Smart Structures and Systems

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Optimal placement of piezoelectric actuator/senor patches pair in sandwich plate by improved genetic algorithm

  • Amini, Amir (Department of Control, Faculty of Computer and Electrical Engineering, University of Kashan) ;
  • Mohammadimehr, Mehdi (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan) ;
  • Faraji, Alireza (Institute of Material and Energy, Iranian space research center)
  • Received : 2020.01.26
  • Accepted : 2020.10.18
  • Published : 2020.12.25
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Abstract

The present study investigates the employing of piezoelectric patches in active control of a sandwich plate. Indeed, the active control and optimal patch distribution on this structure are presented together. A sandwich plate with honeycomb core and composite reinforced by carbon nanotubes in facesheet layers is considered so that the optimum position of actuator/sensor patches pair is guaranteed to suppress the vibration of sandwich structures. The sandwich panel consists of a search space which is a square of 200 × 200 mm with a numerous number of candidates for the optimum position. Also, different dimension of square and rectangular plates to obtain the optimal placement of piezoelectric actuator/senor patches pair is considered. Based on genetic algorithm and LQR, the optimum position of patches and fitness function is determined, respectively. The present study reveals that the efficiency and performance of LQR control is affected by the optimal placement of the actuator/sensor patches pair to a large extent. It is also shown that an intelligent selection of the parent, repeated genes filtering, and 80% crossover and 20% mutation would increase the convergence of the algorithm. It is noted that a fitness function is achieved by collection actuator/sensor patches pair cost functions in the same position (controllability). It is worth mentioning that the study of the optimal location of actuator/sensor patches pair is carried out for different boundary conditions of a sandwich plate such as simply supported and clamped boundary conditions.

Keywords

Acknowledgement

The authors would like to thank the referees for their valuable comments. Also, they are thankful to the University of Kashan for supporting this work by Grant No. 891238/8 and the Iranian Nanotechnology Development Committee for their financial support.

