Advertisement

Archives of Computational Methods in Engineering

, Volume 6, Issue 4, pp 305–329 | Cite as

Design of piezocomposite materials and piezoelectric transducers using topology optimization— Part III

  • E. C. Nelli Silva
  • N. Kikuchi
Article

Summary

Following the topic introduced in [1, 2] this paper discusses the design of piezoelectric transducers used in applications such as acoustic wave generation and resonators. These applications require goals in the transducer design such as high electromechanical energy conversion for a certain transducer vibration mode and narrowband or broadband response. The development of these devices has been based on the use of simple analytical models, test of prototypes, and analysis by the finite element method. However, in all cases the design is limited to a parametric optimization where only some dimensions of a chosen transducer configuration are optimized. By changing the topology of these devices or their components, we may obtain devices with better performance since the design space of solutions is enlarged. Based on this idea, we have proposed the use of topology optimization for designing these devices. This method consists of finding the distribution of the material and void phases in the design domain that optimizes a defined objective function. The optimized solution is obtained using Sequential Linear Programming (SLP). Considering acoustic wave generation and resonator applications, three kinds of objective functions were defined: maximize the energy conversion for a specific mode or a set of modes; design a transducer with specified frequencies; and design a transducer with narrowband or broadband response. Although only two-dimensional plane strain transducer topologies have been considered in order to illustrate the implementation of the method, it can be extended to three-dimensional topologies. Transducer designs were obtained that conform to the desired design requirements and have better performance characteristics than other common designs.

