Seismic metamaterials
Encyclopedia
Seismic metamaterials, are metamaterial
s which are designed to counteract the adverse effects of seismic waves on artificial structures, which exist on or near the surface of the earth. seismic metamaterials were still in the development stage.
of the seismic waves depends on density
and elasticity
of the earthen 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.
, could be directed around the building, leaving the building unscathed, by using seismic metamaterials. The very long wavelength
s of earthquake waves would be shortened as they interact with the metamaterial
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
. 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.
Giant polymer
-made split ring resonator
s 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.
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 an split ring resonator designed as an anisotropic metamaterial.
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.
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 material
s.
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.
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.
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.
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.
s are then applied to waves of force that travel through the Earth, which is an elastic body
. 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 disperesed 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.
Metamaterial
Metamaterials are artificial materials engineered to have properties that may not be found in nature. Metamaterials usually gain their properties from structure rather than composition, using small inhomogeneities to create effective macroscopic behavior....
s which are designed to counteract the adverse effects of seismic waves on artificial structures, which exist on or near the surface of the earth. seismic metamaterials were still in the development stage.
The mechanics of seismic waves
More than a million earthquakes are recorded each year, by a worldwide system of earthquake detection stations. The propagation velocityVelocity
In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...
of the seismic waves depends on density
Density
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...
and elasticity
Elasticity (physics)
In physics, elasticity is the physical property of a material that returns to its original shape after the stress that made it deform or distort is removed. The relative amount of deformation is called the strain....
of the earthen materials. In other words, the speeds of the seismic waves vary as they travel through different materials in the earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...
. The two main components of a seismic event are body waves and surface waves. Both of these have different modes of wave propagation.
Dissipating ocean surface waves with seismic metamaterials
Computations showed that seismic waves traveling toward a buildingBuilding
In architecture, construction, engineering, real estate development and technology the word building may refer to one of the following:...
, could be directed around the building, leaving the building unscathed, by using seismic metamaterials. The very long wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
s of earthquake waves would be shortened as they interact with the metamaterial
Metamaterial
Metamaterials are artificial materials engineered to have properties that may not be found in nature. Metamaterials usually gain their properties from structure rather than composition, using small inhomogeneities to create effective macroscopic behavior....
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
Metamaterial cloaking is the scientific application of metamaterials in order to achieve invisibility-cloaking. This is accomplished by manipulating the paths traversed by light through a novel optical material....
. This method was first understood with electromagnetic cloaking metamaterials
Metamaterial cloaking
Metamaterial cloaking is the scientific application of metamaterials in order to achieve invisibility-cloaking. This is accomplished by manipulating the paths traversed by light through a novel optical material....
- the electromagnetic
Electromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...
energy is in effect
Effective field theory
In physics, an effective field theory is, as any effective theory, an approximate theory, that includes appropriate degrees of freedom to describe physical phenomena occurring at a chosen length scale, while ignoring substructure and degrees of freedom at shorter distances .-The renormalization...
directed around an object, or hole, and protecting buildings from seismic waves employs this same principle.
Giant polymer
Polymer
A polymer is a large molecule composed of repeating structural units. These subunits are typically connected by covalent chemical bonds...
-made split ring resonator
Split Ring Resonator
A split-ring resonator is a component of a Negative index metamaterial , also known as Double negative metamaterials or Left-handed medium . It also component of other types of metamaterial such as Single Negative metamaterial . SRRs are also used for research in Terahertz metamaterials,...
s combined with other metamaterials are designed to couple at the seismic wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
. Concentric
Concentric
Concentric objects share the same center, axis or origin with one inside the other. Circles, tubes, cylindrical shafts, disks, and spheres may be concentric to one another...
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.
Electromagnetics cloaking principles for seismic metamaterials
For seismic metamaterials to protect surface structures, the proposal includes a layered structure of metamaterials, separated by elastic platesPlating
Plating is a surface covering in which a metal is deposited on a conductive surface. Plating has been done for hundreds of years, but it is also critical for modern technology...
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 an split ring resonator designed as an anisotropic metamaterial.
The configuration can be viewed as alternating layers of "homogeneous
Homogeneity (physics)
In general, homogeneity is defined as the quality or state of being homogeneous . For instance, a uniform electric field would be compatible with homogeneity...
isotropic dielectric material" A with "homogeneous isotropic dielectric material" B. Each dielectric
Dielectric
A dielectric is an electrical insulator that can be polarized by an applied electric field. When a dielectric is placed in an electric field, electric charges do not flow through the material, as in a conductor, but only slightly shift from their average equilibrium positions causing 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.
