Skip to main content

Advertisement

SpringerLink
Log in

Topology optimization of periodic barriers for surface waves

  • Industrial Application Paper
  • Published:
Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

Dispersion engineering is always the important topic in the field of artificial periodic structures. In particular, topology optimization of composite structures with expected bandgaps plays a key role. However, most reported studies focused on topology optimization for bulk waves, and the optimization for surface wave bandgaps (SWBGs) is still missing. In this paper, we develop a topology optimization framework based on the genetic algorithm and finite element method to design periodic barriers embedded in semi-infinite space for reducing surface waves on demand. The objective functions for SWBGs are proposed based on the energy distribution properties of surface waves. The numerical results show that the optimization framework has stable convergence for this problem and is effective to optimize SWBGs. Considering large SWBGs and low filling fraction of solids, we investigate single- and multi-objective optimizations, respectively, and obtain novel wave barriers with good performance. The beneficial configuration features and mechanism of broadband SWBGs from the optimized results are explored. The results indicate that for the first-order SWBG, most optimized structures consist of a main scatterer at the center and some subsidiary scatterers near the surface. The rigid body resonance of the main scatterer determines the lower edge of SWBG, and the subsidiary scatterers can regulate the upper edge. Higher-order SWBGs are generated from the interaction of multiple scatterers, whose relative distance has a great influence on the position of SWBGs. The optimized structures can make the surface waves propagate far away from the surface within the frequencies of bandgaps, leading to a strong attenuation of surface vibration. In practice, our topological optimization framework is promising in designing high-performance surface wave devices and novel isolating structures for earthquake or environmental vibration in civil engineering.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

Data availability statement

All data used during the study are available from the corresponding author by request.

References

  • Achenbach J (1973) Wave propagation in elastic solids. North Holland, Amsterdam

    MATH  Google Scholar 

  • Bilal OR, Hussein MI (2011) Ultrawide phononic band gap for combined in-plane and out-of-plane waves. Phys Rev E 84:65701

    Article  Google Scholar 

  • Chen Y, Guo D, Li YF, Li G, Huang X (2019) Maximizing wave attenuation in viscoelastic phononic crystals by topology optimization. Ultrasonics 94:419–429

    Article  Google Scholar 

  • Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197

    Article  Google Scholar 

  • Dolatshahi KM, Rezaie A, Rafiee-Dehkharghani R (2020) Topology optimization of wave barriers for mitigation of vertical component of seismic ground motions. J Earthq Eng 24(1):84–108

    Article  Google Scholar 

  • Dong HW, Su XX, Wang YS (2014a) Multi-objective optimization of two-dimensional porous phononic crystals. J Phys D Appl Phys 47(15):155301

    Article  Google Scholar 

  • Dong HW, Su XX, Wang YS, Zhang C (2014b) Topology optimization of two-dimensional asymmetrical phononic crystals. Phys Lett A 378(4):434–441

    Article  Google Scholar 

  • Dong HW, Su XX, Wang YS, Zhang C (2014c) Topological optimization of two-dimensional phononic crystals based on the finite element method and genetic algorithm. Struct Multidiscip Optim 50(4):593–604

    Article  MathSciNet  Google Scholar 

  • Dong HW, Wang YS, Wang YF, Zhang C (2015) Reducing symmetry in topology optimization of two-dimensional porous phononic crystals. AIP Adv 5(11):117149

    Article  Google Scholar 

  • Dong HW, Zhao SD, Wang YS, Zhang C (2017) Topology optimization of anisotropic broadband double-negative elastic metamaterials. J Mech Phys Solids 105:54–80

    Article  MathSciNet  Google Scholar 

  • Dong HW, Zhao SD, Wei P, Cheng L, Wang YS, Zhang C (2019) Systematic design and realization of double-negative acoustic metamaterials by topology optimization. Acta Mater 172:102–120

