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# Seismic metamaterials

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### Seismic metamaterials

Seismic metamaterials, are metamaterials which are designed to counteract the adverse effects of seismic waves on artificial structures, which exist on or near the surface of the earth.[1][2][3] As of 2009 seismic metamaterials were still in the development stage.[1][2]

## The mechanics of seismic waves

More than a million earthquakes are recorded each year, by a worldwide system of earthquake detection stations. The propagation velocity of the seismic waves depends on density and elasticity of the earth materials. In other words, the speeds of the seismic waves vary as they travel through different materials in the earth. The two main components of a seismic event are body waves and surface waves. Both of these have different modes of wave propagation.[4]

## Dissipating ocean surface waves with seismic metamaterials

Computations showed that seismic waves traveling toward a building, could be directed around the building, leaving the building unscathed, by using seismic metamaterials. The very long wavelengths of earthquake waves would be shortened as they interact with the metamaterials; the waves would pass around the building so as to arrive in phase as the earthquake wave proceeded, as if the building was not there. The mathematical models produce the regular pattern provided by Metamaterial cloaking. This method was first understood with electromagnetic cloaking metamaterials - the electromagnetic energy is in effect directed around an object, or hole, and protecting buildings from seismic waves employs this same principle.[1][2]

Giant polymer-made split ring resonators combined with other metamaterials are designed to couple at the seismic wavelength. Concentric layers of this material would be stacked, each layer separated by an elastic medium. The design that worked is ten layers of six different materials, which can be easily deployed in building foundations. As of 2009, the project is still in the design stage.[1][2]

### Electromagnetics cloaking principles for seismic metamaterials

For seismic metamaterials to protect surface structures, the proposal includes a layered structure of metamaterials, separated by elastic plates in a cylindrical configuration. A prior simulation showed that it is possible to create concealment from electromagnetic radiation with concentric, alternating layers of electromagnetic metamaterials. That study was is in contrast to concealment by inclusions in a split ring resonator designed as an anisotropic metamaterial.[5]

The configuration can be viewed as alternating layers of "homogeneous isotropic dielectric material" A with "homogeneous isotropic dielectric material" B. Each dielectric material is much thinner than the radiated wavelength. As a whole, such structure is an anisotropic medium. The layered dielectric materials surround an "infinite conducting cylinder". The layered dielectric materials radiate outward, in a concentric fashion, and the cylinder is encased in the first layer. The other layers alternate and surround the previous layer all the way to the first layer. Electromagnetic wave scattering was calculated and simulated for the layered (metamaterial) structure and the split-ring resonator anistropic metamaterial, to show the effectiveness of the layered metamaterial.[5]

### Acoustic cloaking principles for seismic metamaterials

The theory and ultimate development for the seismic metamaterial is based on coordinate transformations achieved when concealing a small cylindrical object with electromagnetic waves. This was followed by an analysis of acoustic cloaking, and whether or not coordinate transformations could be applied to artificially fabricated acoustic materials.[3]

Applying the concepts used to understand electromagnetic materials to material properties in other systems shows them to be closely analogous. Wave vector, wave impedance, and direction of power flow are universal. By understanding how permittivity and permeability control these components of wave propagation, applicable analogies can be used for other material interactions.[6]

In most instances, applying coordinate transformation to engineered artificial elastic media is not possible. However, there is at least one special case where there is a direct equivalence between electromagnetics and elastodynamics. Furthermore, this case appears practically useful. In two dimensions, isotropic acoustic media and isotropic electromagnetic media are exactly equivalent. Under these conditions, the isotropic characteristic works in anisotropic media as well.[6]

It has been demonstrated mathematically that the 2D Maxwell equations with normal incidence apply to 2D acoustic equations when replacing the electromagnetic parameters with the following acoustic parameters: pressure, vector fluid velocity, fluid mass density and the fluid bulk modulus. The compressional wave solutions used in the electromagnetic cloaking are transferred to material fluidic solutions where fluid motion is parallel to the wavevector. The computations then show that coordinate transformations can be applied to acoustic media when restricted to normal incidence in two dimensions.[6]

Next the electromagnetic cloaking shell is referenced as an exact equivalence for a simulated demonstration of the acoustic cloaking shell. Bulk modulus and mass density determine the spatial dimensions of the cloak, which can bend any incident wave around the center of the shell. In a simulation with perfect conditions, because it is easier to demonstrate the principles involved, there is zero scattering in any direction.[6]

### The seismic cloak

The main principles underpinning the protection of structures from seismic waves are then applied to waves of force that travel through the Earth, which is an elastic body.[3][6] Travelling pressure waves are always generated with longitudinal polarization. This means that the ground is alternately compressed and dilated in the direction of propagation. Travelling shear waves are transverse, or perpendicular to the direction of propagation. One of the effects of the metamaterial is to de-couple these components of the seismic wave. By applying these principles, it is possible to design a cylindrical, seismic metatmaterial cloak to remedy the destructive effects of coupled pressure and shear waves that would travel through the same earthen geometrical plane as the structure. The components of the seismic waves should work together to disrupt the elastic earth, on which a building is anchored. However, it can be demonstrated through computation and visual simulation that the waves are in fact dispersed around the location of the building. The frequency range of this capability is shown to have no limitation regarding the radiated frequency. The cloak itself demonstrates no forward or back scattering, hence, the seismic cloak becomes an effective medium.[3]

## References

1. ^ a b c d Johnson, R. Colin (2009-07-23). "Metamaterial cloak could render buildings 'invisible' to earthquakes". EETimes.com. Retrieved 2009-09-09.
2. ^ a b c d Barras, Colin (2009-06-26). "Invisibility cloak could hide buildings from quakes". New Scientist. Retrieved 2009-10-20.
3. ^ a b c d Brun, M.; S. Guenneau; and A.B. Movchan (2009-02-09). "Achieving control of in-plane elastic waves". Appl. Phys. Lett. 94 (61903): 1–7.
4. ^ Krebs, Robert E. (2003). The basics of earth science. Westport, CT, USA: Greenwood Publishing Group, Incorporated. pp. 32–33.
5. ^ a b Huang, Ying; Feng, Y; Jiang, T (2007-08-21). "Electromagnetic cloaking by layered structure of homogeneous isotropic materials". Optics Express 15 (18): 11133–11141.
6. ^ a b c d e Cummer, Steven A; David Schurig (2007-03-02). "One path to acoustic cloaking". New Journal of Physics 9 (3): 1–7.
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