Skip to main content
Log in

Thermal tuning of band gap properties in planar stretch-dominated lattices with tailorable coefficient of thermal expansion

  • Published:
Applied Physics A Aims and scope Submit manuscript

Abstract

The development of the current technology has increased the requirement for the versatility of acoustic metamaterials. In this study, the band gap (BG) tuning of the stretch-dominated thermal expansion lattice metamaterials with different configurations composed of triangular units is studied using the finite element method, and a design method for metamaterials tuned by external temperature changes in multiple frequency ranges is proposed. The results indicate that the stretch-dominated thermal expansion material can maintain the original customized thermal expansion performance while possessing the characteristics of the BG in addition to realizing different degrees of BG tunability when the temperature changes. The results provide a theoretical basis for attaining the thermal expansion/tunable BG dual-objectives design. The objective is to achieve the dual goals of tailorable coefficient of thermal expansion and tunable BG design through reasonable material selection and shape optimization.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. M.S. Kushwaha, P. Halevi, L. Dobrzynski, B. Djafari-Rouhani, Acoustic band structure of periodic elastic composites. Phys. Rev. Lett. 71(13), 2022–2025 (1993)

    Article  ADS  Google Scholar 

  2. S.K. Manvir, Manvir, Classical Band Structure of Periodic Elastic Composites. Int. J. Mod. Phys. B 10(09), 977–1094 (1996)

    Article  Google Scholar 

  3. J.S. Jensen, Phononic band gaps and vibrations in one- and two-dimensional mass-spring structures. Opt. Commun. 266(5), 1053–1078 (2003)

    Google Scholar 

  4. E. Yablonovitch, Inhibited spontaneous emission in solid-state electronics. Phys. Rev. Lett. 58(20), 2059–2062 (1987)

    Article  ADS  Google Scholar 

  5. S. Ping et al., Locally resonant sonic materials. (Wave -scattering yields amplitude reduction.) (Brief Article). Phys. B-condens. Matter 4050(1–4), 201–205 (2003)

    Google Scholar 

  6. Zhao, H.G, et al., Novel Acoustic Materials--Phononic Crystals. Materials Science and Engineering, 2003.(Chinese)

  7. W. Xu et al., Multi-objective topology optimization of two-dimensional multi-phase microstructure phononic crystals. Mater. Today Commun. 22, 100801 (2019)

    Article  Google Scholar 

  8. Y. Huang, S. Liu, J. Zhao, Optimal design of two-dimensional band-gap materials for uni-directional wave propagation. Struct. Multidiscip. Optim. 48(3), 487–499 (2013)

    Article  MathSciNet  Google Scholar 

  9. Z. Lu et al., A tunable dielectric elastomer acoustic absorber. Acta Acust. Acust. 101(4), 863–86 (2015)

    Article  Google Scholar 

  10. C.J. Rupp, M.L. Dunn, K. Maute, Switchable phononic wave filtering, guiding, harvesting, and actuating in polarization-patterned piezoelectric solids. Appl. Phys. Lett. 96(11), 341–877 (2010)

    Article  Google Scholar 

  11. Zi-Gui, et al., Temperature effect on the bandgaps of surface and bulk acoustic waves in two-dimensional phononic crystals Ultrasonics Ferroelectrics and Frequency Control. IEEE Trans. on 52(3), 365–370 (2005)

    Google Scholar 

  12. W.P. Yang, L.W. Chen, The tunable acoustic band gaps of two-dimensional phononic crystals with a dielectric elastomer cylindrical actuator. Smart Mater. Struct 17(1), 015011 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  13. K.L. Jim et al., Thermal tuning of phononic bandstructure in ferroelectric ceramic/epoxy phononic crystal. Appl. Phys. Lett. 94(19), 193501–193501 (2009)

    Article  ADS  Google Scholar 

  14. Z. Hou, F. Wu, Y. Liu, Phononic crystals containing piezoelectric material. Solid State Commun. 130(11), 745–749 (2004)

    Article  ADS  Google Scholar 

  15. W.F.L.Y. Yize, Tuning of band gaps for a two-dimensional piezoelectric phononic crystal with a rectangular lattice. Acta. Mech. Sin. 25(1), 65–71 (2009)