References

  1. Aglietti, G.S., Langley, R.S., Rogers, E. and Gabriel, S.B. (2004), "Model building and verification for active control of microvibrations with probabilistic assessment of the effects of uncertainties", Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci., 218, 389-399. https://doi.org/10.1177/095440620421800404.
  2. AkhavanAlavi, S.M., Mohammadimehr, M. and Edjtahed, S.H. (2019), "Active control of micro Reddy beam integrated with functionally graded nanocomposite sensor and actuator based on linear quadratic regulator method", Eur. J. Mech. A Solids, 74, 449-461. https://doi.org/10.1016/j.euromechsol.2018.12.008.
  3. Alipour, A. and Zareian, F. (2008), "Study Rayleigh damping in structures; unceratinties and treatments", Proceedings of the 14th World Conference on Earthquake Engineering, Beijing, China, October.
  4. Amini, A., Mohammadimehr, M. and Faraji, A. (2019), "Active control to reduce the vibration amplitude of the solar honeycomb sandwich panels with CNTRC facesheets using piezoelectric patch sensor and actuator", Steel Compos. Struct., Int. J., 32(5), 671-686. https://doi.org/10.12989/scs.2019.32.5.671.
  5. Argha, A., Su, S.W., Savkin, A. and Celler, B. (2019), "A framework for optimal actuator/sensor selection in a control system", Int. J. Control, 92(2), 242-260. https://doi.org/10.1080/00207179.2017.1350755.
  6. Ashwin, U., Raja, S. and Dwarakanathan, D. (2009), "A finite element based substructuring procedure for design analysis of large smart structural system", Smart Mater. Struct., 18(4), 045006. https://doi.org/10.1088/0964-1726/18/4/045006.
  7. Babaeeian, M. and Mohammadimehr, M. (2020), "Investigation of the time elapsed effect on residual stress measurement in a composite plate by DIC method", Opt. Lasers Eng., 128, 106002. https://doi.org/10.1016/j.optlaseng.2020.106002.
  8. Bendine, K., Boukhoulda, F.B., Haddag, B. and Nouari, M. (2019), "Active vibration control of composite plate with optimal placement of piezoelectric patches", Mech. Adv. Mater. Struct., 26(4), 341-349. https://doi.org/10.1080/15376494.2017.1387324.
  9. Daraji, A., Hale, J.M. and Ye, J. (2017), "New methodology for optimal placement of piezoelectric sensor/actuator pairs for active vibration control of flexible structures", ASME J. Vib. Acoust., 140(1), 011015. https://doi.org/10.1115/1.4037510.
  10. Demetriou, M.A. (2000), "A numerical algorithm for the optimal placement of actuators and sensors for flexible structures", Proceedings of the 2000 American Control Conference, Chicago, USA, June.
  11. Demetriou, M.A. and Borggaard, J. (2003), "Optimization of an integrated actuator placement and robust control scheme for distributed parameter processes subject to worst-case spatial disturbance distribution", Proceedings of the 2003 American Control Conference, Denver, USA, June.
  12. Dorato, P., Abdallah, C.T. and Cerone, V. (2000), Linear Quadratic Control: An Introduction, Krieger Publishing Company, Florida, USA.
  13. Ghasemi A.R. and Meskini, M. (2019), "Free vibration analysis of porous laminated rotating circular cylindrical shells", J. Vib. Control, 25(18), 2494-2508. https://doi.org/10.1177/1077546319858227.
  14. Ghasemi, H., Park, H.S. and Rabczuk, T. (2017), "Level-set based IGA formulation for topology optimization of flexoelectric materials", Comput. Methods Appl. Mech. Eng., 313, 239-258. https://doi.org/10.1016/j.cma.2016.09.029.
  15. Ghasemi, H., Park, H.S. and Rabczuk, T. (2018), "A multi-material level set-based topology optimization of flexoelectric composites", Comput. Methods Appl. Mech. Eng., 332, 47-62. https://doi.org/10.1016/j.cma.2017.12.005.
  16. Ghorbanpour Arani, A., Rousta Navi, B. and Mohammadimehr, M. (2016), "Surface stress and agglomeration effects on nonlocal biaxial buckling polymeric nanocomposite plate reinforced by CNT using various approaches", Adv. Compos. Mater., 25(5), 423-441. https://doi.org/10.1080/09243046.2015.1052189.
  17. Ilchmann, A., Leben, L., Witschel, J. and Worthmann, K. (2018), "Optimal control of differential-algebraic equations from an ordinary differential equation perspective", Optim. Control Appl. Methods, 40(2), 351-366. https://doi.org/10.1002/oca.2481.
  18. Jia, S. and Shan, J. (2018), "Optimal actuator placement for constrained gyroelastic beam considering control spillover", J. Guid. Control Dyn., 41(9), 2073-2081. https://doi.org/10.2514/1.G003560.
  19. Kumar, K.R. and Narayanan, S. (2007), "The optimal location of piezoelectric actuators and sensors for vibration control of plates", Smart Mater. Struct., 16(6), 2680. https://doi.org/10.1088/0964-1726/16/6/073.
  20. Manohar, K., Nathan Kutz, J. and Brunton, S. (2018), "Optimal sensor and actuator placement using balanced model reduction", arXiv, 2018, 1812.01574.
  21. Martynowicz, P. (2019), "Real-time implementation of nonlinear optimal-based vibration control for a wind turbine model", J. Low Freq. Noise Vib. Active Control, 38(3-4), 1635-1650. https://doi.org/10.1177/1461348418793346.
  22. Mohammadimehr, M. and Mehrabi, M. (2018), "Electro-thermo-mechanical vibration and stability analyses of double-bonded micro composite sandwich piezoelectric tubes conveying fluid flow", Appl. Math. Model., 60, 255-272. https://doi.org/10.1016/j.apm.2018.03.008.
