Abstract
In this contribution a fourth-order differential equation of the functionally graded material (FGM) beam deflection with longitudinal variation of the effective material properties has been derived where the second order beam theory has been applied for establishing the equilibrium- and kinematics beam equations. Not only the shear forces deformation effect and the effect of consistent mass distribution and mass moment of inertia but also the effect of large axial force has been taken into account. Numerical experiments will be done concerning the calculation of the eigenfrequencies and corresponded eigenmodes of chosen one-layer beams and multilayered FGM sandwich beams. Effect of the axial forces on the free vibration has been studied and evaluated. The solution results will be compared with those obtained by using a very fine mesh of 2D plane elements of the FEM software ANSYS.
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