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Optimization and Engineering

, Volume 19, Issue 1, pp 19–38 | Cite as

Design methodology of magnetic fields and structures for magneto-mechanical resonator based on topology optimization

  • Akihiro Takezawa
  • Jaewook Lee
  • Mitsuru Kitamura
Article
  • 218 Downloads

Abstract

Magneto-mechanical resonators—magnetically-driven vibration devices—are used in many mechanical and electrical devices. We develop topology optimization (TO) to configure the magnetic fields of such resonators to enable large vibrations under specified current input to be attained. A dynamic magneto-mechanical analysis in the frequency domain is considered where we introduce the surface magnetic force calculated from the Maxwell stress tensor. The optimization problem is then formulated involving specifically the maximization of the dynamic compliance. This formulation is implemented using the solid-isotropic-material-with-penalization method for TO by taking into account the relative permeability, Young’s modulus, and the mass density of the magnetic material as functions of the density function. Through the 2D numerical studies, we confirm that this TO method works well in designing magnetic field patterns and providing matching between the external current frequency and eigenfrequency of the vibrating structure.

Keywords

Topology optimization Magneto-mechanical analysis Resonator Frequency response analysis Finite element method 

References

  1. Allaire G (2001) Shape optimization by the homogenization method. Springer, New YorkMATHGoogle Scholar
  2. Allaire G (2007) Conception optimale de structures. Springer, BerlinMATHGoogle Scholar
  3. Bendsøe MP (1989) Optimal shape design as a material distribution problem. Struct Optim 1(4):193–202CrossRefGoogle Scholar
  4. Bendsøe MP, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71(2):197–224MathSciNetCrossRefMATHGoogle Scholar
  5. Bendsøe MP, Sigmund O (2003) Topology optimization: theory, methods, and applications. Springer, BerlinMATHGoogle Scholar
  6. Bruns TE, Sigmund O, Tortorelli DA (2002) Numerical methods for the topology optimization of structures that exhibit snap-through. Int J Numer Methods Eng 55(10):1215–1237CrossRefMATHGoogle Scholar
  7. Fleury C, Braibant V (1986) Structural optimization: a new dual method using mixed variables. Int J Numer Methods Eng 23:409–428MathSciNetCrossRefMATHGoogle Scholar
  8. Ha Y, Cho S (2006) Design sensitivity analysis and topology optimization of eigenvalue problems for piezoelectric resonators. Smart Mater Struct 15(6):1513CrossRefGoogle Scholar
  9. Lee J, Kikuchi N (2010) Structural topology optimization of electrical machinery to maximize stiffness with body force distribution. IEEE Trans Magn 46(10):3790–3794CrossRefGoogle Scholar
  10. Lee J, Yoon SW (2015) Optimization of magnet and back iron topologies in electromagnetic vibration energy harvesters. IEEE Trans Magn 51(6):1–7. doi: 10.1109/TMAG.2014.2382596 Google Scholar
  11. Lee J, Seo JH, Kikuchi N (2010) Topology optimization of switched reluctance motors for the desired torque profile. Struct Multidiscip Optim 42(5):783–796CrossRefGoogle Scholar
  12. Lee J, Dede EM, Nomura T (2011) Simultaneous design optimization of permanent magnet, coils, and ferromagnetic material in actuators. IEEE Trans Magn 47(12):4712–4716CrossRefGoogle Scholar
  13. Lee J, Dede EM, Banerjee D, Iizuka H (2012) Magnetic force enhancement in a linear actuator by air-gap magnetic field distribution optimization and design. Finite Elements Anal Des 58:44–52CrossRefGoogle Scholar
  14. Ma ZD, Kikuchi N, Hagiwara I (1993) Structural topology and shape optimization for a frequency response problem. Comput Mech 13(3):157–174MathSciNetCrossRefMATHGoogle Scholar
  15. Maeda Y, Nishiwaki S, Izui K, Yoshimura M, Matsui K, Terada K (2006) Structural topology optimization of vibrating structures with specified eigenfrequencies and eigenmode shapes. Int J Numer Methods Eng 67:597–628MathSciNetCrossRefMATHGoogle Scholar
