Vibration damping of piezo actuating composite beams based on the multi-objective genetic algorithm

Document Type : Research Article

Authors

1 Department of Mechanical Engineering, Sirjan University of Technology, Sirjan, Iran

2 Department of Design and Manufacture, Shaid Bahonar Copper Industries Co. (CSP), Kerman, Iran

3 Department of Mechanical Engineering, Takestan branch, Islamic Azad University, Takestan, Iran

Abstract

In this work, a multi-objective optimization process based on the genetic algorithm is employed to damp the vibrations of a piezo actuating composite beam. A new mathematical model for the control effort is proposed and optimized with two objective functions. Conflicting objectives are considered as the displacement of the beam and the second derivative of the control voltage. The coefficients of the proposed control voltage model are regarded as the design variables for this optimization process. The corresponding Pareto front represents non-dominated optimum solutions with different choices to designers. The time behaviors of displacement, velocity and acceleration as well as the related control effort at the midpoint of the beam for three optimum design points are illustrated. The simulation of the time responses of a selected optimum point exhibits the advantage of the planned optimum strategy with regard to those stated in some research such as the cases used in the maximum principle for the same structure.

Highlights

  • A new control model is proposed to damp vibrations of a piezo actuating beam.
  • A multi-objective algorithm is applied to optimize the model with two objective functions.
  • The corresponding Pareto front is represented to display non-dominated optimum solutions.
  • Results reveal advantages of the strategy compared with the maximum principle method.

