Dynamic characteristics of the blisk with synchronized switch damping based on negative capacitor

In this paper, we propose a method to suppress the vibration of the integral bladed disk ('blisk' for short) in aero-engines using synchronized switch damping based on negative capacitor (SSDNC). Different from the classical piezoelectric shunt damping, SSDNC is a type of nonlinear piezoelectric damping. A multi-harmonic balance method combined with the alternating frequency/time method (MHBM-AFT) is used to predict and further analyze the dynamic characteristics of the electromechanical system, and an arc-length continuation technique is used to improve the convergence of the method. In order to validate the algorithm as well as to recognize the characteristics of the system with SSDNC, a two degree-of-freedom (2-DOF) system with SSDNC is studied at first. The nonlinear complex modal information is calculated and compared with those of the corresponding system with a linear RL shunt circuit. The results indicate that the natural frequencies and modal damping ratio do not change with the modal amplitude, which means that SSDNC has the same modal damping corresponding to different system energy levels. In addition, SSDNC can improve the damping level of all the modes nearly without affecting the natural frequencies of the system. Then, the forced response of the blisk with SSDNC in the frequency domain is calculated and analyzed, including a tuned blisk, which is excited by the traveling wave excitation with a single harmonic and multi-harmonic, and a mistuned blisk, which is excited by traveling wave excitation with a single harmonic and multi-harmonic. We present two advantages of the SSDNC technique when compared with piezoelectric shunt damping. First, SSDNC can suppress the vibration of the blisk under a multi-harmonic wideband the traveling wave, and second, the vibration suppression performance of SSDNC is insensitive to the mistuning of mechanical parameters of the blisk. The results will be of great significance in overcoming the problem of the amplitude magnification induced by the inevitable mistuning of the blisk in aero-engines.