  23. Mohammadimehr, M., Mohammadimehr, M.A. and Dashti, P. (2016), "Size-dependent effect on biaxial and shear nonlinear buckling analysis of nonlocal isotropic and orthotropic micro-plate based on surface stress and modified couple stress theories using differential quadrature method", Appl. Math. Mech., 37(4), 529-554. https://doi.org/10.1007/s10483-016-2045-9.
  24. Mohammadimehr, M., Mohammadi-Dehabadi, A.A. and Maraghi, Z.K. (2017), "The effect of non-local higher order stress to predict the nonlinear vibration behavior of carbon nanotube conveying viscous nanoflow", Physica B Condens. Matter, 510, 48-59. https://doi.org/10.1016/j.physb.2017.01.014.
  25. Mohammadimehr, M., Emdadi, M., Afshari, H. and Rousta Navi, B. (2018a), "Bending, buckling and vibration analyses of MSGT microcomposite circular-annular sandwich plate under hydro-thermo-magneto-mechanical loadings using DQM", Int. J. Smart Nano Mater., 9(4), 233-260. https://doi.org/10.1080/19475411.2017.1377312.
  26. Mohammadimehr, M., Mohammadi-Dehabadi, A.A., Alavi, S.M.A., Alambeigi, K., Bamdad, M., Yazdani, R. and Hanifehlou, S. (2018b), "Bending, buckling and free vibration analyses of carbon nanotube reinforced composite beams and experimental tensile test to obtain the mechanical properties of nanocomposite", Steel Compos. Struct., Int. J., 29(3), 405-422. http://dx.doi.org/10.12989/scs.2018.29.3.405.
  27. Nanthakumar, S.S., Lahmer, T., Zhuang, X., Zi, G. and Rabczuk, T. (2017), "Detection of material interfaces using a regularized level set method in piezoelectric structures", Inverse Probl. Sci. Eng., 24(1), 153-176. http://dx.doi.org/10.1080/17415977.2015.1017485.
  28. Nestorovic, T., Trajkov, M. and Garmabi, S.M. (2015), "Optimal placement of piezoelectric actuators and sensors on a smart beam and a smart plate using multi-objective genetic algorithm", Smart Struct. Syst., Int. J., 15(4), 1041-1062. https://doi.org/10.12989/sss.2015.15.4.1041.
  29. Ogata, K. (2010), Modern Control Engineering, Prentice Hall, India.
  30. Rajabi, J. and Mohammadimehr, M. (2019), "Bending analysis of a micro sandwich skew plate using extended Kantorovich method based on Eshelby-Mori-Tanaka approach", Comput. Concrete, Int. J., 23(5), 361-376. http://dx.doi.org/10.12989/cac.2019.23.5.361.
  31. Rao, K.V., Raja, S. and Gowda, T.M. (2014a), "Finite element modeling and bending analysis of piezoelectric sandwich beam with debonded actuators", Smart Struct. Syst., Int. J., 13(1), 55-80. https://doi.org/10.12989/sss.2014.13.1.055.
  32. Rao, K.V., Raja, S. and Munikenche, T. (2014b), "Finite element modeling and bending analysis of piezoelectric sandwich beam with debonded actuators", Smart Struct. Syst., Int. J., 13(1), 55-80. https://doi.org/10.12989/sss.2014.13.1.055.
  33. Rostami, R., Irani, M. and Mohammadimehr, M. (2019), "Vibration control of the rotating sandwich cylindrical shell considering functionally graded core and functionally graded magneto-electro-elastic layers by using differential quadrature method", J. Sandw. Struct. Mater., 2019, 1099636218824139. https://doi.org/10.1177/1099636218824139.
  34. Rudolf, C., Martin, T. and Wauer, J. (2010), "Control of PKM machine tools using piezoelectric self-sensing actuators on basis of the functional principle of a scale with a vibrating string", Smart Struct. Syst., Int. J., 6(2), 167-182. https://doi.org/10.12989/sss.2010.6.2.167.
  35. Sakha, M.S., Shaker, H.R. and Tahavori, M. (2017), "Optimal sensors and actuators placement for large-scale switched systems", Int. J. Dyn. Control, 7(1), 147-156. https://doi.org/10.1007/s40435-018-0446-7.
  36. Tanimoto, Y., Nishiwaki, T., Shiomi, T. and Maekawa, Z. (2001), "A numerical modeling for eigenvibration analysis of honeycomb sandwich panels", Compos. Interf., 8(6), 393-402. https://doi.org/10.1163/156855401753424433.
  37. Tham, V.V, Quoc, T.H. and Tu, T.M. (2018), "Optimal placement and active vibration control of composite plates integrated piezoelectric sensor/actuator pairs", Viet. J. Sci. Technol., 56. 113. https://doi.org/10.15625/2525-2518/56/1/8824.
  38. Xue, K., Igarashi, A. and Kachi, T. (2018), "Optimal sensor placement for active control of floor vibration considering spillover effect associated with modal filtering", Eng. Struct., 165, 198-209. https://doi.org/10.1016/j.engstruct.2018.03.024.
  39. Yang, B., Miao, J., Fan, Z., Long, J. and Liu, X. (2018), "Modified cuckoo search algorithm for the optimal placement of actuators problem", Appl. Soft Comput., 67, 48-60. https://doi.org/10.1016/j.asoc.2018.03.004.
  40. Yassin, B., Lahcen, A. and Zeriab, E.S.M. (2018), "Hybrid optimization procedure applied to optimal location finding for piezoelectric actuators and sensors for active vibration control", Appl. Math. Model., 62, 701-716. https://doi.org/10.1016/j.apm.2018.06.017.
  41. Yin, H., Dong, K., Pan, A., Peng, Z., Jiang, Z. and Li, S. (2019), "Optimal sensor placement based on relaxation sequential algorithm", Neurocomputing, 344, 28-36. https://doi.org/10.1016/j.neucom.2018.03.088.
  42. Zare, A., Mohammadi, H., Dhingra, N.K., Jovanovic, M.R. and Georgiou, T.T. (2018), "Proximal algorithms for large-scale statistical modeling and optimal sensor/actuator selection", arXiv, 2018, 1807.01739.