Acoustic cloaking principles for seismic metamaterials
The theory and ultimate development for the seismic metamaterial is based on coordinate transformations achieved when concealingNegative index metamaterials
Negative index metamaterials or negative index materials are artificial structures where the refractive index has a negative value over some frequency range. This does not occur in any known natural materials, and thus is only achievable with engineered structures known as metamaterials...
a small cylindrical object with electromagnetic waves. This was followed by an analysis of acoustic
Acoustics
Acoustics is the interdisciplinary science that deals with the study of all mechanical waves in gases, liquids, and solids including vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician while someone working in the field of acoustics...
cloaking, and whether or not coordinate transformations could be applied to artificially fabricated acoustic material
Acoustic metamaterials
Acoustic metamaterials are artificially fabricated materials designed to control, direct, and manipulate sound in the form of sonic, infrasonic, or ultrasonic waves, as these might occur in gases, liquids, and solids. The hereditary line into acoustic metamaterials follows from theory and research...
s.
Applying the concepts used to understand electromagnetic
Electromagnetism
Electromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...
materials to material properties in other systems shows them to be closely analogous. Wave vector
Wave vector
In physics, a wave vector is a vector which helps describe a wave. Like any vector, it has a magnitude and direction, both of which are important: Its magnitude is either the wavenumber or angular wavenumber of the wave , and its direction is ordinarily the direction of wave propagation In...
, wave impedance
Wave impedance
The wave impedance of an electromagnetic wave is the ratio of the transverse components of the electric and magnetic fields . For a transverse-electric-magnetic plane wave traveling through a homogeneous medium, the wave impedance is everywhere equal to the intrinsic impedance of the medium...
, and direction of power flow are universal. By understanding how permittivity
Permittivity
In electromagnetism, absolute permittivity is the measure of the resistance that is encountered when forming an electric field in a medium. In other words, permittivity is a measure of how an electric field affects, and is affected by, a dielectric medium. The permittivity of a medium describes how...
and permeability
Permeability (electromagnetism)
In electromagnetism, permeability is the measure of the ability of a material to support the formation of a magnetic field within itself. In other words, it is the degree of magnetization that a material obtains in response to an applied magnetic field. Magnetic permeability is typically...
control these components of wave propagation
Wave propagation
Wave propagation is any of the ways in which waves travel.With respect to the direction of the oscillation relative to the propagation direction, we can distinguish between longitudinal wave and transverse waves....
, 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. 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.
It has been demonstrated mathematically that the 2D Maxwell equations with normal incidence apply to 2D acoustic
Acoustics
Acoustics is the interdisciplinary science that deals with the study of all mechanical waves in gases, liquids, and solids including vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician while someone working in the field of acoustics...
equations when replacing the electromagnetic parameters with the following acoustic parameters: pressure, vector fluid velocity
Flow velocity
In fluid dynamics the flow velocity, or velocity field, of a fluid is a vector field which is used to mathematically describe the motion of a fluid...
, fluid mass density and the fluid bulk modulus
Bulk modulus
The bulk modulus of a substance measures the substance's resistance to uniform compression. It is defined as the pressure increase needed to decrease the volume by a factor of 1/e...
. 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
The main priniples underpinning the protection of structures from seismic waveSeismic wave
Seismic waves are waves of energy that travel through the earth, and are a result of an earthquake, explosion, or a volcano that imparts low-frequency acoustic energy. Many other natural and anthropogenic sources create low amplitude waves commonly referred to as ambient vibrations. Seismic waves...
s are then applied to waves of force that travel through the Earth, which is an elastic body
P-wave
P-waves are a type of elastic wave, also called seismic waves, that can travel through gases , solids and liquids, including the Earth. P-waves are produced by earthquakes and recorded by seismographs...
. Travelling pressure waves are always generated with longitudinal polarization. This means that the ground is alternately compressed and dilated in the direction of propagation
Wave propagation
Wave propagation is any of the ways in which waves travel.With respect to the direction of the oscillation relative to the propagation direction, we can distinguish between longitudinal wave and transverse waves....