Keywords

Design Variable Topology Optimization Design Domain Piezoelectric Transducer Design Curve 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Silva, E.C.N., J.S.O. Fonseca, F.M. de Espinosa, A.T. Crumm, G.A. Brady, J.W. Halloran and N. Kikuchi (1999), “Design of Piezocomposite Materials and Piezoelectric Transducers Using Topology Optimization—Part I”,Archives of Computational Methods in Engineering, Vol.6 No.2, 117–182.CrossRefMathSciNetGoogle Scholar
  2. 2.
    Silva, E.C.N., S. Nishiwaki, and N. Kikuchi (1999), “Design of Piezocomposite Materials and Piezoelectric Transducers Using Topology Optimization—Part II”,Archives of Computational Methods in Engineering, Vol.6 No. 3, 191–222.MathSciNetGoogle Scholar
  3. 3.
    Kunkel, H.A., S. Locke, and B. Pikeroen (1990), “Finite Element Analysis of Vibrational Modes in Piezoelectric Ceramic Disks”,IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control,37 No. 4, 316–328.CrossRefGoogle Scholar
  4. 4.
    Simson, É.A. and A. Taranukha (1993), “Optimization of the Shape of a Quartz Resonator”,Acoustical Physics,39 No. 5, 472–476.Google Scholar
  5. 5.
    Challande, P. (1990), “Optimizing Ultrasonic Transducers Based on Piezoelectric Composites Using a Finite-Element Method”,IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control,37, No. 2, 135–140.CrossRefGoogle Scholar
  6. 6.
    Sato J., M. Kawabuchi, and A. Fukumoto (1979), “Dependence of the Electromechanical Coupling Coefficient on the Width-to-thickness Ratio of Plank-shaped Piezoelectric Transducers Used for Electronically Scanned Ultrasound Diagnostic Systems”,The Journal of the Acoustical Society of America,66, No. 6, 1609–1611.CrossRefGoogle Scholar
  7. 7.
    Naillon, M., R.H. Coursant, F. Besnier (1983), “Analysis of Piezoelectric Structures by a Finite Element Method”,Acta Electronica,25 4, 341–362.Google Scholar
  8. 8.
    Lerch, R. (1990), “Simulation of Piezoelectric Devices by Two- and Three-Dimensional Finite Elements”,IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control,37 No. 2, 233–247.CrossRefMathSciNetGoogle Scholar
  9. 9.
    Guo, N., P. Cawley, and D. Hitchings (1992), “The Finite Element Analysis of the Vibration Characteristics of Piezoelectric Discs”,Journal of Sound and Vibration,159 No. 1, 115–138.MATHCrossRefGoogle Scholar
  10. 10.
    Yong, Y-K. (1995), “A New Storage Scheme for the Lanczos Solution of Large Scale Finite Element Models of Piezoelectric Resonators”,Proceedings of IEEE Ultrasonics Symposium, 1633–1636.Google Scholar
  11. 11.
    Yong, Y-K. and Y. Cho (1994), “Algorithms for Eigenvalue Problems in Piezoelectric Finite Element Analysis”,Proceedings of IEEE Ultrasonics Symposium, 1057–1062.Google Scholar
  12. 12.
    Yang, R.J. and C.H. Chuang (1994), “Optimal Topology Design Using Linear Programming”,Computers & Structures,52 No. 2, 265–275.MATHCrossRefGoogle Scholar
  13. 13.
    Sigmund, O. (1996), “On the Design of Compliant Mechanisms Using Topology Optimization”,Danish Center for Applied Mathematics and Mechanics, Report No. 535.Google Scholar
  14. 14.
    Ma, Z-D., N. Kikuchi, and H.-C. Cheng (1995), “Topological Design for Vibrating Structures”,Computer Methods in Applied Mechanics and Engineering,121, 259–280.MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Díaz, A.R. and N. Kikuchi (1992), “Solutions to Shape and Topology Eigenvalue Optimization Problems Using a Homogenization Method”,International Journal for Numerical Methods in Engineering,35, 1487–1502.MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Yao, Q. and L. Bjorno (1997), “Broadband Tonpilz Underwater Acoustic Transducers Based on Multimode Optimization”,IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control,44 No. 5, 1060–1066.Google Scholar
  17. 17.
    Vanderplaatz, G.N. (1984),Numerical Optimization Techniques for Engineering Design: with Applications, McGraw-Hill, NY.Google Scholar
  18. 18.
    Hanson, R. and K. Hiebert (1981), “A Sparse Linear Programming Subprogram”,Sandia National Laboratories, Technical Report SAND81-0297.Google Scholar
  19. 19.
    Bendsøe, M.P. (1989), “Optimal Shape Design as a Material Distribution Problem”,Structural Optimization,1, 192–202.CrossRefGoogle Scholar
  20. 20.
    Bremicker, M., M. Chirehdast, N. Kikuchi, and Y. Papalambros (1991), “Integrated Topology and Shape Optimization in Structural Design”,Mechanics of Structures and Machines,19 No. 4, 551–587.CrossRefGoogle Scholar
  21. 21.
    Meric, R.A. and S. Saigal (1991), “Shape Sensitivity Analysis of Piezoelectric Structures by the Adjoint Variable Method”,AIAA Journal,29 No. 8, 1313–1318.Google Scholar
  22. 22.
    Smith, W.A. and B.A. Auld (1991), “Modeling 1–3 Composite Piezoelectrics: Thickness-Mode Oscillations”,IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control,38 No. 1, 40–47.CrossRefGoogle Scholar
  23. 23.
    Bandyopadhyay, A., R.K. Panda, V.E. Janas, M.K. Agarwala, S.C. Danforth, and A. Safari (1997), “Processing of Piezocomposites by Fused Deposition Technique”,Journal of the American Ceramic Society,80 No. 6, 1366–1372.CrossRefGoogle Scholar
  24. 24.
    Haftka, R.T., Z. Gürdal, and M.P. Kamat (1992),Elements of Structural Optimization, Dordrecht: Kluwer Academic.MATHGoogle Scholar

Copyright information

© CIMNE, Barcelona (Spain) 1999

Authors and Affiliations

  • E. C. Nelli Silva
    • 1
  • N. Kikuchi
    • 1
  1. 1.Department of Mechanical Engineering and Applied MechanicsThe University of MichiganAnn ArborUSA

Personalised recommendations