Advertisement

Design of Acoustic Metamaterials Through Nonlinear Programming

  • Andrea Bacigalupo
  • Giorgio GneccoEmail author
  • Marco Lepidi
  • Luigi Gambarotta
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10122)

Abstract

The dispersive wave propagation in a periodic metamaterial with tetrachiral topology and inertial local resonators is investigated. The Floquet-Bloch spectrum of the metamaterial is compared with that of the tetrachiral beam lattice material without resonators. The resonators can be designed to open and shift frequency band gaps, that is, spectrum intervals in which harmonic waves do not propagate. Therefore, an optimal passive control of the frequency band structure can be pursued in the metamaterial. To this aim, suitable constrained nonlinear optimization problems on compact sets of admissible geometrical and mechanical parameters are stated. According to functional requirements, sets of parameters which determine the largest low-frequency band gap between selected pairs of consecutive branches of the Floquet-Bloch spectrum are soughted for numerically. The various optimization problems are successfully solved by means of a version of the method of moving asymptotes, combined with a quasi-Monte Carlo multi-start technique.

Keywords

Metamaterials Wave propagation Passive control Relative band gap optimization Nonlinear programming 

References

  1. 1.
    Bacigalupo, A., Gambarotta, L.: Homogenization of periodic hexa- and tetra-chiral cellular solids. Compos. Struct. 116, 461–476 (2014)CrossRefGoogle Scholar
  2. 2.
    Bacigalupo, A., De Bellis, M.L.: Auxetic anti-tetrachiral materials: equivalent elastic properties and frequency band-gaps. Compos. Struct. 131, 530–544 (2015)CrossRefGoogle Scholar
  3. 3.
    Bacigalupo, A., Gambarotta, L.: Simplified modelling of chiral lattice materials with local resonators. Int. J. Solids Struct. 83, 126–141 (2016)CrossRefGoogle Scholar
  4. 4.
    Bacigalupo A., Lepidi M.: A lumped mass beam model for the wave propagation in anti-tetrachiral periodic lattices. In: XXII AIMETA Congress, Genoa, Italy (2015)Google Scholar
  5. 5.
    Bacigalupo, A., Lepidi, M.: High-frequency parametric approximation of the Floquet-Bloch spectrum for anti-tetrachiral materials. Int. J. Solids Struct. 97, 575–592 (2016)CrossRefGoogle Scholar
  6. 6.
    Bacigalupo, A., Lepidi, M., Gnecco, G., Gambarotta, L.: Optimal design of auxetic hexachiral metamaterials with local resonators. Smart Mater. Struct. 25(5), 054009 (2016)CrossRefGoogle Scholar
  7. 7.
    Bigoni, D., Guenneau, S., Movchan, A.B., Brun, M.: Elastic metamaterials with inertial locally resonant structures: application to lensing and localization. Phys. Rev. B 87, 174303 (2013)CrossRefGoogle Scholar
  8. 8.
    Brillouin, L.: Wave Propagation in Periodic Structures, 2nd edn. Dover, New York (1953)zbMATHGoogle Scholar
  9. 9.
    Gnecco, G., Sanguineti, M.: Regularization techniques and suboptimal solutions to optimization problems in learning from data. Neural Comput. 22, 793–829 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Gnecco, G., Gori, M., Sanguineti, M.: Learning with boundary conditions. Neural Comput. 25, 1029–1106 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Lepidi M., Bacigalupo A.: Passive control of wave propagation in periodic anti-tetrachiral metamaterials. In: VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS), Hersonissos, Crete Island (2016)Google Scholar
  12. 12.
    Liu, X.N., Hu, G.K., Sun, C.T., Huang, G.L.: Wave propagation characterization and design of two-dimensional elastic chiral metacomposite. J. Sound Vib. 330, 2536–2553 (2011)CrossRefGoogle Scholar
  13. 13.
    Niederreiter H.: Random number generation and Quasi-Monte Carlo methods. SIAM (1992)Google Scholar
  14. 14.
    Phani, A.S., Woodhouse, J., Fleck, N.A.: Wave propagation in two-dimensional periodic lattices. J. Acoust. Soc. Am. 119, 1995–2005 (2006)CrossRefGoogle Scholar
  15. 15.
    Spadoni, A., Ruzzene, M., Gonnella, S., Scarpa, F.: Phononic properties of hexagonal chiral lattices. Wave Motion 46, 435–450 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Svanberg, K.: The method of moving asymptotes - a new method for structural optimization. Int. J. Numer. Meth. Eng. 24, 359–373 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM J. Optim. 12, 555–573 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Tan, K.T., Huang, H.H., Sun, C.T.: Optimizing the band gap of effective mass negativity in acoustic metamaterials. Appl. Phys. Lett. 101, 241902 (2012)CrossRefGoogle Scholar
  19. 19.
    Tee, K.F., Spadoni, A., Scarpa, F., Ruzzene, M.: Wave propagation in auxetic tetrachiral honeycombs. J. Vib. Acoust. ASME 132, 031007–1/8 (2010)Google Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Andrea Bacigalupo
    • 1
  • Giorgio Gnecco
    • 1
    Email author
  • Marco Lepidi
    • 2
  • Luigi Gambarotta
    • 2
  1. 1.IMT School for Advanced StudiesLuccaItaly
  2. 2.DICCAUniversity of GenoaGenoaItaly

Personalised recommendations