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http://dx.doi.org/10.12989/sss.2015.15.5.1177

Optimal control and design of composite laminated piezoelectric plates  

ALamir, ALhadi E. (Department of Mathematics, Najran university)
Publication Information
Smart Structures and Systems / v.15, no.5, 2015 , pp. 1177-1202 More about this Journal
Abstract
The present paper is concerned with the optimal control and/or design of symmetric and antisymmetric composite laminate with two piezoelectric layers bonded to the opposite surfaces of the laminate, and placed symmetrically with respect to the middle plane. For the optimal control problem, Liapunov-Bellman theory is used to minimize the dynamic response of the laminate. The dynamic response of the laminate comprises a weight sum of the control objective (the total vibrational energy) and a penalty functional including the control force. Simultaneously with the active control, thicknesses and the orientation angles of layers are taken as design variables to achieve optimum design. The formulation is based on various plate theories for various boundary conditions. Explicit solutions for the control function and controlled deflections are obtained in forms of double series. Numerical results are given to demonstrate the effectiveness of the proposed control and design mechanism, and to investigate the effects of various laminate parameters on the control and design process.
Keywords
piezoelectric; actuators; minimizing the dynamic response; optimal design; composite laminated plates; plate theories;
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Times Cited By KSCI : 4  (Citation Analysis)
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1 Behjat, B. and Khoshravan, M.R. (2012), "Nonlinear analysis of functionally graded laminates considering piezoelectric effect", J. Mech. Sci. Technol., 26(8), 2581-2588.   DOI   ScienceOn
2 Fares, M.E., Youssif, Y.G. and Alamir, A.E. (2002), "Optimal design and control of composite laminated plates with various boundary conditions using various plate theories", Compos. Struct., 56(1), 1-12.   DOI
3 Foda, M.A. and Alsaif, K.A. (2012), "Vibration mitigation of composite laminated satellite solar panels using distributed piezoelectric patches", Smart Struct. Syst., 10(2), 111-130.   DOI
4 Frecker M.I. (2002), "A review of current research activities in optimization of smart structures and actuators", Smart Struct. Mater., 4693, 112-123.
5 Gabralyan, M.S. (1975), "About stabilization of mechanical systems under continuous forces", YGU Yervan, 2, 47-56.
6 Gupta, V., Sharma, M. and Thakur, N. (2011), "Mathematical modeling of actively controlled piezo smart structures: a review", Smart Struct. Syst., 8(3), 275-302.   DOI
7 Kapuria, S., Kumari, P. and Nath, J.K. (2010), "Efficient modeling of smart piezoelectric composite laminates: a review", Acta. Mech., 214, 31-48.   DOI
8 Kapuria, S. and Yaqoob, M. (2013), "Active vibration control of smart plates using directional actuation and sensing capability of piezoelectric composites", Acta. Mech., 224(6), 1185-1199.   DOI   ScienceOn
9 Khdeir, A.A. and Aldraihem, O.J. (2013), "Analytical investigation of laminated arches with extension and shear piezoelectric actuators", Eur. J. Mech. A - Solids, 37, 185-192.   DOI
10 Molter, A., da Silveira, O.A.A., Fonseca, J.S.O. and Bottega, V. (2010), "Simultaneous piezoelectric actuator and sensor placement optimization and control design of manipulators with flexible links using SDRE method", Math. Probl. Eng., 2010, 1-23.
11 Nanda, N. and Nath, Y. (2012), "Active control of delaminated composite shells with piezoelectric sensor/actuator patches", Struct. Eng. Mech., 42(2), 211-228.   DOI
12 Narwal, K. and Chhabra, D. (2012), "Analysis of simple supported plate for active vibration control with piezoelectric sensors and actuators", J. Mech. Civil. Eng., 1(1), 26-39.   DOI
13 Padula, S.L. and Kincaid, R.K. (1999), Optimization strategies for sensor and actuator placement, NASA/TM-1999-209126, NASA, Langley Research Center.
14 Qiu, Z.C., Zhang, X.M., Wu, H.X. and Zhang, HH. (2007), "Optimal placement and active vibration control for piezoelectric smart flexible cantilever plate", J. Sound Vib., 301, 521-543.   DOI   ScienceOn
15 Wang, J.Z., Wang, X.M. and Zhou, Y.H. (2012), "A wavelet approach for active-passive vibration control of laminated plates", Acta Mech Sinica, 28(2), 520-531.   DOI
16 Reece, P.L. (2007), Smart Materials And Structures: new research, Nova Science Publishers, New York, USA.
17 Sadek, I., Kucuk, I., Zeini, E. and Adali, S. (2009), "Optimal boundary control of dynamics responses of piezo actuating micro-beams", Appl. Math. Model., 33, 3343-3353.   DOI
18 Wang, J., Ding, G. and Qin, Y. (2007), Optimal Shape Control of Multilayered Piezoelectric Smart Plate Structure, Springer, Berlin, Germany.
19 Xu, B., Ou, J.P. and Jiang, J.S. (2013), "Integrated optimization of structural topology and control for piezoelectric smart plate based on genetic algorithm", Finite Elem. Anal. Des., 64, 1-12.   DOI
20 Zoric, N.D., Simonovic, A.M., Mitrovic, Z.S. and Stupar, S.N. (2013), "Optimal vibration control of smart composite beams with optimal size and location of piezoelectric sensing and actuation", J. Intel. Mat. Syst. Str., 24 (4), 499-526.   DOI