Journal of Materials Science: Materials in Electronics

, Volume 30, Issue 17, pp 16527–16538 | Cite as

Design, analysis, and optimization of a magnetoelectric actuator using regression modeling, numerical simulation and metaheuristics algorithm

  • M. Sadeghi
  • Y. HojjatEmail author
  • M. Khodaei


In this study, a new method was proposed for the design of composite magnetoelectric actuator. Design of experiment (DOE) was utilized to investigate the mutual effect of geometric parameters. Moreover, the effect of impedance phase angle, magnetic field, and bias field were studied through finite element (FE) modeling. Resonance frequency, displacement value, magnetoelectric coefficient, and mode shape were considered as response variables. Analysis of variance (ANOVA), regression modeling and response surface method (RSM) were used to investigate the pair-wise effect of input parameters on the response variables. ANOVA results showed that the magnetoelectric length and piezoelectric thickness are the most important parameters affecting the magnetoelectric performance. The optimization process was performed using Metaheuristics algorithm. Optimum results were verified using magnetoelectric measurement setup and Laser Doppler Vibrometry device. The accuracy of the FE model in resonance frequency prediction was estimated at 97%. The prediction error of the FE model for the magnetoelectric voltage parameter was 14.6%, which was about 12.9% better than the regression model. The confirmation test showed that the regression modeling can only predict magnetoelectric behavior and for determining magnetoelectric performance, a precise FE model would be more reliable. Such proposed optimization technique can be used in the design of magnetoelectric composites.



The authors would like to thank Prof. Yumei Wen and Prof. Ping Li (Lab of sensor and Instrument system, Electronic Department, Shanghai Jiao Tong University, Shanghai, China) for their technical support in manufacturing, characterization, and measurements of the magnetoelectric samples.

Supplementary material

10854_2019_2029_MOESM1_ESM.docx (375 kb)
Supplementary material 1 (DOCX 374 kb)


