Vibration suppression of a cermet functional gradient cantilevered plate

PDF(2209 KB)

Journal of Vibration and Shock ›› 2022, Vol. 41 ›› Issue (20) : 185-194.

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

Author information +

History +

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

Key words

functionally graded material(FGM) / cantilever plate / aerodynamics force / vibration suppression / full-dimensional state observer

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

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

References

[1] 尹硕辉，余天堂，刘鹏. 基于等几何有限元法的功能梯度板自由振动分析[J]. 振动与冲击，2013，32(24)：180-186.
YIN Shuohui, YU Tiantang, LIU Peng. Free vibration analysis of functionally graded plates using isogeometric finite element method [J]. Journal of Vibration and Shock, 2013，32（24）：180-186.
[2] 周凤玺，李世荣. 功能梯度材料矩形板的三维静动态响应分析[J]. 力学学报，2010，42(2)：325-331.
ZHOU Fengxi, LI Shirong. Three-dimensional analysis for static bending and fre evibration of functionally graded rectangular plate [J]. Chinese Journal of Theoretical and Applied Mechanics, 2010，42(2)：325-331.
[3] YANG J, SHEN H S. Dynamic response of initially stressed functionally graded rectangular thin plates[J]. Composite Structures, 2001, 54(4)：497-508.
[4] YANG J, SHEN H S. Vibration characteristics and transient response of shear deformable functionally graded plates in thermal environment[J]. Journal of Sound and Vibration, 2002, 255(3)：579-602.
[5] HUANG X L, SHEN H S. Vibration and dynamic response of functionally graded plates with piezoelectric actuators in thermal environments[J]. Journal of Sound and Vibration, 2006, 289 (1)：25-53.
[6] ZHANG J, LI T Y, ZHU X. Free vibration analysis of FGM plates based on Rayleigh-Ritz method[J]. Vibroengineering Procedia, 2018，21：53-58.
[7] KATILI I， BATOZ J L, MAKNUN I J, et al. On static and free vibration analysis of FGM plates using an efficient quadrilateral finite element based on DSPM[J]. Composite Structures, 2021，261：113514.
[8] TALHA M, SINGH B N. Stochastic vibration characteristics of finite element modelled functionally gradient plates[J]. Composite Structures, 2015, 130：95-106.
[9] 王忠民, 邹德志. 面内平动功能梯度斜板的主动振动控制[J]. 振动与冲击, 2016, 35(15): 86-92.
WANG Zhongmin, ZOU Dezhi. Active vibration control of in-plane translating skew plate made of functionally graded materials [J]. Journal of Vibration and Shock, 2016, 35(15): 86-92.
[10] 张博, 丁虎, 陈立群. 基于压电纤维复合材料的旋转叶片主动控制[J]. 力学学报, 2021, 53(4):1093-1102.
ZHANG Bo, DING Hu, CHEN Liqun. Active vibration control of a rotating blade based on macro fiber composite [J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(4)：1093-1102.
[11] 唐冶, 王涛, 丁千. 主动控制压电旋转悬臂梁的参数振动稳定性分析[J].力学学报, 2019, 51(6):1872-1881.
TANG Ye, WANG Tao, DING Qian. Stability analysis on parametric vibration of piezoelectric rotating cantilever beam with active control [J].
Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(6)：1872-1881.
[12] 刘涛, 汪超, 刘庆运，等. 基于等几何方法的压电功能梯度板动力学及主动振动控制分析[J]. 工程力学, 2020，37(12)：228-242.
LIU Tao, WANG Chao, LIU Qingyun, et al. Analysis for dynamic and active vibration control of piezoelectric functionally graded plates based on isogeometric method [J]. Engineering Mechanics, 2020，37(12)：228-242.
[13] 沐旭升,邹奇彤,黄锐,等.体自由度颤振主动抑制的多输入/多输出自抗扰控制律设计[J].振动工程学报,2020,33(5)：910-920.
MU Xusheng, ZOU Qitong, HUANG Rui, et al. Design of multiple-input/multiple-output active disturbance rejection controller for body-freedom flutter suppression [J]. Journal of Vibration Engineering, 2020,33(5)：910-920.
[14] LIU T, LI C D, WANG C, et al. A simple-FSDT-based isogeometric method for piezoelectric functionally graded plates[J]. Mathematics, 2020, 8(12)：2177-2177.
[15] ZORIĆ N D, TOMOVIĆ A M, OBRADOVIĆ A M, et al. Active vibration control of smart composite plates using optimized self-tuning fuzzy logic controller with optimization of placement, sizing and orientation of PFRC actuators[J]. Journal of Sound and Vibration, 2019, 456：173-198.
[16] LI J Q, XUE Y, LI F M, et al. Active vibration control of functionally graded piezoelectric material plate[J]. Composite Structures, 2018, 207：509-518.
[17] HE X Q, NG T Y, SIVASHANKER S, et al. Active control of FGM plates with integrated piezoelectric sensors and actuators[J]. Computational Mechanics, 2003, 31(9)：350-358.
[18] BENDINE K, BOUKHOULDA F B, HADDAG B, et al. Active vibration control of composite plate with optimal placement of piezoelectric patches[J]. Mechanics of Advanced Materials and Structures, 2019, 26(4)：341-349.
[19] XUE Y, LI J Q, LI F M, et al. Active control of plates made of functionally graded piezoelectric material subjected to thermo-electro-mechanical loads[J]. International Journal of Structural Stability and Dynamics, 2019, 19(9)：377-389.
[20] TIAN J, GUO Q, SHI G. Laminated piezoelectric beam element for dynamic analysis of piezolaminated smart beams and GA-based LQR active vibration control[J]. Composite Structures, 2020, 252： 112480.
[21] HU J, ZHAN K. Topological design of piezoelectric actuator layer for linear quadratic regulator control of thin-shell structures under transient excitation[J]. Smart Materials and Structures, 2019, 28(9)：？.
[22] SONG Z G, LI F M, CARRERA E, et al. A new method of smart and optimal flutter control for composite laminated panels in supersonic airflow under thermal effects[J]. Journal of Sound and Vibration, 2018, 414：218 -232.
[23] SUSHEEL C K, SHARMA A, KUMAR R, et al. Geometrical nonlinear characteristics of functionally graded structure using functionally graded piezoelectric materials[J]. Journal of Sandwich Structures and Materials, 2020, 22(2)：370-401.
[24] SHEN H S. Functionally graded materials: nonlinear analysis of plates and shells[M]. New York：CRC Press, 2009.
[25] REDDY J N. Mechanics of laminated composite plates and shells theory and analysis[M]. New York：CRC Press, 2004.
[26] NADER J. Piezoelectric-based vibration control from macro to micro/nanoscale systems[M]. New York：Springer, 2010.
[27] RAHMANI B, SHENAS A G. Robust vibration control of laminated rectangular composite plates in hygrothermal and thermal environment[J]. Composite Structures. 2017, 179：665-681.
[28] LU S F, JIANG Y, ZHANG W, et al. Vibration suppression of cantilevered piezoelectric laminated composite rectangular plate subjected to aerodynamic force in hygrothermal environment[J]. European Journal of Mechanics / A Solids， 2020, 83：104002.
[29] FULLER C R, ELLIOTT S J, NELAON P A. Active Control of Vibration[M]. New York：Elsevier, 2014.