examined using multiple scale methods and experimental tests. At first step, the nonlinear equations governing the problem are written using von Karman's assumption. In the next step, to solve nonlinear equations and calculate natural frequency, the problem is solved using multiple scale method and frequency charts are extracted as a function of the amplitude of vibration. . The design of the setup has been done in such a way that it is possible to simulate the boundary conditions. In the first phase, experimental tests was performed on a 0.3 mm thick aluminum sheet, which did not produce the desired results due to the thinness of the sheet. Other tests are dome with a thickness of 1 mm. By stimulating the sheet around the natural frequencies and recording the amplitude of the oscillations, the amplitude diagrams are extracted as a function of the frequency. The results of the practical test indicate that the natural frequency decreases as the amplitude of the oscillations increases. In analytical solution, however, the results show the increase in the frequency with increasing amplitude. According to the literature, this discrepancy may be because of the plate imperfection
  9. Keywords:
  10. Nonlinear Vibration ; Circular Plate ; Experimental Vibration ; Multiple Scales Method (MMS) ; End Conditions ; Time Scale ; Von Karman Theory

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