Patent Description:
The present disclosure relates to devices for sound suppression, and more particularly, to devices that also allow air flow through the device while suppressing sound transmission through the device.

It is known to suppress propagation of sound by a variety of means, such as sound-absorbing insulation and sound-deflecting surfaces. Some devices, such as noise-canceling headphones for example, dampen propagation of undesirable sound by combining that undesirable sound with a copy of that sound, which copy is the inverse of the undesirable sound. Publications <CIT>, <CIT> or <CIT> disclose known sound silencing apparatus of this type.

If the undesirable sound has a known frequency, some devices dampen the undesirable sound at that specific frequency by combining the undesirable sound with an inverted copy of that sound (e.g., a copy that is inver180 degrees out of phase with the undesirable sound).

A species of some such prior art devices is known as a "Herschel-Quincke tube" (or "HQ tube"). An HQ tube has a first duct through which sound may propagate, and a second duct through which sound may propagate. A propagating sound signal enters both the first duct and the second duct, and propagates through both ducts until the ducts meet, and the signal propagating through the second duct merges with the signal propagating through the first duct.

The ability of an HQ tube to reduce a sound signal propagating in a medium, at a given frequency having a corresponding wavelength (λ), arises not from the length of the first duct (L1), nor from the length of the second duct (L2), but instead on the difference between the length of the first duct and the length of the second duct (i.e., L2-L1). In an HQ tube, the difference in length between the first duct the second duct (i.e., L2-L1) is one-half of the wavelength (<NUM>λ) (or Nλ+<NUM>λ, where N is an integer) of the frequency of the sound signal, so that the point where the ducts meet and their respective signal merge, the signal propagating in the second duct is <NUM> degrees out of phase with the signal in the first duct. For example, a first duct may have a length of <NUM>λ and the second duct may have a length of <NUM>λ, so that the difference between those lengths is <NUM>λ - <NUM>λ = <NUM>λ.

Among other things, this means that the manufacture of an HQ tube requires that both ducts be fabricated to a high degree of precision, to assure the required difference between their respective lengths. Moreover, such devices require a tradeoff between the quantity of open space through which a fluid can flow, and their ability to dampen sound transmission (i.e., their transmission loss). In other words, the amount of open area is sacrificed to obtain desired acoustic performance.

Some examples of prior art HQ tubes are described below.

<FIG> schematically illustrates a prior art exhaust silencer according to the first figure of <CIT> to Venter.

In Venter's device (<FIG>), reference numeral <NUM> refers generally to an exhaust silencer for an internal combustion engine. The exhaust silencer <NUM> has an inlet opening <NUM> and an outlet opening <NUM> spaced axially from the inlet opening <NUM>. The silencer includes a cylindrical shell (or casing) <NUM>, and a core <NUM> inside the shell <NUM>. The core includes a central axial tube <NUM> which defines at least one axial flow passage <NUM>. The core has at least one helical baffle <NUM> which defines a helical passage <NUM> around the axial passage <NUM>, within the shell <NUM>. The axial flow passage <NUM> has an upstream axial inlet <NUM> and has a transverse outlet <NUM> directed transversely outwardly into the helical passage <NUM> in the downstream half of the helical passage. The transverse outlet <NUM> is provided by a plurality of openings arranged as a cluster at the downstream end of the axial passage <NUM>, and between the last two vanes <NUM> and <NUM> of the helical baffle <NUM>.

Venter's silencer <NUM> has an inlet chamber <NUM> which includes a frusto-conical shaped part <NUM> defined by a funnel-shaped inlet connection <NUM>, which has an axial length, about half the diameter of the cylindrical shell <NUM>. The inlet chamber also has a cylindrical part <NUM> which has an axial length about half the diameter of the cylindrical shell <NUM>. Likewise, the silencer has an outlet chamber <NUM> extending downstream from the helical passage, also of frusto-conical shape defined by a funnel-shaped outlet connection <NUM> which also has an axial length, about half the diameter of the cylindrical shell <NUM>. The baffle <NUM> is wound wormscrew fashion around the central axial tube <NUM> in order to define the helical passage <NUM>. The upstream open end <NUM> of the axial flow passage, is disposed at the downstream end of the cylindrical part <NUM> of the inlet chamber <NUM>. The central axial tube <NUM> defining the axial flow passage <NUM>, is blanked off by a transverse barrier <NUM> aligned with its upstream axial inlet <NUM> and downstream from its transverse outlet <NUM>.

