Semi-inverse method for vibration and buckling of axially functionally graded beams

In this study, vibration and buckling of axially functionally graded simply supported beams is analyzed by using the semi-inverse method. Euler-Bernoulli beam theory was used in the analysis. By using a pre-specified frequency and buckling loads, variation of the Young's modulus in the axial direction is obtained in terms of the axial coordinate. It is found that the Young's modulus changes exponentially between the edges of the beam for the vibration and buckling problem.