The Influence of Clamping, Structure Geometry, and Material on Seismic Metamaterial Performance

Abstract

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.

A Ternary Seismic Metamaterial for Low Frequency Vibration Attenuation

“…We assume that the three components of the metamaterial are isotropic and linear elastic materials. According to the elastic dynamic theory, the elastic motion equation with respect to the displacement is established [ 22 , 46 ]. where λ and are the Lamé constant, ρ is the mass density, is the body force, is the time, is the displacement, is the position coordinates.…”

“…Here, we give a dispersion analysis process for finite element analysis to obtain the dispersion curve between frequency ω and wave vector k. We assume that the three components of the metamaterial are isotropic and linear elastic materials. According to the elastic dynamic theory, the elastic motion equation with respect to the displacement is established [22,46].…”

“…Based on the concept of phononic crystal, seismic metamaterials can block the propagation of elastic waves in a certain frequency range, which is called band gap [ 14 , 15 , 16 , 17 , 18 , 19 , 20 ]. Therefore, seismic metamaterial shows broad development prospects for the low-frequency vibration attenuation induced by elastic wave [ 21 , 22 , 23 , 24 ]. Local resonance phononic crystal proposed by Liu et al provided a new idea to design seismic metamaterial for low frequency vibration attenuation [ 25 ].…”

Gradient V-Shaped and N-Shaped Seismic Metamaterials

“…The square shape enhances the performance of the seismic metamaterial compared to the cross-like steel section. Varma et al [13] studied the inclusion of steel shapes configured as square, circular, and notchshaped square. They found that the square steel configuration is superior to the other two under the same filling ratio.…”