. 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
COMSOL Multiphysics
COMSOL Multiphysics is a finite element analysis, solver and Simulation software / FEA Software package for various physics and engineering applications, especially coupled phenomena, or multiphysics. COMSOL Multiphysics also offers an extensive interface to MATLAB and its toolboxes for a large...
that the waves are in fact disperesed 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
Scattering is a general physical process where some forms of radiation, such as light, sound, or moving particles, are forced to deviate from a straight trajectory by one or more localized non-uniformities in the medium through which they pass. In conventional use, this also includes deviation of...
, hence, the seismic cloak becomes an effective medium.
See also
- Acoustic metamaterialsAcoustic metamaterialsAcoustic metamaterials are artificially fabricated materials designed to control, direct, and manipulate sound in the form of sonic, infrasonic, or ultrasonic waves, as these might occur in gases, liquids, and solids. The hereditary line into acoustic metamaterials follows from theory and research...
- MetamaterialMetamaterialMetamaterials are artificial materials engineered to have properties that may not be found in nature. Metamaterials usually gain their properties from structure rather than composition, using small inhomogeneities to create effective macroscopic behavior....
- Negative index metamaterialsNegative index metamaterialsNegative index metamaterials or negative index materials are artificial structures where the refractive index has a negative value over some frequency range. This does not occur in any known natural materials, and thus is only achievable with engineered structures known as metamaterials...
- Metamaterial antennasMetamaterial antennasMetamaterial antennas are a class of antennas which use metamaterials to increase performance of miniaturized antenna systems. Their purpose, as with any electromagnetic antenna, is to launch energy into free space...
- Photonic crystalPhotonic crystalPhotonic crystals are periodic optical nanostructures that are designed to affect the motion of photons in a similar way that periodicity of a semiconductor crystal affects the motion of electrons...
- SuperlensSuperlensA superlens, super lens or perfect lens is a lens which uses metamaterials to go beyond the diffraction limit. The diffraction limit is an inherent limitation in conventional optical devices or lenses. In 2000, a type of lens was proposed, consisting of a metamaterial that compensates for wave...
- Split-ring resonator
- Terahertz metamaterialsTerahertz metamaterialsTerahertz metamaterials are a new class of composite, artificial materials which interact at terahertz frequencies. The terahertz frequency range used in materials research is usually defined as 0.1 to 10 THz...
- Tunable metamaterialsTunable metamaterialsA tunable metamaterial is a metamaterial with a variable response to an incident electromagnetic wave. This includes remotely controlling how an incident electromagnetic wave interacts with a metamaterial. This means the capablitity to determine whether the EM wave is transmitted, reflected, or...
- Photonic metamaterialsPhotonic metamaterialsPhotonic metamaterials, also known as Optical metamaterials, are a type of electromagnetic metamaterial, which are designed to interact with optical frequencies which are terahertz , infrared , and eventually, visible wavelengths. As a type of metamaterial, the periodic structures are made up of...
Material properties
- Acoustic dispersionAcoustic dispersionAcoustic dispersion is the phenomenon of a sound wave separating into its component frequencies as it passes through a material. The phase velocity of the sound wave is viewed as a function of frequency...
- Bulk modulusBulk modulusThe bulk modulus of a substance measures the substance's resistance to uniform compression. It is defined as the pressure increase needed to decrease the volume by a factor of 1/e...
- Constitutive equationConstitutive equationIn physics, a constitutive equation is a relation between two physical quantities that is specific to a material or substance, and approximates the response of that material to external forces...
- Elastic wave
- Equation of stateEquation of stateIn physics and thermodynamics, an equation of state is a relation between state variables. More specifically, an equation of state is a thermodynamic equation describing the state of matter under a given set of physical conditions...
- Linear elasticityLinear elasticityLinear elasticity is the mathematical study of how solid objects deform and become internally stressed due to prescribed loading conditions. Linear elasticity models materials as continua. Linear elasticity is a simplification of the more general nonlinear theory of elasticity and is a branch of...
- Permeability
- PermittivityPermittivityIn electromagnetism, absolute permittivity is the measure of the resistance that is encountered when forming an electric field in a medium. In other words, permittivity is a measure of how an electric field affects, and is affected by, a dielectric medium. The permittivity of a medium describes how...
- Stress (mechanics)
- Thermodynamic stateThermodynamic stateA thermodynamic state is a set of values of properties of a thermodynamic system that must be specified to reproduce the system. The individual parameters are known as state variables, state parameters or thermodynamic variables. Once a sufficient set of thermodynamic variables have been...