Coupled vibration characteristics of shear flexible thin-walled functionally graded sandwich I-beams

This paper presents the general shear flexible thin-walled beam theory to study the coupled vibration characteristics of sandwich I-beams made of functionally graded materials (FGMs). This model accounts for the structural coupling coming from the material anisotropy and the transverse shear and the restrained warping induced shear deformation. The mechanical properties of beam such as Young's and shear moduli and material density are assumed to be continuously graded through the wall thickness according to a power law distribution of volume fraction of ceramic and metal. The seven coupled equations of motion are derived from Hamilton's principle. To solve the dynamic problems, three different types of finite beam elements, namely, linear, quadratic and cubic elements are employed with the scope to discretize the equations of motion. For the purpose of model validation, the results obtained in the present analysis are verified against those given in literature. Through numerical examples, two types of material distributions are considered to investigate the effects of shear deformation, gradient index, thickness ratio of ceramic, boundary conditions, and span-to-height ratio on the dynamic responses of FGM bisymmetric and mono-symmetric I-beams. Particularly, the crossover phenomenon in vibration modes is investigated with respect to changes in gradient index and thickness ratio of ceramic.