Perturbations Methods in Structural Dynamics and Applications to Cyclic Symmetric Domains

The design of components must take into account the irregularities inherent to the manufacturing process. When the structures have close eigenvalues, small mass and stiffness variations or the damping generate strong variations of the eigenmodes: these structures are then not robust. Here, their dynamics has been analyzed by perturbation method, in the dissipative cases and with coupling within a light fluid. A new perturbation method allows first order developments whatever the spectral density may be. Applications to many different vibration problems are presented: aeroelasticity, mode veering problem, maximum amplitude of forced response in cyclic symmetric domains, with detuning and/or mistuning, i.e., the most important reliability problem in turbomachinery. The results of this study provide a new estimation of the amplification factor and damping due to mistuning and aerodynamic coupling.