Seismic waves damping with arrays of inertial resonators

By Y. Achaoui, B. Ungureanu, Stefan Enoch, St'ephane Brul'e, Sébastien Guenneau. 2015

138 citations recorded by the source corpus.

We investigate the elastic stop band properties of a theoretical cubic array of iron spheres connected to a bulk of concrete via iron or rubber ligaments. Each sphere can move freely within a surrounding air cavity, but ligaments couple it to the bulk and further facilitate bending and rotational motions. Associated low frequency local resonances are well predicted by an asymptotic formula. We find complete stop bands (for all wave-polarizations) in the frequency range $[16,21]$ Hertz (resp. $[6,11]$ Hertz) for $7.4$-meter (resp. $0.74$-meter) diameter iron spheres with a $10$-meter (resp. $1$-meter) center-to-center spacing, when they are connected to concrete via steel (resp. rubber) ligaments. The scattering problem shows that only bending modes are responsible for damping and that rotational modes are totally overwritten by bending modes. Regarding seismic applications, we further consider soil as a bulk medium, in which case the relative bandwidth of the low frequency stop band can be enlarged through ligaments of different sizes that allow for well separated bending and rotational modes. We finally achieve some damping of elastodynamic waves from $8$ to $49$ Hertz (relative stop band of $143$ percent) for iron spheres $0.74$-meter in diameter that are connected to soil with six rubber ligaments of optimized shapes. These results represent a preliminary step in the design of seismic shields placed around, or underneath, the foundations of large civil infrastructures.

Subfields: Biomedical Engineering, Civil and Structural Engineering, Ocean Engineering

View Paper: https://www.semanticscholar.org/paper/21158f2977e512f3400736e90307279b85ed43e7

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Biomedical Engineering

Citations in the corpus

Tailoring Structure‐Borne Sound through Bandgap Engineering in Phononic Crystals and Metamaterials: A Comprehensive Review (2022, background): “[102,103] introduced the idea of using a forest as a lattice where each tree behaves as a resonator with flexural vibration to strongly attenuate seismic waves [107].”
Clamped seismic metamaterials: ultra-low frequency stop bands (2017, background): “The frequency bandwidth of wave protection can be enlarged by considering arrays of resonant cylinders with different eigenfrequency for two-dimensional stop-bands [42], or cubic arrays of resonant spheres [43] for 3D stop-bands, but such mechanical metamaterials would be hard to implement at the ci”
Emergence of seismic metamaterials: Current state and future perspectives (2017, background): “The frequency bandwidth of wave protection can be enlarged by considering arrays of resonant cylinders with different eigenfrequency for two-dimensional stopbands [47], or cubic arrays of resonant spheres [48] for 3D stop-bands, but such mechanical metamaterials would be hard to implement at the civ”