Applied Mathematics and Mechanics

, Volume 37, Issue 5, pp 639–646 | Cite as

Modelling and analysis of circular bimorph piezoelectric actuator for deformable mirror

  • Hairen WangEmail author
  • Ming Hu
  • Zhenqin Li


A theoretical model of a circular flexure-mode piezoelectric bimorph actuator is established. The circular bimorph structure, consisting of two flexible layers of piezoelectric material and a layer of metallic material in the middle, is powered to the flexural deformation. The analytical solutions including the statics solution and the dynamics solution are derived from the 3D equations of the linear theory of piezoelectricity. Numerical results are included to show the circular bimorph piezoelectric actuator (CBPA) performance, depending on the physical parameters.

Key words

piezoelectric actuator circular bimorph structure flexure-mode 

Chinese Library Classification


2010 Mathematics Subject Classification



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  1. [1]
    Schmutz, L. Adaptive optics: a modern cure for Newton tremors. Photon Spectra, 27, 119–128 (1993)Google Scholar
  2. [2]
    Babcock, H. W. The possibility of compensating astronomical seeing. Publications of the Astronomical Society of the Pacific, 65, 229–236 (1953)CrossRefGoogle Scholar
  3. [3]
    Woolf, N. Adaptive optics. Proceedings of IAU Colloquium, Garching, Germany, 221–233 (1984)Google Scholar
  4. [4]
    Tyson, R. Principles of Adaptive Optics, CRC Press, Boca Raton (2010)CrossRefGoogle Scholar
  5. [5]
    Hom, C. L., Dean, P. D., and Winzer, S. R. Simulating electrostrictive deformable mirrors I: nonlinear static analysis. Smart Materials and Structures, 8, 691–699 (1999)CrossRefGoogle Scholar
  6. [6]
    Ning, Y. Performance Test and Application Study of a Bimorph Deformable Mirror (in Chinese), Ph.D. dissertation, National University of Defense Technology (2008)Google Scholar
  7. [7]
    Wilson, R., Franza, F., and Noethe, L. Active optics I: a system for optimizing the optical quality and reducing the costs of large telescopes. Journal of Modern Optics, 34, 485–509 (1987)CrossRefGoogle Scholar
  8. [8]
    Hom, C. L. Simulating electrostrictive deformable mirrors II: nonlinear dynamic analysis. Smart Materials and Structures, 8, 700–708 (1999)CrossRefGoogle Scholar
  9. [9]
    Lin, X. D., Xue, C., Liu, X. Y., Wang, J. L., and Wei, P. F. Current status and research development of wavefront correctors for adaptive optics. Chinese Optics, 4, 337–351 (2012)Google Scholar
  10. [10]
    Webber, K. G., Hopkinson, D. P., and Lynch, C. S. Application of a classical lamination theory model to the design of piezoelectric composite unimorph actuators. Journal of Intelligent Material Systems and Structures, 17, 29–34 (2006)CrossRefGoogle Scholar
  11. [11]
    Hagood, N. W., Chung, W. H., and von Flotow, A. Modelling of piezoelectric actuator dynamics for active structural control. Journal of Intelligent Material Systems and Structures, 1, 327–354 (1990)CrossRefGoogle Scholar
  12. [12]
    Hwang, W. S. and Park, H. C. Finite element modeling of piezoelectric sensors and actuators. AIAA Journal, 31, 930–937 (1993)CrossRefGoogle Scholar
  13. [13]
    Goldfarb, M. and Celanovic, N. A lumped parameter electromechanical model for describing the nonlinear behavior of piezoelectric actuators. Journal of Dynamic Systems, Measurement, and Control, 119, 478–485 (1997)CrossRefzbMATHGoogle Scholar
  14. [14]
    Liu, L., Tan, K. K., Chen, S., Teo, C. S., and Lee, T. H. Discrete composite control of piezoelectric actuators for high-speed and precision scanning. IEEE Transactions on Industrial Informatics, 9, 859–868 (2013)CrossRefGoogle Scholar
  15. [15]
    Vashist, S. K. and Chhabra, D. Optimal placement of piezoelectric actuators on plate structures for active vibration control using genetic algorithm. Proccedings of the SPIE, 9057, 905720 (2014)CrossRefGoogle Scholar
  16. [16]
    Wang, H. R. Analytical analysis of a beam flexural-mode piezoelectric actuator for deformable mirrors. Journal of Astronomical Telescopes, Instruments, and Systems, 1, 049001 (2015)CrossRefGoogle Scholar
  17. [17]
    Kamada, T., Fujita, T., Hatayama, T., Arikabe, T., Murai, N., Aizawa, S., and Tohyama, K. Active vibration control of frame structures with smart structures using piezoelectric actuators (vibration control by control of bending moments of columns). Smart Materials and Structures, 6, 448–456 (1997)CrossRefGoogle Scholar
  18. [18]
    Crawley, E. F. and de Luis, J. Use of piezoelectric actuators as elements of intelligent structures. AIAA Journal, 25, 1373–1385 (1987)CrossRefGoogle Scholar
  19. [19]
    Freeman, R. and Garcia, H. High-speed deformable mirror system. Applied Optics, 21, 589–595 (1982)CrossRefGoogle Scholar
  20. [20]
    Wang, H. R., Hu, H. P., Yang, J. S., and Hu, Y. T. Spiral piezoelectric transducer in torsional motion as low-frequency power harvester. Applied Mathematics and Mechanics (English Edition), 34, 589–596 (2013) DOI 10.1007/s10483-013-1693-xCrossRefGoogle Scholar
  21. [21]
    Wang, H. R., Xie, J. M., Xie, X., Hu, Y. T., and Wang, J. Nonlinear characteristics of circular-cylinder piezoelectric power harvester near resonance based on flow-induced flexural vibration mode. Applied Mathematics and Mechanics (English Edition), 35, 229–236 (2014) DOI 10.1007/s10483-014-1786-6MathSciNetCrossRefGoogle Scholar
  22. [22]
    Wang, H. R., Xie, X., Hu, Y., and Wang, J. Weakly nonlinear characteristics of a three-layer circular piezoelectric plate-like power harvester near resonance. Journal of Mechanics, 30, 97–102 (2014)CrossRefGoogle Scholar
  23. [23]
    Wang, H. R., Hu, Y., and Wang, J. On the nonlinear behavior of a multilayer circular piezoelectric plate-like transformer operating near resonance. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 60, 752–757 (2013)CrossRefGoogle Scholar
  24. [24]
    Yang, J. An Introduction to the Theory of Piezoelectricity, Springer, New York (2005)zbMATHGoogle Scholar
  25. [25]
    Wang, J., Wang, H. R., Hu, H., Luo, B., Hu, Y., and Wang, J. On the strain-gradient effects in micro piezoelectric-bimorph circular plate power harvesters. Smart Materials and Structures, 21, 015006 (2012)CrossRefGoogle Scholar
  26. [26]
    Huang, Y. and Huang, W. Modeling and analysis of circular flexural-vibration-mode piezoelectric transformer. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 57, 2764–2771 (2010)CrossRefGoogle Scholar
  27. [27]
    Auld, B. A. Acoustic Fields and Waves in Solids, Krieger Publishing Company, Malabar (1973)Google Scholar

Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Purple Mountain ObservatoryChinese Academy of SciencesNanjingChina
  2. 2.Key Laboratory for Radio AstronomyChinese Academy of SciencesNanjingChina
  3. 3.Institute of Geodesy and GeophysicsChinese Academy of SciencesWuhanChina
  4. 4.School of Materials and MetallurgyNortheastern UniversityShenyangChina

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