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Free Vibration and Buckling Analysis of Functionally Graded Beams with an Edge Crack

Sherafatnia, Khalil | 2010

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 41180 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Farrahi, Gholamhossein
  7. Abstract:
  8. Cracks significantly change the vibration response of structures. Cracks which exist in structures as a defect in the material or created by repeated loads, reduce the natural frequencies and change the vibration mode shapes. Therefore with measuring the vibration response of structures, the existence and position of cracks are detected. This research analytically investigates the free vibration and elastic buckling of a beam made of functionally graded materials (FGM) with open edge cracks using Reddy's beam theory and the rotational spring model. It is assumed that the material properties vary along the beam thickness according to a power law distribution in terms of volume fraction of material constituents and the lateral normal stress of the beam is zero. Then the governing equations of motion were derived from Hamilton's principle. Analytical solutions of the natural frequencies, critical buckling load, and the corresponding mode shapes were obtained for a cracked FGM beam with clamped-free boundary condition. Detailed parametric study was conducted to show influences of the crack location and depth, material properties and slenderness ratio on the flexural vibration and buckling characteristics of cracked FGM beams
  9. Keywords:
  10. Free Vibration ; Stability ; Surface Crack ; Functionally Graded Materials (FGM) ; Third Order Shear Deformation Beam Theory

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