Exact Solution for Free Vibration Analysis of FGM Beams

This study relates the exact solution for free-vibration analysis of beams in material gradient (FGMs) subjected to the different conditions of support using the Euler Bernoulli theory (CBT). It is assumed that the material properties continuously change across the thickness of the beam according to the exponential function (E-FGM). The equations of motion are obtained by applying the principle of virtual works on beams and fundamental frequencies are found by solving the equations governing the eigenvalue problems. Numerical results are presented to describe the influence of the material on the fundamental frequencies of the beam for different state boundaries.