  1. 1.
    J. Zhang, P. Li, Y. Wen, W. He, A. Yang, C. Lu, Shear-mode self-biased magnetostrictive/piezoelectric laminate multiferroic heterostructures for magnetic field detecting and energy harvesting. Sens. Actuators A 214, 149–155 (2014)CrossRefGoogle Scholar
  2. 2.
    D. Huang, C. Lu, H. Bing, Self-biased magnetoelectric coupling characteristics of three-phase composite transducers with nanocrystallin soft magnetic alloy. Appl. Phys. A 120(1), 115–120 (2015)CrossRefGoogle Scholar
  3. 3.
    S. Reis et al., Optimized anisotropic magnetoelectric response of Fe61.6Co16.4Si10.8B11.2/PVDF/Fe61.6Co16.4Si10.8B11.2laminates for AC/DC magnetic field sensing. Smart Mater. Struct. 25(5), 055050 (2016)CrossRefGoogle Scholar
  4. 4.
    N. Castro, S. Reis, M.P. Silva, V. Correia, S. Lanceros-Mendez, P. Martins, Development of a contactless DC current sensor with high linearity and sensitivity based on the magnetoelectric effect. Smart Mater. Struct. 27(6), 065012 (2018)CrossRefGoogle Scholar
  5. 5.
    W. Huang et al., “Ferroelectric domain switching dynamics and memristive behaviors in BiFeO3-based magnetoelectric heterojunctions,” Journal of Physics D: Applied Physics, vol. 51, no. 23, p. 234005, 2018/05/17 2018Google Scholar
  6. 6.
    J. Zhang et al., Theory of tunable magnetoelectric inductors in ferrite-piezoelectric layered composite. J. Phys. D 52(16), 165001 (2019)CrossRefGoogle Scholar
  7. 7.
    C.W. Nan, M.I. Bichurin, S. Dong, D. Viehland, G. Srinivasan, Multiferroic magnetoelectric composites: historical perspective, status, and future directions,”. J. Appl. Phys. 103(3), 1 (2008)CrossRefGoogle Scholar
  8. 8.
    J. Ma, J. Hu, Z. Li, C.W. Nan, Recent progress in multiferroic magnetoelectric composites: from bulk to thin films. Adv. Mater. 23(9), 1062–1087 (2011)CrossRefGoogle Scholar
  9. 9.
    U. Laletsin, N. Padubnaya, G. Srinivasan, C.P. Devreugd, Frequency dependence of magnetoelectric interactions in layered structures of ferromagnetic alloys and piezoelectric oxides. Appl. Phys. A 78(1), 33–36 (2004)CrossRefGoogle Scholar
  10. 10.
    K. Bi, Y.G. Wang, W. Wu, Tunable resonance frequency of magnetoelectric layered composites. Sens. Actuators A 166(1), 48–51 (2011)CrossRefGoogle Scholar
  11. 11.
    H. Palneedi et al., Highly tunable magnetoelectric response in dimensional gradient laminate composites of Fe-Ga alloy and Pb(Mg1/3Nb2/3)O3-Pb(Zr, Ti)O3 single crystal. J. Alloys Compd. 765, 764–770 (2018)CrossRefGoogle Scholar
  12. 12.
    T.I. Muchenik, E.J. Barbero, Prediction of extrinsic charge, voltage, and work-conversion factors for laminated magnetoelectric composites. Smart Mater. Struct. 25(1), 015006 (2015)CrossRefGoogle Scholar
  13. 13.
    E. Freeman et al., Improving the magnetoelectric performance of Metglas/PZT laminates by annealing in a magnetic field. Smart Mater. Struct. 26(8), 085038 (2017)CrossRefGoogle Scholar
  14. 14.
    A.-P. Wang et al., Influence of composition ratio on ferroelectric, magnetic and magnetoelectric properties of PMN–PT/CFO composite thin films. J. Mater. Sci.: Mater. Electron. 29(12), 10164–10169 (2018)Google Scholar
  15. 15.
    L. Chen, Y. Wang, The effects of the soft magnetic alloys’ material characteristics on resonant magnetoelectric coupling for magnetostrictive/piezoelectric composites. Smart Mater. Struct. 28(4), 045003 (2019)CrossRefGoogle Scholar
  16. 16.
    M.P. Silva, P. Martins, A. Lasheras, J. Gutiérrez, J.M. Barandiarán, S. Lanceros-Mendez, Size effects on the magnetoelectric response on PVDF/Vitrovac 4040 laminate composites. J. Magn. Magn. Mater. 377, 29–33 (2015)CrossRefGoogle Scholar
  17. 17.
    L. Chen, P. Li, Y.M. Wen, Y. Zhu, Tunable characteristics of bending resonance frequency in magnetoelectric laminated composites. Chin. Phys. B 22(7), 1–5 (2013)Google Scholar
  18. 18.
    S. Dinesh Kumar, J. Magesh, V. Subramanian, Tuning of bandwidth by superposition of bending and radial resonance modes in bilayer laminate composite. Mater. Des. 122, 315–321 (2017)CrossRefGoogle Scholar