As shown, Venter's axial flow passage <NUM> is capped by its transverse barrier <NUM>, and a wave propagating through Venter's axial flow passage <NUM> can only exit the axial flow passage <NUM> in a radial direction, through the holes of its transverse outlet <NUM>, which outlet is within the confines of its cylindrical shell (or casing) <NUM>. Consequently, the joining of a wave propagating through the axial flow passage <NUM> and a wave propagating through its helical passage <NUM> can occur only within the silencer <NUM>. As such, the junction of Venter's axial flow passage <NUM> and its helical passage <NUM> may be may be described as being "ducted.

<FIG> schematically illustrates a prior art noise suppressor for a gas duct <NUM> according to the second figure of <CIT>.

Graefenstein's duct <NUM> includes a central pipe <NUM>, and with three spiral channels <NUM>, <NUM>, <NUM>, in contact with the outside lateral surface of pipe <NUM>.

As shown in <FIG>, spiral channels <NUM>, <NUM>, <NUM> join the central pipe <NUM> in an axial direction (outlet opening <NUM>).

Consequently, the joining of a wave propagating through Graefenstein's central pipe <NUM> and a wave propagating through its three spiral channels <NUM>, <NUM>, <NUM> can occur only within the central pipe <NUM>. As such, the junction of Graefenstein's central pipe <NUM> and its spiral channels <NUM>, <NUM>, <NUM> may be described as being "ducted.

<FIG> schematically illustrates a prior art split path silencer <NUM>. according to the first figure of <CIT>. Brown's silencer <NUM> includes an outer shell <NUM> having an inlet opening <NUM> (with ramped section <NUM>) and an outlet opening <NUM>. Within the outer shell <NUM>, Brown's silencer <NUM> includes a baffle <NUM> wound around an inner tube <NUM>. Sound may propagate through the inner tube <NUM> in a direction <NUM>, and sound may travel through the channel defined by the baffle <NUM> in a direction <NUM>. The inner tube <NUM> has an exit opening <NUM> positioned proximate to, but a distance away from, the outlet opening <NUM> of the outer shell <NUM>.

As shown in <FIG>, the channel formed by Brown's baffle <NUM> exits into a space within the shell (or casing) <NUM>. Consequently, the joining of a wave propagating through Brown's inner tube <NUM> and a wave propagating through the channel formed by its baffle <NUM> can occur only within the shell (or casing) <NUM>. As such, the junction of Brown's inner tube <NUM> and the channel formed by its baffle <NUM> may be described as being "ducted.

According to the invention, a sound silencing apparatus comprises a first channel open to propagation of a first wave at a target frequency therethrough, and having a first inlet and a first outlet, wherein the first channel is configured, to its dimensions, to remain in a continuum state in the presence of a wave at the target frequency; one or more second channels, each open to propagation of a second wave at the target frequency therethrough and configured, by specification of physical dimensions, to resonate at the target frequency, and each having a second inlet and a second outlet; wherein each of the one or more second channels is disposed, relative to the first channel, such that the second wave at the target frequency exiting the one or more second outlets is capable of destructively interfering with the first wave at the target frequency exiting the first channel.

In some such apparatuses, the first channel is open to the flow of a fluid therethrough.

In some embodiments, the first channel is configured to not resonate at the target frequency.

In some embodiments, wherein the first wave is a sound wave, the destructive interference dampens the sound wave at the target frequency, to reduce transmission of the sound wave exiting the first channel by at least <NUM> percent.

In some embodiments, wherein the first wave is a sound wave, the destructive interference dampens the sound wave at the target frequency, to dampen the sound wave exiting the first channel by at least <NUM> dB.

In some embodiments, the first channel has a first area (A1) in cross-section, and the second channels define a second area in cross-section (A2), and the ratio of the first area (A1) to the sum of the first area (A1) and the second area (A2) [A1/(A1+A2)] is greater than <NUM>.

