The influence of clamping, structure geometry and material on seismic metamaterial performance

T. Venkatesh Venkatesh Varma (1) , Bogdan Ungureanu (2) , Saikat Sarkar (1) , Richard Craster (2, 3, 4) , Sébastien Guenneau (3) , Stéphane Brûlé (5)

1 IITI - Indian Institute of Technology Indore
2 Department of Mathematics [Imperial College London]
3 Abraham de Moivre
4 Department of Mechanical Engineering [Imperial College London]
5 FRESNEL - Institut FRESNEL

Diverting and controlling the impact of elastic vibrations upon an infrastructure is a major challenge for seismic hazard mitigation and for the reduction of machine noise and vehicle vibration in the urban environment. Seismic metamaterials (SMs), with their inherent ability to manipulate wave propagation, provide a key route for overcoming the technological hurdles involved in this challenge. Engineering the structure of the SM serves as a basis to tune and enhance its functionality, and inspired by split rings, swiss-rolls, notch-shaped, and labyrinthine designs of elementary cells in electromagnetic and mechanical metamaterials, we investigate altering the structure geometries of SMs with the aim of creating large bandgaps in a subwavelength regime. Interestingly, clamping an SM to the bedrock creates a zero frequency stopband, but further effects can be observed in the higher frequency regime due to their specific geometry. We show that square stiff inclusions perform better in comparison to circular ones while keeping the same filling fraction. En route to enhancing the bandgap, we have also studied the performance of SMs with different constituent materials; we find that steel columns, as inclusions, show large bandgaps, however, the columns are too large for steel to be a feasible material in practical or financial terms. Non-reinforced concrete would be preferable for industry level scaling up of the technology because, concrete is cost-effective, easy to cast directly at the construction site and easy to provide arbitrary geometry of the structure. As a part of this study, we show that concrete columns can also be designed to exhibit bandgaps if we cast them within a soft soil coating surrounding the protected area for various civil structures like a bridge, building, oil pipelines, etc. Although our motivation is for ground vibration, and we use the frequencies, lengthscales, and material properties relevant for that application, it is notable that we use the equations of linear elasticity, and our investigation is more broadly relevant in solid mechanics.

Mots clés: seismic metamaterial; transmission diagram; dispersion curves; bandgap; geophysics; computational physics; inertial resonators; Floquet-Bloch waves

Domaines: Dynamique, vibrations

T. Venkatesh Venkatesh Varma, Bogdan Ungureanu, Saikat Sarkar, Richard Craster, Sébastien Guenneau, et al.. The influence of clamping, structure geometry and material on seismic metamaterial performance. Frontiers in Materials, 2021, 8, pp.603820. ⟨10.3389/fmats.2021.603820⟩. ⟨hal-03448055⟩