Thermoelastic dynamic stability of thin-walled beams with graded material properties

The dynamic stability of functionally graded thin-walled beams allowing for shear deformability is investigated in this article. The analysis is based on a model that has small strains and moderate rotations which are formulated through the adoption of a second-order non-linear displacement field. The beam is subjected to axial external dynamic loading. The model takes into account thermoelastic effects. The heat conduction equation is solved in order to characterize the temperature in the cross-sectional domain. Galerkin's and Bolotin's methods are employed with the scope to discretize the governing equations and to determine the regions of dynamic stability, respectively. Regions of stability are evaluated and expressed in non-dimensional form. 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 stability regions. The effects of temperature gradients, shear flexibility and axial inertia, in beams with different cross-sections and different types of graded material are analyzed as well.