Vibration behavior of bi-dimensional functionally graded beams

Based on Euler-Bemoulli beam theory and continuous element method, the free vibration of bi-climensional functionally graded beams is investigated. It is assumed that the material properties vary exponentially along the beam thickness and length. The characteristic frequency equations of beams with different boundary conditions are obtained by transfer matrix method. The validity of the proposed method is assessed through comparison with available results. Parametric studies are earned out to analyze the influences of the gradient indexes and the beam slendemess ratio on the natural fr equencies of bi-dimensional functionally graded beams.