A study on the dynamics of rotating beams with functionally graded properties

The constant needs of the industry impel the engineering community in seeking of new concepts and new strategies in order to improve the structural response of structures as well as to enhance the endurance of materials. This is particularly true in the case of rotating blades that are subjected to severe environmental conditions such as high temperatures as well as mechanical conditions such as high rotating accelerations, centrifugal forces, geometric stiffening, among others. It is well known that flexible beams become stiffer when subjected to high speed rotations, because of the axial-bending coupling associated to the large displacements of the beam cross-section. This is called geometric stiffening effect and it was analyzed over the last decades in many beam applications from blade problems to drill-string modeling. In this paper a rotating nonlinear beam model accounting for arbitrary axial deformations is developed. The beam is made of functionally graded materials (FGM). This model is also employed to analyze other simplified models based on isotropic materials or composite materials, that are particular cases of the present formulation. The assumption of steady-state values of centrifugal loads is evaluated. It has to be said that there is a lack of information about modeling of beams made of functionally graded materials and this paper is intended to be a contribution on the subject.