Free Vibration Analysis of Functionally Graded Beams with Cracks

Document Type : Research Paper


1 Department of Production and Automation, Faculty of Mechanical Engineering, University of Prishtina “Hasan Prishtina”, 10000 Prishtina, Kosovo

2 Department of Mechanical Engineering, Faculty of Engineering, Nigde Omer Halisdemir University, 51245 Nigde, Turkey


This study introduces the free vibration analysis of multilayered symmetric sandwich Timoshenko beams, made of functionally graded materials with two edge cracked, using the finite element method and linear elastic fracture mechanic theory. The FG beam consists of 50 layers, located symmetrically to the neutral plane, whose material properties distribution change along the beam thickness, according to power and exponential laws. The constituent of each layer of the beam is different, but each layer is isotropic and homogeneous. Natural frequency values of a cantilever beam are calculated using a developed MATLAB code. There is good agreement between the present results and the published results from the literature. A detailed study is carried out to observe the effect of crack location, crack depth ratio, power law index and material distribution on the first four natural frequencies.


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