Design modification of cyclically periodic structure using Gaussian process

Cyclically periodic structures, such as blade-disk assembly in turbo-machinery, are widely used in engineering practice. While these structures are generally designed to be periodic with identical substructures, it is well-known that small random uncertainties exist among substructures which in certain cases may cause drastic change in the dynamic responses, a phenomenon known as vibration localization. Previous studies have illustrated that the introduction of small design modifications, i.e., intentional mistuning, may alleviate such vibration localization. The design objective here thus is to identify proper deign modification that can reduce the response variation under uncertainties. In this research, we first develop a perturbation-based approach to efficiently quantify the variation of forced response of a periodic structure, without and with the design modification, under uncertainties. We then propose a Gaussian process emulation which enables us to evaluate the objective function over the design space by using only a small number of design candidates. The combination of these algorithms allows us to perform effective design modification to minimize the response variation in nearly periodic structures.