Dynamics of a functionally graded Timoshenko beam considering new spectrums

Dynamics of a functionally graded (FG) beam were studied using Timoshenko and Euler-Bernoulli (EB) beam theories. Wave propagation of infinite beams and vibration analysis of simply supported FG beams were investigated. Variation of the material properties were assumed in the power law form. It was obtained that unlike isotropic beams, axial and transverse waves are coupled in FG beams due to unsymmetric material variation in the thickness direction of the beam. Two and three dispersion curves were obtained for EB and Timoshenko beam theory, respectively. All of these modes are axial-flexural coupled modes and coupling degree depends on material distribution with respect to mid-surface of the beam. The spectrums of different beams may be classified considering corresponding mode shapes. Wave propagation and vibration properties were discussed considering their mode shapes. It is seen that, unlike isotropic beams, pure shear mode is not possible for FG beams.