Modeling and Analyzing the Free Vibration of Simply Supported Functionally Graded Beam

Euler, Timoshenko and high shear deformation theories to analyze the free vibration of functionally graded (FG) beam were developed. The mechanical properties this assumed differ in thickness direction according model a power-law distribution. principle Hamilton was used find equations motion. For vibration, analytical solution these presented using Navier method. effect power index, aspect ratio, modulus on dimensionless frequency studied numerically by Ansys software analytically different Fortran program. obtained results from programs compared with each other some previous research. Results showed an excellent agreement numerical that use new FG especially based first leads reduction frequency. It may be concluded that, including shear’s decrease From modeling analysis model, it is possible know what appropriate design for reduce vibration.