Parametric reduction techniques for the simulation of mistuning in bladed disks

In bladed disks' dynamics the so called "mistuning" is the effect of uncertainties which break the ideally tuned configuration imposed at the design stage. Nowadays, the mistuning topic takes a great relevance in the turbomachinery field, since it is associated to a behaviour which is not predictable by analyses done with cyclic symmetry and leads to non conservative results in terms of peak amplitudes at resonance. From a numerical point of view, the study of mistuning requires the simulation of the whole bladed disk and consequently leads to high computational costs: for this purpose it is necessary to develop reduction techniques that must also take into account the perturbation of a design parameter. This thesis focuses on the formulation of an effective parametric reduction technique in order to estimate the natural frequencies, the modeshapes and the forced response of structures characterized by a variation in one of their geometric parameters. Some specific methods, acting on the mass and stiffness matrices through an approach based on interpolation, are analyzed emphasizing the advantages and the drawbacks, especially when associated with a reduction technique as the Craig-Bampton CMS. The application of the above mentioned methods starts from a simple one-dimensional MDOF system created in Matlab and then focuses on more complex models such as a 3D cantilever beam and a dummy blade, previously meshed in HyperMesh and then imported into ANSYS for the structural analysis. Subsequently, the outcome of the thesis will be useful for the simulation of the dynamic behaviour of a bladed disk characterized by blades having different thickness.