    Article  Google Scholar 

  • Du Q, Zeng Y, Xu Y, Yang H, Zeng Z (2018) H-fractal seismic metamaterial with broadband low-frequency bandgaps. J Phys D Appl Phys 51(10):105104

    Article  Google Scholar 

  • Gazonas GA, Weile DS, Wildman R, Mohan A (2006) Genetic algorithm optimization of phononic bandgap structures. Int J Solids Struct 43(18–19):5851–5866

    Article  Google Scholar 

  • Goo S, Kook J, Wang S (2020) Topology optimization of vibroacoustic problems using the hybrid finite element–wave based method. Comput Method Appl M 364:112932

    Article  MathSciNet  Google Scholar 

  • Guo X, Zhang W, Zhong W (2014) Doing topology optimization explicitly and geometrically—a new moving morphable components based framework. J Appl Mech 81(85):081009

    Article  Google Scholar 

  • Halkjær S, Sigmund O, Jensen JS (2005) Inverse design of phononic crystals by topology optimization. Zeitschrift für Krist Mater 220(9–10):895–905

    Google Scholar 

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

    Article  Google Scholar 

  • Hedayatrasa S, Abhary K, Uddin M, Ng C-T (2016a) Optimum design of phononic crystal perforated plate structures for widest bandgap of fundamental guided wave modes and maximized in-plane stiffness. J Mech Phys Solids 89:31–58

    Article  MathSciNet  Google Scholar 

  • Hedayatrasa S, Abhary K, Uddin MS, Guest JK (2016b) Optimal design of tunable phononic bandgap plates under equibiaxial stretch. Smart Mater Struct 25:55025

    Article  Google Scholar 

  • Holland JH (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor

    Google Scholar 

  • Hussein MI, Hamza K, Hulbert GM, Saitou K (2007) Optimal synthesis of 2D phononic crystals for broadband frequency isolation. Waves Random Complex Media 17(4):491–510

    Article  MathSciNet  Google Scholar 

  • Imani M, Ghoreishi SF (2020) Bayesian optimization objective-based experimental design. In Proceedings of the 2020 American Control Conference (ACC 2020) IEEE

  • Imani M, Dougherty ER, Braga-Neto U (2020) Boolean Kalman filter and smoother under model uncertainty. Automatica 111:108609

  • Kushwaha MS, Halevi P, Dobrzynski L, Djafari-Rouhani B (1993) Acoustic band structure of periodic elastic composites. Phys Rev Lett 71:2022–2025

    Article  Google Scholar 

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

  • Li YF, Huang X, Zhou S (2016b) Topological design of cellular phononic band gap crystals. Materials 9(3):186

  • Li YF, Meng F, Li S, Jia B, Zhou S, Huang X (2018) Designing broad phononic band gaps for in-plane modes. Phys Lett A 382(10):679–684

    Article  Google Scholar 

  • Miniaci M, Krushynska A, Bosia F, Pugno NM (2016) Large scale mechanical metamaterials as seismic shields. New J Phys 18(8):083041

    Article  Google Scholar 

  • Pu X, Shi Z (2017) A novel method for identifying surface waves in periodic structures. Soil Dyn Earthq Eng 98:67–71

    Article  Google Scholar 

  • Rupp CJ, Evgrafov A, Maute K, Dunn ML (2007) Design of phononic materials/structures for surface wave devices using topology optimization. Struct Multidiscip Optim 34:111–121

    Article  MathSciNet  Google Scholar 

  • Sigmund O, Jensen JS (2003) Systematic design of phononic band–gap materials and structures by topology optimization. Philos Trans R Soc London Ser A Math Phys Eng Sci 361:1001–1019

    Article  MathSciNet  Google Scholar 

  • Van Hoorickx C, Sigmund O, Schevenels M, Lazarov BS, Lombaert G (2016) Topology optimization of two-dimensional elastic wave barriers. J Sound Vib 376:95–111

