Free vibration and buckling analyses of functionally graded beams with edge cracks

This paper presents a theoretical investigation in free vibration and elastic buckling of beams made of functionally graded materials (FGMs) containing open edge cracks by using Bernoulli-Euler beam theory and the rotational spring model. It is assumed that the material properties vary along the beam thickness only according to exponential distributions. Analytical solutions of the natural frequencies, critical buckling load, and the corresponding mode shapes are obtained for cracked FGM beams with clamped-free, hinged-hinged, and clamped-clamped end supports. A detailed parametric study is conducted to show the influences of the location and total number of cracks, material properties, slenderness ratio, and end supports on the flexural vibration and buckling characteristics of cracked FGM beams.