Various embodiments include an apparatus that allows substantial fluid flow (e.g., airflow) through the apparatus, while mitigating the propagation of noise through the apparatus, and while providing a form factor that is significantly more compact that known devices.

Moreover, embodiments allow a designer to specify and adjust one or both of the frequency or frequencies at which the apparatus mitigates noise propagation, and/or the bandwidth around the frequency or frequencies at which the apparatus mitigates noise propagation.

The term "un-ducted" means a space downstream from a device is not bounded by a duct, e.g., which duct is an integral part of the device.

The term "acoustic wave" is a wave that propagates through a fluid by means of adiabatic compression and decompression.

The term "acoustic energy" means energy carried by, or propagated by, an acoustic wave.

The term "axial" means a direction parallel to an axis.

The term "axially oriented" means, with respect to an axis, oriented in a direction parallel to the axis.

The term "axis of fluid flow" means a direction in which fluid may flow.

The term "continuum state" means, with regard to a signal having a spectrum of frequencies, that the signal maintains energy in frequencies across that spectrum.

The term "destructive interference" or "destructively interfering" refers to the phenomenon in which two individual waves incident at a common point superpose to form a resultant wave having an amplitude equal to the difference in the individual amplitudes, respectively, of the individual waves.

The term "fluid" refers to any medium that is capable of flowing and though which a wave may propagate, including, but not limited to, a gas, a liquid, or combinations thereof.

The term "free space" (or "unbounded" space) in reference to a metamaterial silencer means space external to the metamaterial silencer, and external to a duct from which acoustic energy is received at the metamaterial silencer, or a duct on a downstream side of the metamaterial silencer.

The term "openness ratio" means, with respect to an apparatus having a first transmission region having a first area (A1), and having a second transmission region having a second area (A2), the ratio of the first area (A1) to the sum of the first area and the second area (A1 + A2) [i.e., openness ratio = A1/(A1 + A2)].

For the purposes of this disclosure and any claims appended hereto, "openness ratio" means, with respect to an apparatus having a first region cross-section area (A1), and a second region having a second cross-section area (A2), the ratio of the first cross-section area (A1) to the sum of the first and second cross-section areas (A1 + A2) [i.e., openness ratio = A1/(A1 + A2)].

The term "radial" means a direction perpendicular to an axis.

To "remain in a continuum state," with regard to a channel though which a signal propagates, means that the channel is configured to pass the signal while maintaining the signal's continuum state. In contrast, a channel that resonates at a frequency within the signal's spectrum would not maintain the signal in the signal's continuum state.

A "set" includes at least one member. For example, a set of channels includes at least one channel.

A "target frequency" is a frequency of acoustic energy for which a bilateral metamaterial silencer tuned or configured to produce destructive interference.

The term "transmittance" means, with regard to the energy of a signal incident on an apparatus, the ratio of the energy that passes through the apparatus to the energy incident on the apparatus.

Some embodiments below are illustrated using gas as the fluid medium in which a signal propagates, and as the fluid medium that flows through the metamaterial silencer. Embodiments are not limited to gas as the fluid medium, however, because that fluid medium may also be a liquid. Consequently, illustrative embodiments described in terms of such gas do not limit such embodiments.

<FIG> schematically illustrates a cross-section view of an embodiment of a metamaterial sound silencer <NUM>.

The metamaterial sound silencer <NUM> has a first transmission region <NUM> that defines an aperture that is open to permit gas flow through the metamaterial silencer <NUM>.

To that end, the first transmission region <NUM> is open, such that a solid object, such as a straight, rigid rod for example, could pass through the first transmission region <NUM> without bending, and without hitting the metamaterial silencer <NUM>. For example, the first transmission region <NUM> may have the shape of a hollow cylinder, defined by an inner ring <NUM> having an inner radial face <NUM> and a thickness <NUM> ("t") (in this embodiment, the thickness may be thought of as the cylinder height). In illustrative embodiments, the thickness <NUM> is also the cylinder height and is therefore the length of the first channel <NUM>. In illustrative embodiments, the thickness <NUM> of the apparatus <NUM> is less than one-quarter of the wavelength of the target frequency, and in some embodiments the thickness <NUM> is less than is less than one-eighth of the wavelength of the target frequency, and in some embodiments the thickness <NUM> is less than one-sixteenth of the wavelength of the target frequency. In preferred embodiments, the channels <NUM>, <NUM> are shorter than one-half of the wavelength of the target frequency.

