Minimizing blade dynamic response in a bladed disk through design optimization

A study is presented on minimizing the maximum dynamic response in a mistuned bladed disk through design optimization. A well-studied spring-lumped-mass system was used to model a bladed disk, and the problem was formulated as a constrained, nonlinear optimization process. Intentional mistuning is introduced by varying the blade mass within a given range. An intentional mistuning pattern described in a polynomial form was then solved iteratively to search for the optimized mistuning pattern that produces the smallest maximum blade response amplitude over a given range of excitation frequencies. It was found that the dynamic amplification factor of the maximum responding blade can be reduced to a range between 20 and 40% less than the tuned system for several combinations of engine excitation orders and coupling ratio. The comparison of results shows that this reduction is more effective than the harmonic or linear mistuning patterns proposed in the literature. The effectiveness of the optimized mistuning patterns was examined through Monte Carlo simulations. The optimized mistuning patterns were found to reduce the maximum blade response for all engine excitation orders in the presence of random mistuning. Hence, it may be possible to reduce significantly the maximum blade response levels in bladed disks by implementing an optimized intentional mistuning pattern.