TY - JFULL AU - Gholam Reza Koochaki PY - 2011/3/ TI - Free Vibration Analysis of Functionally Graded Beams T2 - International Journal of Mechanical and Mechatronics Engineering SP - 513 EP - 517 VL - 5 SN - 1307-6892 UR - https://publications.waset.org/pdf/1975 PU - World Academy of Science, Engineering and Technology NX - Open Science Index 50, 2011 N2 - This work presents the highly accurate numerical calculation of the natural frequencies for functionally graded beams with simply supported boundary conditions. The Timoshenko first order shear deformation beam theory and the higher order shear deformation beam theory of Reddy have been applied to the functionally graded beams analysis. The material property gradient is assumed to be in the thickness direction. The Hamilton-s principle is utilized to obtain the dynamic equations of functionally graded beams. The influences of the volume fraction index and thickness-to-length ratio on the fundamental frequencies are discussed. Comparison of the numerical results for the homogeneous beam with Euler-Bernoulli beam theory results show that the derived model is satisfactory. ER -