A homogenized model for the analysis of the vibration localization phenomenon in rotationally periodic structures

Rotationally periodic structures, like turbines, bladed disks, stators and rotors of electric machineries or satellite antennae, play an important role in many fields of the technology. It is well known that when even small structural imperfections are present, destroying the perfect periodicity of the structure, each couple of degenerate modal frequencies splits into two different values (mistuning) and the corresponding modal shapes exhibit peaks of vibration amplitude (localization phenomenon). In this paper a continuous model describing the in-plane vibrations of an imperfect bladed rotor is derived via the homogenization theory, and is applied to the analysis of the localization phenomenon. Imperfections are modeled as perturbations of mass and bending stiffness of some blades, and a perturbation approach is adopted in order to find out the split eigenfrequencies and eigenmodes of the imperfect structure. Numerical simulations show that the proposed model is suitable and effective for the identification and analysis of the localization phenomenon, requiring much lower computational effort than classical finite element models.