Vibration suppression of a cermet functional gradient cantilevered plate
L Shufeng1,LI Hongjie1,ZHANG Wei2,SONG Xiaojuan3
1. Department of Mechanics, Inner Mongolia University of Technology, Hohhot 010051, China;
2. Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Structures, Faculty of Materials and Manufacturing, Beijing University of Technology, Beijing 100124, China;
3. College of Mechanical Engineering, Inner Mongolia University of Technology, Hohhot 010051, China
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
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