    Article  Google Scholar 

  16. J.F. Robillard et al., Tunable magnetoelastic phononic crystals. Appl. Phys. Lett. 95(12), 8759 (2009)

    Article  Google Scholar 

  17. Y. Wang et al., Tuning of band gaps for a two-dimensional piezoelectric phononic crystal with a rectangular lattice. Acta Mech. Sin. 25(1), 65–71 (2009)

    Article  ADS  Google Scholar 

  18. K. Bertoldi, M.C. Boyce, Mechanically triggered transformations of phononic band gaps in periodic elastomeric structures. Phys. Rev. B 77(5), 439–446 (2008)

    Article  Google Scholar 

  19. J.H. Jang et al., Combining pattern instability and shape-memory hysteresis for phononic switching. Nano Lett. 9(5), 2113–2119 (2009)

    Article  ADS  Google Scholar 

  20. J. Lehman, R. Lakes, Stiff lattices with zero thermal expansion and enhanced stiffness via rib cross section optimization. Int. J. Mech. Mater. Des. 9(3), 213–225 (2013)

    Article  Google Scholar 

  21. J. Lehman, R.S. Lakes, Stiff, strong, zero thermal expansion lattices via material hierarchy. Compos. Struct. 107, 654–663 (2014)

    Article  Google Scholar 

  22. Y. Zhang et al., A new design for enhanced stiffness of dual-constituent triangular lattice metamaterial with unbounded thermal expansion. Mater. Res. Express (2018). https://doi.org/10.1088/2053-1591/aae5be

    Article  ADS  Google Scholar 

  23. Y.C. Zhang et al., A new design of dual-constituent triangular lattice metamaterial with unbounded thermal expansion. Acta Mech. Sin. (2019). https://doi.org/10.1088/2053-1591/aae5be

    Article  MathSciNet  Google Scholar 

  24. K. Wei et al., Planar lattices with tailorable coefficient of thermal expansion and high stiffness based on dual-material triangle unit. J. Mech. Phys. Solids 86, 173–191 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  25. K. Wei et al., Lightweight composite lattice cylindrical shells with novel character of tailorable thermal expansion. Int. J. Mech. Sci. 137, 77–85 (2018)

    Article  Google Scholar 

  26. K. Wei et al., Three dimensional lightweight lattice structures with large positive, zero and negative thermal expansion. Compos. Struct. 188, 287–296 (2018)

    Article  Google Scholar 

  27. W. Kai et al., A cellular metastructure incorporating coupled negative thermal expansion and negative Poisson’s ratio. Int. J. Solids Struct. 150, 255–267 (2018)

    Article  Google Scholar 

  28. Wei, K., et al., Additively manufactured bi-material metamaterial to program a wide range of thermal expansion. Materials & design, 2021. 198: p. 109343.

  29. H. Xu, A. Farag, D. Pasini, Routes to program thermal expansion in three-dimensional lattice metamaterials built from tetrahedral building blocks. J. Mech. Phys. Solids 117, 54–87 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  30. H. Xu et al., Thermally actuated hierarchical lattices with large linear and rotational expansion. J. Appl. Mech. 86(11), 111011 (2019)

    Article  ADS  Google Scholar 

  31. M.M. Toropova, C.A. Steeves, Robust lightweight multifunctional thermally tailored lattices. Smart Mater. Struct. 29, 035011 (2019)

    Article  ADS  Google Scholar 

  32. Liu, Y, Finite element simulation of elastic waves in 2-D artificial periodic structures[D], Harbin Institute Technology, 2019.(Chinese)

  33. C.A. Steeves et al., Concepts for structurally robust materials that combine low thermal expansion with high stiffness. J. Mech. Phys. Solids 55(9), 1803–1822 (2007)

    Article  ADS  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China (No. 11502149, 11302135), Natural Science Foundation of Liaoning Province (Nos. 2019-ZD-0229, 2019-ZD-0228 and 2019-ZD-0297), Scientific Research Fund of Liaoning Provincial Education Department (No. JYT19056). The financial contributions are gratefully acknowledged. We would like to thank Editage (www.editage.cn) for English language editing.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Weikai Xu.

Additional information

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

Lv, S., Xu, W., Bai, L. et al. Thermal tuning of band gap properties in planar stretch-dominated lattices with tailorable coefficient of thermal expansion. Appl. Phys. A 127, 425 (2021). https://doi.org/10.1007/s00339-021-04570-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00339-021-04570-1

Keywords

Navigation