  16. McPherson A (2010) The magnetic resonator piano: electronic augmentation of an acoustic grand piano. J New Music Res 39(3):189–202CrossRefGoogle Scholar
  17. Nguyen TH, Paulino GH, Song J, Le CH (2010) A computational paradigm for multiresolution topology optimization (mtop). Struct Multidiscip Optim 41(4):525–539MathSciNetCrossRefMATHGoogle Scholar
  18. Nishiwaki S, Saitou K, Min S, Kikuchi N (2000) Topological design considering flexibility under periodic loads. Struct Multidiscip Optim 19(1):4–16CrossRefGoogle Scholar
  19. Nocedal J, Wright S (2006) Numerical optimization, 2nd edn. Springer, New YorkMATHGoogle Scholar
  20. Pedersen NL (2000) Maximization of eigenvalues using topology optimization. Struct Multidiscip Optim 20(1):2–11CrossRefGoogle Scholar
  21. Reichel EK, Riesch C, Weiss B, Jakoby B (2008) A vibrating membrane rheometer utilizing electromagnetic excitation. Sens Actuator Phys 145:349–353CrossRefGoogle Scholar
  22. Rubio WM, Silva ECN, Paulino GH (2009) Toward optimal design of piezoelectric transducers based on multifunctional and smoothly graded hybrid material systems. J Intell Mater Syst Struct 20(14):1725–1746CrossRefGoogle Scholar
  23. Rubio WM, Paulino GH, Silva ECN (2011) Tailoring vibration mode shapes using topology optimization and functionally graded material concepts. Smart Mater Struct 20:025009CrossRefGoogle Scholar
  24. Shim H, Moon H, Wang S, Hameyer K (2008) Topology optimization for compliance reduction of magnetomechanical systems. IEEE Trans Magn 44(3):346–351CrossRefGoogle Scholar
  25. Silva ECN, Kikuchi N (1999) Design of piezoelectric transducers using topology optimization. Smart Mater Struct 8(3):350CrossRefGoogle Scholar
  26. Svanberg K (1987) The method of moving asymptotes- a new method for structural optimization. Int J Numer Methods Eng 24(2):359–373MathSciNetCrossRefMATHGoogle Scholar
  27. Takezawa A, Kitamura M (2014) Phase field method to optimize dielectric devices for electromagnetic wave propagation. J Comput Phys 257PA:216–240MathSciNetCrossRefMATHGoogle Scholar
  28. Takezawa A, Nishiwaki S, Kitamura M (2010) Shape and topology optimization based on the phasefield method and sensitivity analysis. J Comput Phys 229(7):2697–2718MathSciNetCrossRefMATHGoogle Scholar
  29. Takezawa A, Yoon GH, Jeong SH, Kobashi M, Kitamura M (2014) Structural topology optimization with strength and heat conduction constraints. Comput Meth Appl Mech Eng 276:341–361MathSciNetCrossRefGoogle Scholar
  30. Tcherniak D (2002) Topology optimization of resonating structures using simp method. Int J Numer Methods Eng 54(11):1605–1622CrossRefMATHGoogle Scholar
  31. Woodson HH, Melcher JR (1985) Electromechanical dynamics, part 2: fields, forces, and motion. Krieger Pub. Co, MalabarGoogle Scholar
  32. Yang B, Lee C, Kee WL, Lim SP (2010) Hybrid energy harvester based on piezoelectric and electromagnetic mechanisms. J Micro/Nanolithogr MEMS MOEMS 9(2):023002CrossRefGoogle Scholar
  33. Yoo J (2002) Reduction of vibration caused by magnetic force in a switched reluctance motor by topology optimization. J Appl Mech 69(3):380–387CrossRefMATHGoogle Scholar
  34. Yoo J, Kikuchi N (2002) Topology optimization for reduction of vibration caused by magnetic harmonic excitation. IEEE Trans Magn 38(6):3643–3649CrossRefGoogle Scholar
  35. Yoo J, Kikuchi N, Volakis JL (2000) Structural optimization in magnetic devices by the homogenization design method. IEEE Trans Magn 36(3):574–580CrossRefGoogle Scholar
  36. Zhang K, Zhang L, Fu L, Li S, Chen H, Cheng ZY (2013) Magnetostrictive resonators as sensors and actuators. Sens Actuator Phys 200:2–10CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Akihiro Takezawa
    • 1
  • Jaewook Lee
    • 2
  • Mitsuru Kitamura
    • 1
  1. 1.Department of Transportation and Environmental Engineering, Graduate School of EngineeringHiroshima UniversityHigashihiroshimaJapan
  2. 2.School of Mechanical EngineeringGwangju Institute of Science and TechnologyGwangjuKorea

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