Free vibration of thin-walled open-section beams with functionally graded materials along the contour direction

An investigation of free vibration of a thin-walled beams with functionally graded materials (FGMs) is presented. The mechanical properties of thin-walled beam are assumed to vary along the contour direction of the thin-walled cross section. Governing differential equations are derived by means of Hamilton's principle. A finite element model is developed to formulate the problem. The natural frequencies and corresponding vibrational modes are obtained for thin-walled FG mono-symmetric I- and channel-sections beams with several different types of material distributions. A numerical comparison is carried out to show the validity of the proposed theory with available results in the literature. Furthermore, effects of gradual law and volume fraction of ceramic on the natural frequencies of beams are also studied. •Formulating free vibration of thin-walled open-section beams with functionally graded materials.•The mechanical properties are assumed to vary along the contour direction.•Considering the coupled axial and bending displacements with several different types of material distributions.•Studying the effects of gradual law and volume fraction of ceramic on the natural frequencies.