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Topology optimization for phononic band gap maximization considering a target driving frequency

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Abstract

A phononic crystal (PnC) is an artificially engineered periodic structure that exhibits extraordinary phenomena, such as a phononic band gap. The phononic band gap refers to a certain range of frequencies within which mechanical waves cannot propagate through the PnC. The main purpose of this paper is to propose a topology optimization formulation for phononic band gap maximization that simultaneously takes into account a target driving frequency. In the proposed topology optimization formulation, a relative band gap is considered as an objective function to be maximized. In addition, an equality constraint is imposed on the central frequency of the band gap. The topology optimization problem is solved using the globally convergent method of moving asymptotes, which is a gradient-based optimization algorithm. Numerical examples are computed to demonstrate the effectiveness of the proposed topology optimization formulation.

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References

  1. H.-W. Dong, X.-X. Su, Y.-S. Wang, C. Zhang, Topological optimization of two-dimensional phononic crystals based on the finite element method and genetic algorithm. Struct. Multidiscip. Optim. 50(4), 593–604 (2014)

    Article  MathSciNet  Google Scholar 

  2. Y.F. Li, X. Huang, S. Zhou, Topological design of cellular phononic band gap crystals. Materials 9(3), 186 (2016)

    Article  Google Scholar 

  3. Y. Fan Li, X. Huang, F. Meng, S. Zhou, Evolutionary topological design for phononic band gap crystals. Struct. Multidiscip. Optim. 54(3), 595–617 (2016)

    Article  MathSciNet  Google Scholar 

  4. C. Barbarosie, M. Neves, Periodic structures for frequency filtering: analysis and optimization. Comput. Struct. 82(17–19), 1399–1403 (2004)

    Article  Google Scholar 

  5. P. Zhang, Z. Wang, Y. Zhang, X. Liang, Multi-band design for one-dimensional phononic crystals. Sci. China Phys. Mech. Astron. 56(7), 1253–1262 (2013)

    Article  Google Scholar 

  6. G. Yi, B.D. Youn, A comprehensive survey on topology optimization of phononic crystals. Struct. Multidiscip. Optim. 54(5), 1315–1344 (2016)

    Article  MathSciNet  Google Scholar 

  7. O. Sigmund, J.S. Jensen, Systematic design of phononic band-gap materials and structures by topology optimization. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 361(1806), 1001–1019 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  8. S. Halkjær, O. Sigmund, J.S. Jensen, Maximizing band gaps in plate structures. Struct. Multidiscip. Optim. 32(4), 263–275 (2006)

    Article  Google Scholar 

  9. S.L. Vatanabe, G.H. Paulino, E.C. Silva, Maximizing phononic band gaps in piezocomposite materials by means of topology optimization. J. Acoust. Soc. Am. 136(2), 494–501 (2014)

    Article  Google Scholar 

  10. O. Sigmund, Morphology-based black and white filters for topology optimization. Struct. Multidiscip. Optim. 33(4–5), 401–424 (2007)

    Article  Google Scholar 

  11. K. Svanberg, A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM J. Optim. 12(2), 555–573 (2002)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This research was supported by the National Research Council of Science & Technology (NST) grant by the Korea Government (MSIT) (No. CAP-17-04-KRISS). This research was also supported by a Grant from the Institute of Advanced Machinery and Design at Seoul National University (SNU-IAMD).

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Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, Seoul National University, Seoul, 08826, Republic of Korea

    Guilian Yi, Yong Chang Shin, Heonjun Yoon, Soo-Ho Jo & Byeng D. Youn

  2. Institute of Advanced Machines and Design, Seoul National University, Seoul, 08826, Republic of Korea

    Byeng D. Youn

  3. OnePredict InC., Seoul, 08826, Republic of Korea

    Byeng D. Youn

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  1. Guilian Yi
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  2. Yong Chang Shin
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  3. Heonjun Yoon
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  4. Soo-Ho Jo
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  5. Byeng D. Youn
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Correspondence to Byeng D. Youn.

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Yi, G., Shin, Y.C., Yoon, H. et al. Topology optimization for phononic band gap maximization considering a target driving frequency. JMST Adv. 1, 153–159 (2019). https://doi.org/10.1007/s42791-019-00019-y

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  • DOI: https://doi.org/10.1007/s42791-019-00019-y

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