Vibration Control of Macro and Micro Mechanical Systems With Piezoelectric Transducers

提出了利用压电换能器进行振动控制的方法。在考虑机电耦合的振动系统有限元表达式的基础上，导出了系统的离散化运动方程。然后应用模态分析建立相应的等效电路模型。对一维振动系统中带压电和不带压电的简单振子进行了数值模拟。结果表明，基于等效模型的解与解析解吻合较好。然后对一个简单的二维悬臂梁进行了被动阻尼控制。为了评估阻尼效果，根据等效电路的电路参数计算损耗因子。对于有效阻尼，存在连接在压电换能器电极上的电阻的最佳值。研究发现，阻尼主要是由悬臂梁与换能器之间的粘接层引起的。最后对悬臂梁系统的主动控制进行了验证。为了评估系统的稳定性，在等效电路的基础上推导了反馈系统的传递函数。结果表明，系统的稳定性由传感器和作动器的放大系数和力系数决定。换句话说，传感器和执行器位置的选择对稳定反馈控制非常重要。我们的下一个项目可能是通过与实验的比较来验证模型。

The vibration control with piezoelectric transducer is presented. Based on the finite element expression for a vibration system with electromechanical coupling included, the discretized equation of motion is derived. Modal Analysis is then applied to develop the corresponding electrical equivalent circuit model. Some numerical demonstrations are made for simple vibrators with and without piezoelectricity, which are assumed to be one-dimensional vibratory systems. It is confirmed that the solutions based on the equivalent model well agree with the analytical ones. The passive damping control is then demonstrated for a simple cantilever beam which is assumed to be two-dimensional. To evaluate the damping effect, the loss factor is calculated based on the circuit parameters of the equivalent circuit. For effective damping, there is the optimum value of the electrical resister which is connected to the electrodes of the piezoelectric transducer. It is found that the damping is mainly caused due to the adhesive layer between the cantilever and the transducer. The active control is lastly demonstrated for the cantilever beam system. To evaluate the stability of the system, the transfer function for the feedback system is derived based on the equivalent circuit. It is shown that the stability of the system is determined by the amplification factor and the force factors of the sensor and the actuator. In other words, the choice of the position of the sensor and actuator is very important for the stable feedback control. Our next project could be to verify the model in comparison with the experiment.