TY - JOUR ID - 72331 TI - Analytic Approach to Free Vibration and Buckling Analysis of Functionally Graded Beams with Edge Cracks using four Engineering Beam Theories JO - International Journal of Engineering JA - IJE LA - en SN - 1025-2495 AU - Sherafatnia, Khalil AU - Farrahi, G. H. AU - Faghidian, S. Ali AD - School of Mechanical Engineering, Sharif University of Technology AD - Department of Mechanical and Aerospace Engineering, Science and Research Branch, Islamic Azad University Y1 - 2014 PY - 2014 VL - 27 IS - 6 SP - 979 EP - 990 KW - functionally graded materials KW - Engineering beam theories KW - Open edge crack KW - Vibration Analysis KW - Buckling Analysis DO - N2 - 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. UR - https://www.ije.ir/article_72331.html L1 - https://www.ije.ir/article_72331_7a2a66e9081466f403433b77af0a25b0.pdf ER -