A seismic metamaterial, is a

metamaterial A metamaterial (from the Greek word μετά ''meta'', meaning "beyond" or "after", and the Latin word ''materia'', meaning "matter" or "material") is any material engineered to have a property that is not found in naturally occurring materials. ...

that is designed to counteract the adverse effects of

seismic waves A seismic wave is a wave of acoustic energy that travels through the Earth. It can result from an earthquake, volcanic eruption, magma movement, a large landslide, and a large man-made explosion that produces low-frequency acoustic energy. S ...

on artificial structures, which exist on or near the surface of the earth. Current designs of seismic metamaterials utilize configurations of boreholes, trees or proposed underground resonators to act as a large scale material. Experiments have observed both reflections and bandgap attenuation from artificially induced seismic waves. These are the first experiments to verify that seismic metamaterials can be measured for frequencies below 100 Hz, where damage from Rayleigh waves is the most harmful to artificial structures.

The mechanics of seismic waves

More than a million

earthquakes An earthquake (also known as a quake, tremor or temblor) is the shaking of the surface of the Earth resulting from a sudden release of energy in the Earth's lithosphere that creates seismic waves. Earthquakes can range in intensity, from ...

are recorded each year, by a worldwide system of earthquake detection stations. The propagation

velocity Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity is a ...

of the

depends on

density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...

and

elasticity Elasticity often refers to: *Elasticity (physics), continuum mechanics of bodies that deform reversibly under stress Elasticity may also refer to: Information technology * Elasticity (data store), the flexibility of the data model and the cl ...

of the earth materials. In other words, the speeds of the seismic waves vary as they travel through different materials in the

earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surfa ...

. The two main components of a seismic event are

body waves Body may refer to: In science * Physical body, an object in physics that represents a large amount, has mass or takes up space * Body (biology), the physical material of an organism * Body plan, the physical features shared by a group of anima ...

and

surface waves In physics, a surface wave is a mechanical wave that propagates along the interface between differing media. A common example is gravity waves along the surface of liquids, such as ocean waves. Gravity waves can also occur within liquids, at th ...

. Both of these have different modes of wave propagation.

Towards Seismic Cloaking

Computations showed that seismic waves traveling toward a

building A building, or edifice, is an enclosed structure with a roof and walls standing more or less permanently in one place, such as a house or factory (although there's also portable buildings). Buildings come in a variety of sizes, shapes, and fun ...

, could be directed around the building, leaving the building unscathed, by using ''seismic metamaterials''. The very long

wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...

s of earthquake waves would be shortened as they interact with the

s; 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 Metamaterial cloaking is the usage of metamaterials in an cloaking device, invisibility cloak. This is accomplished by manipulating the paths traversed by light through a novel optical material. Metamaterials direct and control the Wave propagati ...

. This method was first understood with electromagnetic cloaking metamaterials - the

electromagnetic In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of a ...

energy is in

effect Effect may refer to: * A result or change of something ** List of effects ** Cause and effect, an idiom describing causality Pharmacy and pharmacology * Drug effect, a change resulting from the administration of a drug ** Therapeutic effect, a ...

directed around an object, or hole, and protecting buildings from seismic waves employs this same principle. Giant

polymer A polymer (; Greek '' poly-'', "many" + ''-mer'', "part") is a substance or material consisting of very large molecules called macromolecules, composed of many repeating subunits. Due to their broad spectrum of properties, both synthetic a ...

-made

split ring resonator A split-ring resonator (SRR) is an artificially produced structure common to metamaterials. Its purpose is to produce the desired magnetic susceptibility (magnetic response) in various types of metamaterials up to 200 Terahertz (unit), terahertz. ...

s combined with other metamaterials are designed to couple at the seismic

Concentric In geometry, two or more objects are said to be concentric, coaxal, or coaxial when they share the same center or axis. Circles, regular polygons and regular polyhedra, and spheres may be concentric to one another (sharing the same center point ...

layers of this material would be stacked, each layer separated by an

elastic Elastic is a word often used to describe or identify certain types of elastomer, elastic used in garments or stretchable fabrics. Elastic may also refer to: Alternative name * Rubber band, ring-shaped band of rubber used to hold objects togeth ...

