Using S/A Piezoelectric Patches for Vibration Damping of Timoshenko Beam Based on Fuzzy-GA Controller Design

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Reference
[1] M.Ebrahimnejad, M.Davaoodi, J.Vaseghi-Amiri, Active Vibration Control of Smart Building
Frames by Feedback Controllers, Vol.1, No.1, pp.73-83, 2010.
[2] J.Arushankar, M.Umapathy, D.Ezhilarasi, Sliding-Mode Controller with Multisensory Data
Fusion for Piezo-Actuated Structure, Vol.61, No.4, pp.346-353, 2011.
[3] N.Ghareeb, R. Schmitdt, Design and Implementation of Linear Controller on Reduced Model of a
Smart Structure, 4th
ECCOMAS the Matic Conference on Computational Methods in Structural Dynamic
and Earthquake Engineering, 2013.
[4]M.Sridevi, P.Madhavasarma, Model Identification and Smart Structural Vibration Control using
Controller, Vol.3, No.4, International Journal on Smart Sensing and Intelligent Systems.
! " # 789 :8 3 = < 7
A > / ? @ < 7
B ?
C ?
A . 6 B .
D 9 . ? .
z
E
CD A . ?
E F
t G
G u ! +6
! +H , G& I&# J 3
K J 3
y(t) > / A
! +6 ,
K 1 /.
K LCA
M
y

25
[5] T.C.Manjunath, B.Bandyopadyay, Controller Design for Euler-Bernoulli Smart Structures using
Robust Decentralized POF via Reduced Order Modeling, International Journal of Mechanical,
Aerospace, Industrial and Mechatronics Engineering, Vol.1, No.6, 2007.
[6] L.R.Karlmax, M.Umapathy, D.Ezhilarasi, Embedded Output Feedback Controllers for Piezoelectric
Actuated Structures , World Journal of Modeling Simulation, Vol.5,No.2,pp.113-119, 2009.
[7] H.Furuya, Placing Actuators on Space Structures by Genetic Algorithms and Effectiveness Indices,
Structural Optimization, Springer-rerlag, 9, 69-75, 1995.
[8] G.L.C.M.de Abreu, S.M.da Conceicao, V.Lopes Jr, M.J.Brennan, M.T.S.Alves, System
Identification and Active Vibration Control of a Flexible Structure, Journal of ASME, Special Issue 2012.
[9]V.Sethi, G.Song, Optimal Vibration Control of a Modal Frame Structure Using Piezoceramic Sensors
and Actuators, Journal of Vibration and Control, 2005.
[10] Y.Yun, Y.Li, Active Vibration Control Based on a 3-DOF Dual Complaint Parallel Robot Using
LQR Algorithm, IEEE/RSJ International Conference on Intelligent Robots and Systems, 2009.
[11] J.Zhang, L.He, E.Wang, R.Gao, A LQR Controller Design for Active Vibration Control of
Flexible Structures, IEEE Pacific-Asia Workshop on Computational Intelligence and Industrial
Application, 2008.
[12] S.B.Choi, S.R.Hong, Active Vibration Control of a Flexible Structure Using an Inertial Type
Piezoelectric Mount, Smart Materials and Structures, 16(2007)25-35, DOI:10.1088/0964-1726/16/1/003
[13]T.C.Manjunath, B.B.Yopadhyay, Vibration Control of a Smart Flexible Cantilever Beam using
Periodic Output Feedback, Asian Journal of Control,Vol.6, No.1, pp.74-87, Mar, 2004.
[14] T.C.Manjunath, B.Bandyopadhyay, Vibration Control of Timoshenko Smart Structures
Using Multirate Output Feedback Based Discrete Sliding Mode Control for SISO systems,
Journal of Sound and Vibration, 326(2009)50-74.
[15]J.M.S.Moit , I.F.P.Coreia, C.M.M.Soares, C.A.M.Soares, Active Control of Adaptive Laminated
Structures with Bonded Piezoelectric Sensors and Actuators, Computers & structures, Vol.82, pp.1349-
1358, 2004.
[16]D.Chhabra, P.Chandna, G.Bhushan, Design and Analysis of Smart Structures for Active Control
using Piezo-Crystals, International Journal of Engineering and Technology, Vol.1, No.3, December,
2011.
[17] http://image.frompo.com/b8e9519f44afaedbd3c09d722f39af40
Using S/A Piezoelectric Patches for Vibration Damping of Timoshenko Beam
Based on Fuzzy-GA Controller Design
M.Hasanlou1
, M.Siavash 2
, A.Bagheri 3
, F.Najafi 4
MS Graduate Student Mechanical Engineering, University of Guilan, Iran

26
MS Graduate Student Mechanical Engineering, University of Guilan, Iran
Professor of Mechanical Engineering, University of Guilan, Iran
Associate Professor of Mechanical Engineering, University of Guilan, Iran
The life of an engineering structure in each industry is a major factor for maintenance of
equipment. The structure can be a beam, plate, shell, panel, or truss. The life of engineering
structures reduces due to vibration amplitude or the design for mechanical system can be far
from the goals of designers. In this study, a cantilever beam, which is turbulent based on
Timoshenko theory modeling and under external flexural force, simulates. In order to obtain
displacement of the beam, piezoelectric sensor is installed as a patch at bottom of the structure
and sends the incoming signal to the fuzzy controller. This controller is optimized based on
single objective genetic algorithm (GA). Then, the best signal is sent from controller to
piezoelectric actuator at the top and at the exact coordinate where the sensor is installed and
completes the control loop for vibration attenuation.
Keyword: Piezoelectric Patches, Vibration Damping, Timoshenko Beam, Fuzzy Controller, Genetic
Algorithm

Using S/A Piezoelectric Patches for Vibration Damping of Timoshenko Beam Based on Fuzzy-GA Controller Design

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Using S/A Piezoelectric Patches for Vibration Damping of Timoshenko Beam Based on Fuzzy-GA Controller Design