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.

在本文中，研究了具有机电耦合边界条件的转子系统在周期性轴向载荷下的动态行为，其中边界条件源自为转子系统的振动控制而开发的环形压电阻尼器。该阻尼器基于压电并联阻尼技术，可产生或多或少的阻尼性能取决于并联电路参数的选择。利用假设模态法和拉格朗日方程，推导出运动方程。实际上，这些方程也可以从一般的强制参量激励陀螺系统推导出来。因此，为了分析这样的系统，首先开发了一种多尺度的方法，其中提出了建立可解性条件的一般程序。随后，该程序用于获得解析不稳定边界和受迫振动响应。分析结果表明，由于引入了分流电路，产生了额外的组合不稳定区域。当参量激励偏心转子旋转时，参量振动叠加在不平衡响应上。随着并联电路电阻值的增加，参数振动和不平衡振动都可以得到显着抑制。对于不平衡的响应，可以观察到共振和反共振现象；而对于参数振动，只存在共振现象。这些现象表明我们可以通过引入压电分流阻尼来实现转子参数振动的良好振动控制性能，只要电路参数调整好。为了验证获得的解析表达式，应用了数值方法。具体而言，离散状态转移矩阵法 (DSTM) 用于验证解析不稳定边界，并进行 Runge-Kutta 方法来验证解析频率响应函数。