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.

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 A cylinder (from ) has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a circle as its base. A cylinder may also be defined as an infini ...

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 Anisotropy () is the property of a material which allows it to change or assume different properties in different directions, as opposed to isotropy. It can be defined as a difference, when measured along different axes, in a material's physic ...

metamaterial. The configuration can be viewed as alternating layers of "

homogeneous Homogeneity and heterogeneity are concepts often used in the sciences and statistics relating to the uniformity of a substance or organism. A material or image that is homogeneous is uniform in composition or character (i.e. color, shape, siz ...

isotropic dielectric material" A. with "homogeneous

isotropic Isotropy is uniformity in all orientations; it is derived . Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix ' or ', hence ''anisotropy''. ''Anisotropy'' is also used to describe ...

dielectric material" B. Each

dielectric In electromagnetism, a dielectric (or dielectric medium) is an electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, electric charges do not flow through the mate ...

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 anisotropic metamaterial, to show the effectiveness of the layered metamaterial.

Acoustic cloaking principles for seismic metamaterials

The theory and ultimate development for the ''seismic metamaterial'' is based on

coordinate transformations In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space. The order of the coordinates is sign ...

achieved when concealing a small cylindrical object with

electromagnetic wave In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visib ...

s. This was followed by an analysis of acoustic cloaking, and whether or not coordinate transformations could be applied to artificially fabricated acoustic materials. Applying the concepts used to understand

materials to material properties in other systems shows them to be closely analogous.

Wave vector In physics, a wave vector (or wavevector) is a vector used in describing a wave, with a typical unit being cycle per metre. It has a magnitude and direction. Its magnitude is the wavenumber of the wave (inversely proportional to the wavelength), ...

wave impedance The wave impedance of an electromagnetic wave is the ratio of the transverse components of the electric and magnetic fields (the transverse components being those at right angles to the direction of propagation). For a transverse-electric-magnetic ...

, and direction of power flow are universal. By understanding how

permittivity In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter ''ε'' ( epsilon), is a measure of the electric polarizability of a dielectric. A material with high permittivity polarizes more in ...

and permeability control these components of

wave propagation Wave propagation is any of the ways in which waves travel. Single wave propagation can be calculated by 2nd order wave equation ( standing wavefield) or 1st order one-way wave equation. With respect to the direction of the oscillation relative to ...

, applicable analogies can be used for other material interactions. 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 Linear elasticity is a mathematical model of how solid objects deform and become internally stressed due to prescribed loading conditions. It is a simplification of the more general nonlinear theory of elasticity and a branch of continuum mec ...

. Furthermore, this case appears practically useful. In two dimensions,

acoustic media and isotropic electromagnetic media are exactly equivalent. Under these conditions, the isotropic characteristic works in

media as well. It has been demonstrated mathematically that the 2D

Maxwell equations Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. T ...

with

normal incidence The angle of incidence, in geometric optics, is the angle between a ray incident on a surface and the line perpendicular (at 90 degree angle) to the surface at the point of incidence, called the normal. The ray can be formed by any waves, such as o ...

apply to 2D acoustic equations when replacing the electromagnetic parameters with the following acoustic parameters:

pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...

, vector fluid velocity, fluid

mass density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematically ...

and the fluid

bulk modulus The bulk modulus (K or B) of a substance is a measure of how resistant to compression the substance is. It is defined as the ratio of the infinitesimal pressure increase to the resulting ''relative'' decrease of the volume. Other moduli describe ...

. 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. 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.

The seismic cloak

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 Scattering is a term used in physics to describe a wide range of physical processes where moving particles or radiation of some form, such as light or sound, are forced to deviate from a straight trajectory by localized non-uniformities (including ...

, hence, the seismic cloak becomes an effective medium.

Seismic Metamaterials Experiments

In 2012, researchers held an experimental field-test in France, with the aim to highlight analogy with phononic crystal.

References

{{reflist, 2 Seismology Metamaterials Continuum mechanics