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Finite Element Model of Vibration Control for an Exponential Functionally Graded Timoshenko Beam with Distributed Piezoelectric Sensor/Actuator

1
Laboratory of Advanced Materials Studies and Applications, FS-EST, Moulay Ismail University, Meknes 50000, Morocco
2
National School of Applied Sciences, Mohammed Premier University, Oujda 60050, Morocco
3
National School of Applied Sciences, Abdelmalek Essaadi University, Tétouan 93030, Morocco
*
Author to whom correspondence should be addressed.
Actuators 2019, 8(1), 19; https://doi.org/10.3390/act8010019
Received: 26 December 2018 / Revised: 18 February 2019 / Accepted: 21 February 2019 / Published: 26 February 2019
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Abstract

This paper presents a dynamic study of sandwich functionally graded beam with piezoelectric layers that are used as sensors and actuators. This study is exploited later in the formulation of the active control laws, while using the optimal control Linear Quadratic Gaussian (LQG), accompanied by the Kalman filter. The mathematical formulation is based on Timoshenko’s assumptions and the finite element method, which is applied to a flexible beam divided into a finite number of elements. By applying the Hamilton principle, the equations of motion are obtained. The vibration frequencies are found by solving the eigenvalue problem. The structure is analytically then numerically modeled and the results of the simulations are presented in order to visualize the states of their dynamics without and with active control. View Full-Text
Keywords: functionally graded materials; piezoelectricity; vibration; Timoshenko’s beam; LQG-Kalman control functionally graded materials; piezoelectricity; vibration; Timoshenko’s beam; LQG-Kalman control
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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El Harti, K.; Rahmoune, M.; Sanbi, M.; Saadani, R.; Bentaleb, M.; Rahmoune, M. Finite Element Model of Vibration Control for an Exponential Functionally Graded Timoshenko Beam with Distributed Piezoelectric Sensor/Actuator. Actuators 2019, 8, 19.

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