Mistuning, imperfections in cyclical symmetry of bladed disks is an inevitable and perilous occurrence due to many factors including manufacturing tolerances and in service wear and tear. It can cause some unpredictable phenomena such as mode splitting, mode localization and dramatic difference in forced vibration response. This survey explains the fundamental techniques of mistuning in some details. For this object, a comprehensive concept of the worst specification is evaluated and formulated as an optimization problem. Then, the worst case optimization problem is utilized for different models like lumped models and large finite element models. Intentional mistuning as well as rearranging method, as an optimization problem, is used to reduce the bad effects of mistuning on the forced vibration response of bladed disk system. Then, the genetic algorithm is used for solving all optimization problems. Next, the efficiency of methods is demonstrated for two different lumped parameter models. Afterward, the formulation of 3D finite element bladed disk model is explained. Then the free and forced vibration response of a 3D sample BD model is evaluated. Next, component mode synthesis (CMS) as a reduce order method (ROM) is used for finding the forced vibration response of both tuned and mistuned BD systems. For this object a novel method is presented that can be used for both small and large mistuned systems. An approximation is utilized to evaluate the harmonic response of small mistuned system. The results of novel method are compared to the results, evaluated by previous methods like Craig Bampton (CB) method. Subsequently, the effects of mistuning on nonlinear mistuned cyclical symmetric systems like BD are shown. The method of multiple scales is used for finding the forced and steady state vibration response of a nonlinear mistuned lumped model. Finally, the aeroelastic behavior of mistuned bladed disk is evaluated by use of panel method as an aerodynamic model and consequently, the bad effect of mistuning on flutter speed is shown.
