Optimization of intentional mistuning patterns for the mitigation of the effects of random mistuning

This paper focuses on the optimization of intentional mistiming patterns for the reduction of the sensitivity of the forced response of bladed disks to random mistuning. Intentional mistiming is achieved here by using two different blade types (denoted as A and B) around the disk. It is thus desired to find the arrangement of these A and B blades (A/B pattern) that leads to the smallest 99th percentile of the amplitude of blade response in the presence of random mistuning. It is first demonstrated that there usually is a large number of local minima and further that the cost of a function evaluation is high. Accordingly, two novel, dedicated optimization algorithms are formulated and validated to address this specific problem. Both algorithms proceed in a two-step fashion. The first step, which consists of an optimization in a reduced space, leads to a series of good initial guesses. A local search from these initial guesses forms the second step of the methods. A detailed validation effort of this new procedure was next achieved on both a single-degree-of- freedom per blade model and a reduced order model of a blisk. In all validation cases, the two novel algorithms were found to converge to the global optimum or very close to it at a small computational cost. Finally, the results of this optimization efforts further demonstrate the value of intentional mistuning to increase the robustness of bladed disks to random mistuning.