压电悬臂梁振动的模态控制

Mode control of vibration in piezoelectric cantilever beam

结合有限元分析方法与模态控制来抑制悬臂梁的振动.采用有限元分析方法研究悬臂梁的动态特性,建立其动力方程.在悬臂梁振动时应力最大或次最大处的上、下表面同位配置压电片,作为抑制悬臂梁振动的致动器.基于模态控制方法,设计了模态传感器和模态致动器.采用模态速度负反馈进行反馈控制,以此计算出各个作为致动器的压电片的控制电压,以抑制悬臂梁的振动.通过算例进行数值仿真,结果表明,以此方法布置压电片和输入控制电压,能迅速抑制悬臂梁的振动,可单独或同时控制几阶模态振动.

Active vibration control for a cantilever beam was studied based on the combination between finite element analysis (FEA) and modal control. Dynamical characteristics of the cantilever beam were analyzed and its dynamical equation was developed by using FEA. Piezoelectric elements were pasted on/under the cantilever beam where stress was the maximum or sub-maximum as actuators to control the vibration of the cantilever beam. Based on the modal control, modal sensors and modal actuators were designed. Negative mode velocity feedback was adopted and the control voltage applied to each piezoelectric element acting as actuator was calculated to control the vibration of the beam. Simulation results show that the vibration of the beam can be suppressed rapidly by applying voltage to the piezoelectric patches displaced in this way, and single mode vibration and multi-mode vibration can be controlled simultaneously.