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Vibration Analysis of Edge Cracked Timoshenko Beam with Continuous Crack Model

Heydari, Mahdi | 2010

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 40261 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Behzad, Mehdi
  7. Abstract:
  8. Structural defects such as cracks may be produced in structures and machineries under fatigue load operating conditions. The presence of crack can lead to catastrophic failures in certain conditions. The occurrence of cracks affects the dynamic and vibration behavior of the structure considerably. These vibrations can be used for identifying the cracks and appropriate actions can be taken to prevent more damage to the system. Therefore, in this thesis vibration analysis of a Timoshenko beam with a vertical and horizontal crack has been considered. A continuous model for vibration analysis of a beam with an open edge crack including the effects of shear deformation and rotary inertia has been used. The crack has been modeled as a continuous disturbance function in displacement field which could be obtained from fracture mechanics. A displacement field is suggested for the beam and the strain and stress fields are calculated. The governing equation of motion for the beam has been obtained using Hamilton principle for both vertical and horizontal cracks. Free and forced vibration analyses have been done. The equation of motion is solved with a modified Galerkin method and the natural frequencies, mode shapes and frequency response functions (FRF) are obtained. An excellent agreement has been observed between the results and results of previous work and finite element.

  9. Keywords:
  10. Forced Vibration ; Free Vibration ; Cracked Timoshenko Beam ; Horizontal Crack

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