A continuous model for the dynamical analysis of mistuned bladed rotors

Ideal bladed rotors are rotationally symmetric, as a consequence they exhibit couples of degenerate eigenmodes at coinciding frequencies. When even small imperfections are present destroying the periodicity of the structure (disorder or mistuning), each couple of degenerate eigenfrequencies splits into two distinct values (frequency split) and the corresponding modal shapes exhibit vibration amplitude peaks concentrated around few blades (localization phenomenon). In this paper a continuous model describing the in-plane vibrations of a mistuned bladed rotor is derived via the homogenization theory. Imperfections are accounted for as deviations of the mass and/or stiffness of some blades from the design value; a perturbation approach is adopted in order to investigate the frequency split and localization phenomena arising in the imperfect structure. Numerical simulations show the effectiveness of the proposed model, requiring much lower computational effort than classical finite element schemes.