Flexural-torsional vibration and buckling of thin-walled bi-directional functionally graded beams

The paper introduces an analysis of flexural-torsional vibration and buckling of thin-walled bi-directional FG beams. Several cross sections have been conducted such as mono-symmetric I-shaped and channel sections in which material properties are assumed to vary across blade thickness and along axial direction. Governing equations and finite element model are developed. The model is capable of capturing all complex eigenvalue problems, also provides a highly accurate prediction of vibrational shapes and buckling capacity. Since the material changes, the obtained results reflect the relative relation between the behaviors of the beam and the transformation of internal properties, for example, Young's modulus, density, etc. Effects of gradient parameters on the vibrational frequencies or limit loads of a thin-walled bi-directional FG beam under various configurations and boundary conditions have also been parametrically studied.