Low-frequency micro-structured mechanical metamaterials

Mechanical metamaterials with a periodic micro-structure of small length scale ( <= 1 cm) and with band gaps at very low frequencies ( <= 5 kHz) are designed, fabricated, and experimentally characterized. This is achieved by the addition of a discrete structurally resonant inclusion with a low natural resonance frequency into a hollow cellular structure. The mechanical eigenfrequencies of the cell are calculated based on a finite element simulation of an infinite array with Floquet-Bloch boundary conditions. The unit cell is optimized to demonstrate a measurable low frequency stop band for longitudinal waves. The scattering response for a finitely thick slab of unit cells is estimated using a numerical method. In this method, frequency domain simulations are performed and the scattering matrix is extracted using two velocity measurements within homogeneous external domains on either side of the heterogeneous slab. An example of such micro-structured array was manufactured with 3D printing and its response was measured under water with a solid polymer plate of similar dimensions for comparison. The experimental data is compared with numerical modeling results with particular attention to the effect of macro-scale finite plate resonances as contrasted with micro-structural effects.