Vibration analysis of thin-walled functionally graded sandwich beams with non-uniform polygonal cross-sections

Abstract

In the paper, an analysis of thin-walled functionally graded straight and curved beams for general non-uniform polygonal cross-sections has been introduced for vibration problems. Higher order beam theory that has fully taken into account major deformations, e.g. in-plane distortion, out-of-plane warping, is adopted by means of beam frame modal approach. In addition with the effects of geometric parameters, the study also deals with some consequences resulting from material anisotropy which in turn tackles better in evaluation behaviors of thin-walled beams that enables analytical modeling to have the potential for further extension. Subsequently, the analysis can be applied for general closed cross-section beams with arbitrary curvatures whereas materials properties are assumed to be graded across the wall thickness following a predefined shape function. A numerical verification for the overall analysis and examples have been carried out based on the available results created from benchmark problems and finite element software simulation found in literature. Then, natural frequencies and vibrational mode shapes have been obtained through a robust framework of finite element method. Finally, a parametric study and discussion towards vibration phenomena are fully investigated referring to gradual law, skin-core-skin effects, etc.