Free Vibration Analysis of FGM Timoshenko Beams by Shooting Method

摘要

Free vibration response of functionally graded material beams were studied based on the first-order shear deformation theory by numerical shooting method. The material properties of the beam are assumed to be varied in the thickness direction as power law distribution. In the mathematical formulation, the axial, transversal, rotational and axial-rotational coupling inertia forces were totally considered. By using shooting method the ordinary differential equations in terms of amplitude functions with different boundary conditions were solved. Dimensionless natural frequencies for different mode shapes were presented. Effects of the power index, the shearing deformation on the natural frequency were examined in detail.