Vibration Control of Macro and Micro Mechanical Systems With Piezoelectric Transducers

介绍了利用压电式换能器进行振动控制的方法。基于考虑机电耦合的振动系统的有限元表达式，推导了离散后的运动方程。在此基础上，利用模态分析建立了相应的电气等效电路模型。对于假设为一维振动系统的有压电体和无压电体的简单振子，进行了一些数值演示。结果表明，基于等效模型的解与解析解吻合较好。然后，对假定为二维的简单悬臂梁进行了被动减振控制。为了评估减振效果，根据等效电路的电路参数计算了损耗因数。对于有效的减振，存在连接到压电式换能器电极上的电阻的最佳值。结果表明，悬臂梁与换能器之间的粘结层是产生减振的主要原因。最后，对悬臂梁系统进行了主动控制。为了评价系统的稳定性，基于等效电路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执行器的放大系数和力系数决定。换言之，传感器和执行器位置的选择对于稳定的反馈控制是非常重要的。我们的下一个项目可能是通过与实验的比较来验证该模型。

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.