Qualitative and quantitative imaging as well as dynamic / mechanical studies of some biological systems, including diatoms, seashells, and insect wings allowed us to identify key features for inspiring the design of a new class of metamaterials valuable for underwater noise reduction applications. These features include, but not limited to, hierarchical and graded organizations of structural elements across multiple length scales, elastic anisotropy, coupling of elastic waves with different polarization, quasi-periodicity, and broken symmetries.
Starting from these observations, we have shown that introducing the concept of structural hierarchy in elastic metamaterials and phononic crystals can lead to a new class of periodic structures capable of generating multiple, highly attenuative and broadband bandgaps at multi-scale frequencies, including the lowest, where the size of the unit cells becomes extremely small (deep sub-wavelength) with respect to the wavelength of the waves in play. The concept of hierarchy is intended in the sense that a representative unit cell of a periodic structure comprises multiple arrangements of non-self-similar inhomogeneities (cavities introduced into a continuous matrix, for instance) at various length scales activating diverse types of scattering mechanisms (Bragg scattering, local resonances, and / or inertial amplification).
We have proposed a couple of preliminary designs of metamaterial unit cell: the first, concerning quasi-Helmholtz resonators with a hierarchical architecture inspired by the multilevel organization of pores typical of the « Coscinodiscus genus frustule ». Preliminary numerical results (with no hierarchical levels, yet) have shown high potential for absorption performance (with the possibility of quasi-perfect absorption under specific assumptions). The second design, coupling shear and longitudinal motion to achieve sound transmission loss through reflection in highly sub-wavelength unit cells. The idea here is that a unit cell mixed polarization will allow us to convert the motion excited at one end of the meta-barrier impinged by an underwater wave (thus, mainly longitudinal) into (partially) shear motion at the other end, limiting, thus, the propagation of sound in water. Preliminary analytical / numerical models predicted a lattice parameter to the maximum wavelength ratio up to 1 / 80 and 20 – 40 dB reduction.
