Design of Acoustic Metamaterials Through Nonlinear Programming
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.
KeywordsMetamaterials Wave propagation Passive control Relative band gap optimization Nonlinear programming
- 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
- 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
- 13.Niederreiter H.: Random number generation and Quasi-Monte Carlo methods. SIAM (1992)Google Scholar
- 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