Vibration control of FGM plate using optimally placed piezoelectric patches


  • Zouaoui SATLA Tissemsilt University, Dept. of Sciences and Technologies
  • Lakhdar Boumia Ahmed Ben Yahia El Wancharissi University – Tissemsilt
  • Mohamed Kherrab Ahmed Ben Yahia El Wancharissi University – Tissemsilt



functionally graded material, piezoelectric, Actuator, Sensor, LQR controller


The aim of this study is to propose a methodology to actively control the vibration of functionally graded plates, with the help of piezoelectric actuators and sensors. The study relays on the classical plate theory to analytically formulate the governing equation of motion, which is then expanded to derive a space state equation of the model. The material properties of the FG plate are assumed to vary along the thickness direction. In order to improve the damping effectiveness, the location of the piezoelectric sensors and actuators is optimally determined using the H2 norm. The necessary control voltage was determined based on optimal LQR and LQG controllers.


K. Bendine et al., Active vibration control of composite plate with optimal placement of piezoelectric patches, Mechanics of Advanced Materials and Structures 26 (2019) 341,

K. Bendine et al., Active vibration control of functionally graded beams with piezoelectric layers based on higher order shear deformation theory, Earthquake Engineering and Engineering Vibration 15 (2016) 611,

G. R. Liu and J. Tani, Surface Waves in Functionally Gradient Piezoelectric Plates, Journal of Vibration and Acoustics 116 (1994) 440,

G. Liu et al., Dispersion of waves and characteristic wave surfaces in functionally graded piezoelectric plates, Journal of Sound and Vibration 268 (2003) 131,

H.-T. Thai and D.-H. Choi, A simple first-order shear deformation theory for the bending and free vibration analysis of functionally graded plates, Composite Structures 101 (2013) 332,

V. Dogan, Nonlinear vibration of FGM plates under random excitation, Composite Structures 95 (2013) 366,

A. H. Baferani, A. R. Saidi, and E. Jomehzadeh, An exact solution for free vibration of thin functionally graded rectangular plates, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 225 (2011) 526,

A. Preumont, Vibration Control of Active Structures: An Introduction, Mathematics and Its Applicatio (Kluwer Academic Publishers, 1997),

V. Fakhari and A. Ohadi, Active robust control of geometrically nonlinear vibration of FGM plate with piezoelectric sensor/ actuator layers, 16th International Congress on Sound and Vibration 3 (2009) 1472

A. H. N. Shirazi, H. Owji, and M. Rafeeyan, Active Vibration Control of an FGM Rectangular Plate using Fuzzy Logic Controllers, Procedia Engineering 14 (2011) 3019,

K. Liew, X. He, and S. Meguid, Optimal shape control of functionally graded smart plates using genetic algorithms, Computational Mechanics 33 (2004) 245,

M. H. Kargarnovin, M. M. Najafizadeh, and N. S. Viliani, Vibration control of a functionally graded material plate patched with piezoelectric actuators and sensors under a constant electric charge, Smart Materials and Structures 16 (2007) 1252,

M. Yiqui and F. Yiming, Nonlinear dynamic response and active vibration control for piezoelectric functionally graded plate, Journal of Sound and Vibration 329 (2010) 2015,

W. Liu, Z. Hou, and M. A. Demetriou, A computational scheme for the optimal sensor/actuator placement of flexible structures using spatial H2 measures, Mechanical Systems and Signal Processing 20 (2006) 881,

A. A. Rader et al., Optimization of Piezoelectric Actuator Configuration on a Flexible Fin for Vibration Control Using Genetic Algorithms, Journal of Intelligent Material Systems and Structures 18 (2007),

D. Halim and S. Reza Moheimani, An optimization approach to optimal placement of collocated piezoelectric actuators and sensors on a thin plate, Mechatronics 13 (2003) 27,

K. Bendine et al., Active Vibration damping of Smart composite beams based on system identification technique, Curved and Layered Structures 5 (2018) 43,

Z. cheng Qiu et al., Optimal placement and active vibration control for piezoelectric smart flexible cantilever plate, Journal of Sound and Vibration 301 (2007) 521,

V. Birman, Plate structures, vol. 178 (Springer Science & Business Media, 2011)

S. R. Moheimani and A. J. Fleming, Piezoelectric transducers for vibration control and damping, vol. 1 (Springer, 2006)

K. Bendine et al., Structural modeling and active vibration control of smart FGM plate through ANSYS, International Journal of Computational Methods 14 (2017) 1750042.




How to Cite

Z. SATLA, L. . Boumia, and M. . Kherrab, “Vibration control of FGM plate using optimally placed piezoelectric patches”, Rev. Mex. Fís., vol. 70, no. 1 Jan-Feb, pp. 011002 1–, Jan. 2024.