The development of additive manufacturing technology makes it possible to realize a designed distribution of material properties in complex geometry. The distribution can be made not only in layers, but also in the axial direction of a beam. Axially functional graded (AFG) beams may play an important role in light-weight design for airfoil structure in aerospace industry. In this research, the free vibration of AFG cantilever beams is studied by using Euler-Bernoulli beam theory. It is taken into consideration that material properties, including elasticity modulus and mass density vary continuously along the axial direction of AFG beam according to an elliptic load distribution based on the life curve of airfoil. The governing differential equations of motion has been analyzed and solved to calculate the natural frequency and fundamental mode shape accurately. In order to verify the accuracy of the present formulation and results, the natural frequencies and fundamental mode shape of several AFG beams are obtained, and compared with the dynamic simulation results from ABAQUS. Good agreement is observed. The results indicate that the proposed method is effective at forecasting the dynamic property of AFG cantilever beams for airfoil structure.

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