Theoretical analysis of a parametrically excited rotor system with electromechanically coupled boundary condition. (10th November 2021) - Tan, Xing; Chen, Guoping; Chen, Weiting; Wang, Zhenyu; He, Huan; He, Jincheng; Wang, Tao
Abstract: In this paper, the dynamic behavior of a rotor system with electromechanically coupled boundary condition under periodic axial load is studied, where the boundary condition is derived from a ring-shaped piezoelectric damper which is developed for vibration control of rotor system. This damper is based on the piezoelectric shunt damping technique, which can produce much or little damping performance depends on the selection of shunt circuit parameters. By using assumed mode method and Lagrange equation, the equations of motion are derived. Actually these equations can also be derived from a general forced parametrically excited gyroscopic system. Thus, to analyze such system, a method of multiple scales is developed firstly, where a general procedure is proposed to establish solvability conditions. Subsequently, this procedure is applied to obtain the analytical instability boundaries and forced vibration responses. The analytical results show that the additional combination instability regions are created due to the introduction of shunt circuit. When the parametrically excited eccentric rotor is rotating, the parametric vibrations are superimposed on the unbalanced responses. As the resistance value of shunt circuit is increasing, both parametric vibrations and unbalance vibrations can be significantly suppressed. For the unbalanced responses, both the resonance and anti-resonance phenomena can be observed; whereas for the parametric vibrations, only the resonance phenomena exist. These phenomena indicate that we may achieve great vibration control performance for the rotor parametric vibrations by introducing the piezoelectric shunt damping, as long as the circuit parameters are well adjusted. To validate the obtained analytical expressions, the numerical methods are applied. Specifically, the discrete state transition matrix method (DSTM) is applied to validate the analytical instability boundaries and the Runge-Kutta method is conducted to verify the analytical frequency response functions.