    Article  Google Scholar 

  • Vatanabe SL, Paulino GH, Silva ECN (2014) Maximizing phononic band gaps in piezocomposite materials by means of topology optimization. J Acoust Soc Am 136(2):494–501

    Article  Google Scholar 

  • Xie L, Xia B, Huang G, Lei J, Liu J (2017) Topology optimization of phononic crystals with uncertainties. Struct Multidiscip Optim 56:1319–1339

    Article  Google Scholar 

  • Xu W, Ning J, Zhang M, Wang W, Yang T (2018) Three-phase microstructure topology optimization of two-dimensional phononic bandgap materials using genetic algorithms. Acta Mech Solida Sin 31(6):775–784

    Article  Google Scholar 

  • Yi G, Youn BD (2016) A comprehensive survey on topology optimization of phononic crystals. Struct Multidiscip Optim 54:1315–1344

    Article  MathSciNet  Google Scholar 

  • Zeng Y, Xu Y, Deng K, Zeng Z, Yang H, Muzamil M, Du Q (2018) Low-frequency broadband seismic metamaterial using I-shaped pillars in a half-space. J Appl Phys 123(21):214901

    Article  Google Scholar 

  • Zhang X, He J, Takezawa A, Kang Z (2018) Robust topology optimization of phononic crystals with random field uncertainty. Int J Numer Methods Eng 115(9):1154–1173

    Article  MathSciNet  Google Scholar 

  • Zhang X, Takezawa A, Kang Z (2019) A phase-field based robust topology optimization method for phononic crystals design considering uncertain diffuse regions. Comput Mater Sci 160:159–172

    Article  Google Scholar 

  • Zhao H, Liu Y, Wang G, Wen J, Yu D, Han X, Wen X (2005) Resonance modes and gap formation in a two-dimensional solid phononic crystal. Phys Rev B 72(1):12301

    Article  Google Scholar 

  • Zhong HL, Wu FG, Yao LN (2006) Application of genetic algorithm in optimization of band gap of two-dimensional phononic crystals. Acta Phy Sin 55:275–280

    Article  Google Scholar 

Download references

Funding

This work is supported by the National Natural Science Foundation of China (11772040).

Author information

Authors and Affiliations

  1. School of Civil Engineering, Beijing Jiaotong University, Beijing, 100044, People’s Republic of China

    Ze Liu & Gui-Lan Yu

  2. Department of Mechanics, School of Mechanical Engineering, Tianjin University, Tianjin, 300350, People’s Republic of China

    Hao-Wen Dong

  3. Department of Mechanical Engineering, The Hong Kong Polytechnic University, Hong Kong, People’s Republic of China

    Hao-Wen Dong

  4. Department of Applied Mechanics, University of Science and Technology Beijing, Beijing, 100083, People’s Republic of China

    Hao-Wen Dong

Authors
  1. Ze Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hao-Wen Dong
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Gui-Lan Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Ze Liu: Data curation, formal analysis, methodology, software, validation, writing original draft, writing review, and editing. Hao-Wen Dong: Formal analysis, methodology, writing review, and editing. Gui-Lan Yu: Formal analysis, funding acquisition, project administration, supervision, writing review, and editing.

Corresponding authors

Correspondence to Hao-Wen Dong or Gui-Lan Yu.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Replication of results

The optimization in this paper is based on the finite element method and genetic algorithm, which are introduced in detail in Section 2 and Section 3, respectively. The simulation is performed in COMSOL Multiphysics 5.2a with Matlab. In Section 4.1.1, we have proved the results can be reproduced. If there is any trouble when calculating, please contact with the corresponding authors.

Additional information

Responsible Editor: Seonho Cho

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, Z., Dong, HW. & Yu, GL. Topology optimization of periodic barriers for surface waves. Struct Multidisc Optim 63, 463–478 (2021). https://doi.org/10.1007/s00158-020-02703-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-020-02703-3

Keywords

Search

Navigation