A modified nonlinear modal synthesis scheme for mistuned blisks with synchronized switch damping

In the authors' previous work (MSSP 2017), we show that the synchronized switch damping based on negative capacitor (SSDNC) is a good candidate for vibration suppression of tuned blisks. In this paper, we consider the mistuned case and propose an efficient numerical approach to accelerate the required statistical analysis. Although SSDNC is a type of nonlinear piezoelectric damping, through an in-depth nonlinear modal analysis, we show that the modal information of the system remains unchanged with respect to the nonlinear modal amplitude. Based on this, an accelerated nonlinear component modal synthesis (NCMS) method is proposed to predict and further analyse the dynamic characteristics of the nonlinear system. The precision and efficiency of the proposed method is compared with that of the multiharmonic balance method. The stochastic characteristics of the blisk are studied with two sources of mistuning. The first one is random stiffness mistuning and the second one is capacitance mistuning. The investigation is carried out with different mistuning levels and under different engine-order excitations. The results show that the NCMS method can accurately predict the forced response of the mistuned blisk with SSDNC, and the calculation cost can be considerably reduced. Two advantages of the SSDNC technique applied to the mistuned blisk have been revealed in the statistical view. The first one is that the SSDNC can suppress the amplified vibration induced by the mistuning of the blisk significantly. The second one is that the vibration-suppression performance of SSDNC is insensitive to the mistuning of the blisk and that of the electrical circuits.