Keywords

Main Subjects

References

[1] H.T. Banks, R.C. Smith, Y. Wang, Smart material structures- Modeling, estimation and control(Book), Chichester, United Kingdom and New York/Paris: John Wiley & Sons/Masson, 1996., (1996).
[2] A. Preumont, Vibration control of active structures: an introduction, Springer, 2002.
[3] H.S. Tzou, H.Q. Fu, A study of segmentation of distributed piezoelectric sensors and actuators, part II: parametric study and active vibration controls, Journal of Sound and Vibration, 172 (1994) 261-275.
[4] C.-K. Lee, Theory of laminated piezoelectric plates for the design of distributed sensors/actuators. Part I: Governing equations and reciprocal relationships, The Journal of the Acoustical Society of America, 87 (1990) 1144-1158.
[5] P. Gaudenzi, R. Carbonaro, E. Benzi, Control of beam vibrations by means of piezoelectric devices: theory and experiments, Composite structures, 50 (2000) 373-379.
[6] M.C. Ray, Optimal control of laminated plate with piezoelectric sensor and actuator layers, AIAA journal, 36 (1998) 2204-2208.
[7] Z.-c. Qiu, X.-m. Zhang, H.-x. Wu, H.-h. Zhang, Optimal placement and active vibration control for piezoelectric smart flexible cantilever plate, Journal of Sound and Vibration, 301 (2007) 521-543.
[8] P. Gardonio, S.J. Elliott, Modal response of a beam with a sensor–actuator pair for the implementation of velocity feedback control, Journal of sound and vibration, 284 (2005) 1-22.
[9] D.J. Inman, Active modal control for smart structures, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 359 (2001) 205-219.
[10] I. Sadek, I. Kucuk, E. Zeini, S. Adali, Optimal boundary control of dynamics responses of piezo actuating micro-beams, Applied Mathematical Modelling, 33 (2009) 3343-3353.
[11] A. Baz, Boundary control of beams using active constrained layer damping, (1997).
[12] T. Kaizuka, N. Tanaka, Active boundary control of a rectangular plate using smart modal sensors, Smart materials and structures, 15 (2006) 1395.
[13] C. Hwu, W.C. Chang, H.S. Gai, Vibration suppression of composite sandwich beams, Journal of sound and vibration, 272 (2004) 1-20.
[14] B.P. Baillargeon, S.S. Vel, Active vibration suppression of sandwich beams using piezoelectric shear actuators: experiments and numerical simulations, Journal of intelligent material systems and structures, 16 (2005) 517-530.
[15] G.E. Stavroulakis, G. Foutsitzi, E. Hadjigeorgiou, D. Marinova, C.C. Baniotopoulos, Design and robust optimal control of smart beams with application on vibrations suppression, Advances in Engineering Software, 36 (2005) 806-813.
[16] N. Vahdati, S. Heidari, A novel semi-active fluid mount using a multi-layer piezoelectric beam, Journal of Vibration and Control, 16 (2010) 2215-2234.
[17] S. Raja, A.A. Pashilkar, R. Sreedeep, J.V. Kamesh, Flutter control of a composite plate with piezoelectric multilayered actuators, Aerospace Science and Technology, 10 (2006) 435-441.
[18] J.-H. Han, J. Tani, J. Qiu, Active flutter suppression of a lifting surface using piezoelectric actuation and modern control theory, Journal of Sound and Vibration, 291 (2006) 706-722.
[19] I. Bruant, L. Proslier, Improved active control of a functionally graded material beam with piezoelectric patches, Journal of Vibration and Control, 21 (2015) 2059-2080.
[20] I. Kucuk, K. Yildirim, I. Sadek, S. Adali, Optimal control of a beam with Kelvin–Voigt damping subject to forced vibrations using a piezoelectric patch actuator, Journal of Vibration and Control, 21 (2015) 701-713.
[21] K. Chandrashekhara, P. Donthireddy, Vibration suppression of composite beams with piezoelectric devices using a higher order theory, (1997).
[22] C.-Y. Hsu, C.-C. Lin, L. Gaul, Vibration and sound radiation controls of beams using layered modal sensors and actuators, Smart Materials and Structures, 7 (1998) 446.
[23] M.-H. Kim, Simultaneous structural health monitoring and vibration control of adaptive structures using smart materials, Shock and Vibration, 9 (2002) 329-339.
[24] E.S. Nehru, Axisymmetric Vibration of Piezo-Lemv Composite Hollow Multilayer Cylinder, International Journal of Mathematics and Mathematical Sciences, 2012 (2012).
[25] X. Xue, J. Tang, Vibration control of nonlinear rotating beam using piezoelectric actuator and sliding mode approach, Journal of Vibration and Control, 14 (2008) 885-908.
[26] B. Sahoo, P.K. Panda, Fabrication of simple and ring-type piezo actuators and their characterization, Smart Materials Research, 2012 (2012).
[27] G. Zenz, A. Humer, Enhancement of the stability of beams with piezoelectric transducers, Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 227 (2013) 744-751.
[28] M.J. Shirazi, H. Salarieh, A. Alasty, R. Shabani, Tip tracking control of a micro-cantilever Timoshenko beam via piezoelectric actuator, Journal of Vibration and Control, 19 (2013) 1561-1574.
[29] A. Lara, J.C. Bruch Jr, J.M. Sloss, I.S. Sadek, S. Adali, Vibration damping in beams via piezo actuation using optimal boundary control, International Journal of Solids and Structures, 37 (2000) 6537-6554.
[30] J.M. Sloss, J.C. Bruch, I.S. Sadek, S. Adali, Maximum principle for optimal boundary control of vibrating structures with applications to beams, Dynamics and Control, 8 (1998) 355-375.
[31] M. Collet, V. Walter, P. Delobelle, Active damping of a micro-cantilever piezo-composite beam, Journal of Sound and Vibration, 260 (2003) 453-476.
[32] G. Ha, J.M. Hale, Sensitivity of piezoelectric sensors fabricated with various types of commercial PZT powder, Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 227 (2013) 363-366.
[33] A.P. Parameswaran, K.V. Gangadharan, Parametric modeling and FPGA based real time active vibration control of a piezoelectric laminate cantilever beam at resonance, Journal of Vibration and Control, 21 (2015) 2881-2895.
[34] L. Xu, S. Du, Dynamic analysis of a short cylinder piezo motor, Journal of Mechanical Science and Technology, 28 (2014) 2953-2961.
[35] J.E. Kim, Dedicated algorithm and software for the integrated analysis of AC and DC electrical outputs of piezoelectric vibration energy harvesters, Journal of Mechanical Science and Technology, 28 (2014) 4027-4036.
[36] R. Rao, Displacement characteristics of a piezoactuator-based prototype microactuator with a hydraulic displacement amplification system, Journal of Mechanical Science and Technology, 29 (2015) 4817-4822.
[37] M. Chung, J. Kim, S. Kim, G. Sung, J. Lee, Effects of hydraulic flow and spray characteristics on diesel combustion in CR direct-injection engine with indirect acting Piezo injector, Journal of Mechanical Science and Technology, 29 (2015) 2517-2528.
[38] L. Xu, J. Xing, Forced response of the inertial piezoelectric rotary motor to electric excitation, Journal of Mechanical Science and Technology, 29 (2015) 4601-4610.
[39] T. Kwon, K.-S. Shin, M. Hyung, K. Eom, T.S. Kim, Fabrication of piezoelectric thick films for development of micromechanical cantilevers, Journal of Mechanical Science and Technology, 29 (2015) 3351-3356.
[40] W. Chen, Y. Cao, J. Xie, Piezoelectric and electromagnetic hybrid energy harvester for powering wireless sensor nodes in smart grid, Journal of Mechanical Science and Technology, 29 (2015) 4313-4318.
[41] A.A. Atai, D. Lak, Analytic investigation of effect of electric field on elasto-plastic response of a functionally graded piezoelectric hollow sphere, Journal of Mechanical Science and Technology, 30 (2016) 113-119.
[42] K.-F. Man, K.-S. Tang, S. Kwong, Genetic algorithms: concepts and applications [in engineering design], IEEE transactions on Industrial Electronics, 43 (1996) 519-534.
 
Journal of Theoretical and Applied Vibration and Acoustics
Volume 6, Issue 2
July 2020
Pages 325-336

Files

Share

How to cite

Statistics