  19. 19.
    L. Chen, P. Li, Y. Wen, Y. Zhu, Resonance magnetoelectric couplings of piezoelectric ceramic and ferromagnetic constant-elasticity alloy composites with different layer structures. J. Alloys Compd. 555, 156–160 (2013)CrossRefGoogle Scholar
  20. 20.
    S. Hohenberger et al., Effect of double layer thickness on magnetoelectric coupling in multiferroic BaTiO3-Bi0.95Gd0.05FeO3 multilayers. J. Phys. D 51(18), 184002 (2018)CrossRefGoogle Scholar
  21. 21.
    C. Tang, C. Lu, Strong self-biased magnetoelectric charge coupling in a homogenous laminate stack for magnetic sensor. J. Alloys Compd. 686, 723–726 (2016)CrossRefGoogle Scholar
  22. 22.
    Z. Tang, J. Chen, Y. Bai, S. Zhao, Magnetoelectric coupling effect in lead-free Bi4Ti3O12/CoFe2O4 composite films derived from chemistry solution deposition. Smart Mater. Struct. 25(8), 085020 (2016)CrossRefGoogle Scholar
  23. 23.
    J.X. Zhang et al., Phase-field model for epitaxial ferroelectric and magnetic nanocomposite thin films. Appl. Phys. Lett. 90(5), 052909 (2007)CrossRefGoogle Scholar
  24. 24.
    H.-M. Zhou, Q. Chen, S.-X. Qu, M.-H. Li, Model of resonance mechanical loss that considers bias field and pre-stress in magnetostricitve/piezoelectric sandwich laminate. J. Alloys Compd. 631, 165–170 (2015)CrossRefGoogle Scholar
  25. 25.
    H. Talleb, Z. Ren, Finite element modeling of magnetoelectric laminate composites in considering nonlinear and load effects for energy harvesting. J. Alloys Compd. 615, 65–74 (2014)CrossRefGoogle Scholar
  26. 26.
    J. Wen, J. Zhang, Y. Gao, A coupling finite element model for analysis the nonlinear dynamic magnetoelectric response of tri-layer laminate composites. Compos. Struct. 166, 163–176 (2017)CrossRefGoogle Scholar
  27. 27.
    D. Tierno, F. Ciubotaru, R. Duflou, M. Heyns, I.P. Radu, C. Adelmann, Strain coupling optimization in magnetoelectric transducers. Microelectron. Eng. 187–188, 144–147 (2018)CrossRefGoogle Scholar
  28. 28.
    X. Mao, Y. Wang, X. Liu, Y. Guo, An adaptive weighted least square support vector regression for hysteresis in piezoelectric actuators. Sens. Actuators A 263, 423–429 (2017)CrossRefGoogle Scholar
  29. 29.
    M. Salim, D. Salim, D. Chandran, H.S. Aljibori, A.S. Kherbeet, Review of nano piezoelectric devices in biomedicine applications. J. Intell. Mater. Syst. Struct. 29(10), 2105–2121 (2018)CrossRefGoogle Scholar
  30. 30.
    L. Wang, Z. Du, C. Fan, L. Xu, H. Zhang, D. Zhao, Magnetoelectric properties of Fe-Ga/BaTiO3 laminate composites. J. Alloys Compd. 509(2), 508–511 (2011)CrossRefGoogle Scholar
  31. 31.
    K. Krishnaiah, P. Shahabudeen, Applied Design OF Experiments and Taguchi Methods (PHI Learning, New Delhi, 2012)Google Scholar
  32. 32.
    M. Kaltenbacher, Numerical Simulation of Mechatronic Sensors and Actuators (Springer, Berlin Heidelberg, 2013)Google Scholar
  33. 33.
    Apc International, Piezoelectric Ceramics: Principles and Applications (APC International, Mackeyville, 2011)Google Scholar
  34. 34.
    S. Chikazumi, C.D. Graham, Physics of Ferromagnetism 2e (International Series of Monographs on Physics) (OUP Oxford, Oxford, 2009)Google Scholar
  35. 35.
    R.H. Myers, D.C. Montgomery, C.M. Anderson-Cook, Response Surface Methodology: Process and Product Optimization Using Designed Experiments (Wiley Series in Probability and Statistics) (Wiley, New York, 2011)Google Scholar
  36. 36.
    K. Najim, E. Ikonen, A.K. Daoud, Stochastic Processes: Estimation (Elsevier Science, Optimisation and Analysis, 2004)Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Electronic Information and Electrical EngineeringShanghai Jiao Tong UniversityShanghaiChina
  2. 2.Faculty of Mechanical EngineeringTarbiat Modares UniversityTehranIran
  3. 3.Faculty of Materials Science and EngineeringK. N. Toosi University of TechnologyTehranIran

Personalised recommendations