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)


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.


Metamaterials Wave propagation Passive control Relative band gap optimization Nonlinear programming 


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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

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