Semi-analytical dynamic modeling and vibration reduction analysis of the blisk structure with piezoelectric shunt damping patches

Abstract

To suppress the harmful vibration of blisks, a method of uniformly distributing piezoelectric shunt damping patches (PSDPs) on blades is described. Taking the simplified blisk as the object, the semi-analytical model of blisk with PSDPs is established and the vibration reduction effect of the piezoelectric shunt damping is analyzed based on the created dynamic model and the experimental system. In the process of modeling, the piezoelectric effect is reasonably simulated, and the electromechanical coupling expressions of the blisk structure with uniformly distributed piezoelectric patches are derived according to the Lagrange energy equations. Further, the resistance (R) and resistance-inductance (RL) series shunt are equivalent to frequency-dependent viscoelastic damping and are introduced into the semi-analytical model of the blisk in the form of complex stiffness. A case study is carried out on the blisk with four equally attached PSDPs. Based on the experimental results, the rationality of the dynamic model is proved. At the same time, theoretical analysis and experiments show that piezoelectric shunt damping has a certain damping effect on the blisk. Finally, based on the established model, the influence of different piezoelectric shunt parameters (resistance values, inductance values), the attachment positions of piezoelectric patches, and different piezoelectric patch types on the vibration reduction effect of the blisk are emphatically analyzed. The results show that there is an optimal resistance value for the R shunt circuit, and an optimal resistance and inductance value for the RL series shunt circuit to make the vibration reduction effect optimal; the piezoelectric patch attached on the root of the blade and selecting piezoelectric patch with large electromechanical coupling coefficient are beneficial to vibration reduction.