Effect of nonlinearity on the dynamic response of mistuned system

Bladed disks may be used in several engineering systems such as fans, impeller pumps, turbine generators and jet engines. Ideally, these systems are tuned and all blades are identical but, in practice there always exist small, random differences among the blades. Mistuning, imperfections in cyclical symmetry of bladed disks is an inevitable and perilous occurrence due to many factors including manufacturing tolerances, variations in material properties and wear in service. Each blade on a disk is almost always slightly different to the others. It can cause some unpredictable phenomena such as dramatic difference in forced vibration response.
In this paper, effects of mistuning on nonlinear behavior of mistuned cyclical symmetric systems like bladed disk are investigated. A nonlinear, mistuned model based on the method of multiple scales is proposed and formulated in which nonlinearity and mistuning parameter is assumed to be small. Several mistuned system were considered and solved by the proposed technique. Numerical results show that only one jump will happen for the tuned system during the excitation and demonstrate that mistuning can lead to repeating and scattering of jump phenomena during the excitation frequency whereas in tuned cyclic system it occurs simultaneously.