金属/陶瓷功能梯度悬臂板的振动抑制研究

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振动与冲击 ›› 2022, Vol. 41 ›› Issue (20) : 185-194.

论文

金属/陶瓷功能梯度悬臂板的振动抑制研究

吕书锋1，李宏洁1，张伟2，宋晓娟3

作者信息 +

Vibration suppression of a cermet functional gradient cantilevered plate

L Shufeng1,LI Hongjie1,ZHANG Wei2,SONG Xiaojuan3

Author information +

文章历史 +

摘要

提出了一种抑制功能梯度材料（functionally graded material ，FGM）悬臂板振动的鲁棒控制方法。悬臂板的材料性能沿厚度方向按体积分数幂律进行梯度分布。采用经典层合板理论、一阶活塞气动力理论、Hamilton原理和Galerkin方法，推导气动力作用下功能梯度悬臂板的动力学方程。为了抑制板的振动，将压电片贴在FGM悬臂板的上下表面分别作为作动器与传感器，利用压电片的正逆压电效应，设计状态反馈控制器，引入全维状态观测器，形成功能梯度悬臂板动力学控制系统的闭环回路。在控制方案上，除了采用鲁棒控制方法外，还采用了线性二次型最优控制(linear quadratic regulator ，LQR)方法对振动抑振效果进行对比分析。采用数值方法研究了体积分数指数和长宽比对FGM悬臂板振动特性的影响。通过比较不同体积分数指数、长宽比、温度以及参数不确定条件下的时间历程图和控制电压图，验证所提控制器的有效性和准确性。
关键词：功能梯度材料(FGM)；悬臂板；气动力；振动抑制；全维状态观测器

Abstract

A robust control method is proposed to suppress the vibration of functionally graded material (FGM) cantilever plate subjected to aerodynamic forces. The material properties of the cantilever plate are distributed graded in the thickness direction according to a volume fraction power law. Based on classical plate theory, first order piston theory, Hamilton principle and Galerkin method, the dynamic equations of functionally graded cantilever plate subjected to aerodynamic forces is derived. To suppress vibration, piezoelectric patches are used as actuators and sensors that are attached to the upper and lower surfaces of the FGM cantilever plate. Based on the positive and negative piezoelectric effects of the piezoelectric plates, a state feedback controller is designed, and a full-dimensional state observer is introduced to form a closed loop of the dynamic control system of functionally graded cantilever plate. Besides the proposed robust control method, the linear quadratic regulator (LQR) is also studied, and the vibration suppression effect of the two methods is analyzed. The effects of volume fraction index and aspect ratio on the dynamic behavior of the FGM cantilever plates are studied. The effectiveness and accuracy of the proposed controller are verified by comparing the time history diagrams and control voltage diagrams under different conditions including the volume fraction index, aspect ratio and temperature and parameter uncertainty.
Key words：functionally graded material(FGM)；cantilever plate；aerodynamics force；vibration suppression；full-dimensional state observer

导出引用

吕书锋1，李宏洁1，张伟2，宋晓娟3. 金属/陶瓷功能梯度悬臂板的振动抑制研究[J]. 振动与冲击, 2022, 41(20): 185-194

L Shufeng1,LI Hongjie1,ZHANG Wei2,SONG Xiaojuan3. Vibration suppression of a cermet functional gradient cantilevered plate[J]. Journal of Vibration and Shock, 2022, 41(20): 185-194

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