Dynamic Stability of Thin-Walled Beams with Graded Material Properties

Abstract

The dynamic stability of functionally graded thin-walled beams allowing for shear deformability is investigated in this article. The structure is subjected to axial external dynamic loading. The analysis is based on a model that has small strains and moderate rotations that are formulated through the adoption of a second-order non-linear displacement field. Galerkin’s and Bolotin’s methods are employed with the scope to discretize the governing equations and to determine the regions of dynamic instability, respectively. Regions of instability are evaluated and are expressed in non-dimensional terms. The influence of the longitudinal vibration on the unstable regions is investigated. The numerical results show the importance of this effect when the forcing frequency approaches to the natural longitudinal frequency, obtaining substantially wider parametric instability regions. The effect of shear flexibility and axial inertia for beams with different cross-sections and different types of graded material are analyzed as well.