Free vibration analysis of functionally graded beams with simply supported edges

Free vibration of simply supported FG beam was investigated. Young’s modulus of beam varies in the thickness direction according to power law and exponential law. Governing equations were found by applying Hamilton’s principle. Navier type solution method was used to obtain frequencies. Different higher order shear deformation theories and classical beam theories were used in the analysis. Free vibration frequencies and some mode shapes were given for different material properties and different slenderness ratios.