Analytic Approach to Free Vibration and Buckling Analysis of Functionally Graded Beams with Edge Cracks using four Engineering Beam Theories

Authors

  • G. H. Farrahi School of Mechanical Engineering, Sharif University of Technology
  • S. Ali Faghidian Department of Mechanical and Aerospace Engineering, Science and Research Branch, Islamic Azad University
Abstract:

A complete investigation on the free vibration and stability analysis of beams made of functionally graded materials (FGMs) containing open edge cracks utilizing four beam theories, Euler-Bernoulli, Rayleigh, shear and Timoshenko, is performed in this research. It is assumed that the material properties vary along the beam thickness exponentially and the cracked beam is modeled as two segments connected by two mass-less springs (extensional and rotational). Then the equations of motion for the free vibrations and buckling analysis are established and solved analytically for clamped-free boundary conditions. A detailed parametric study is performed to examine the influences of the location and depth of the crack, material properties and slenderness ratio of the beam on the free vibration and buckling characteristics of cracked FGM beams for each of the four engineering beam theories.

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Journal title

volume 27  issue 6

pages  979- 990

publication date 2014-06-01

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