Free Vibration Analysis of Functionally Graded Materials Non-uniform Beams

In this article, nonuniformity effects on free vibration analysis of functionally graded beams is discussed. Variation in material properties is modeled after power law and exponential models and the nonuniformity is assumed to be exponentially varying in the width along the beams with constant thickness. Analytical solution is achieved for free vibration with simply supported conditions. Results show that functionally graded material (FGM) accompanying section variation have a significant effect on natural frequencies of FGM nonuniform beams. In order to show this dependency, Al/Al2O3 composite beam is modeled and the first three natural frequencies with simply supported boundary conditions is obtained for different power law and exponential parameters which shows a great sensitivity to nonuniformity in different shape modes.