In the embodiment of <FIG>, the first transmission region <NUM> defines a fluid flow axis <NUM> along which fluid (e.g., gas and/or liquid) may flow through the first transmission region <NUM>, and therefore through the metamaterial silencer <NUM>.

The first transmission region <NUM>, when in a gaseous environment, has a first acoustic impedance (Z1) and a first acoustic refractive index (n1). In contrast to the second transmission region <NUM>, the first transmission region <NUM> is configured (e.g., due to its dimensions) not to resonate at the target frequency.

The metamaterial sound silencer <NUM> has a second transmission region <NUM>. In general, the second transmission region <NUM> includes a set of one or more conduits, each conduit in the set configured to resonate at a target frequency. The second transmission region <NUM> has an inlet and an outlet, such that a wave may propagate through the second transmission region <NUM> from its inlet to its outlet. In illustrative embodiments, a fluid may flow through the second transmission region <NUM> from its inlet to its outlet.

Several noteworthy properties of the metamaterial silencer <NUM> are described below.

The first transmission region <NUM> has a first region area ("A1") facing the impinging acoustic signal, and the second transmission region <NUM> has a second region area ("A2") facing the impinging acoustic signal.

The ratio (A1/A1+A2) of the area (A1) of the first transmission region <NUM> to the sum of that area plus the area (A2) of the second transmission region <NUM> may be considered as a metric of the openness, to fluid flow, of the metamaterial silencer <NUM>. This ratio may be referred to as an "openness" ratio, and may be expressed, for example, as a fraction or a percentage of the apparatus that is open to fluid flow. Illustrative embodiments described herein enable the metamaterial silencer <NUM> to have an openness ratio of at least <NUM> (or <NUM>%), or more. For example, some embodiments have an openness ratio of <NUM> (<NUM>%), <NUM> (<NUM>%), <NUM> (<NUM>%), or greater, for example up to <NUM> (<NUM>%), all while maintaining its ability to dampen a signal. Such metamaterial silencers may be referred to as an "ultra-open metamaterial" ("UOM"), and are in marked contrast to prior art devices, which could have openness ratios not exceeding <NUM>%, for example.

Also, as explained in more detail below, when the metamaterial silencer <NUM> is disposed in a fluid (e.g., gaseous) environment, the first transmission region <NUM> has a first acoustic impedance (which may be referred to as "Z1") and a first acoustic refractive index (which may be referred to as "n1"), and the second transmission region <NUM> has a second acoustic impedance (which may be referred to as "Z2") and a second acoustic refractive index (which may be referred to as "n2"). The first acoustic impedance (Z1), the first acoustic refractive index (n1), the second acoustic impedance (Z2), and the second acoustic refractive index (n2) are determined at least in part by the physical dimensions of the metamaterial silencer <NUM>.

Transmittance is a quantitative measure of the transmission of wave energy (e.g., acoustic energy) of an impinging signal through the metamaterial silencer <NUM> from the upstream side <NUM> to the downstream side <NUM>. For example, transmittance may be specified as a ratio of the energy transmitted from the metamaterial silencer <NUM> (e.g., output from the downstream side <NUM> of the metamaterial silencer <NUM>) to the energy received by the metamaterial silencer <NUM> (e.g., input to the first transmission region <NUM>). In other words, acoustic transmittance is ratio of the transmitted energy to the incident energy. For example, if a signal impinges a metamaterial silencer <NUM> with a given amount of energy, and the energy transmitted from the metamaterial silencer <NUM> is only <NUM> percent (<NUM>%) of the energy received into the first transmission region <NUM>, then the ratio of <NUM>/<NUM>, or <NUM>. Stated alternately, the metamaterial silencer <NUM> has dampened the signal by <NUM>%, or <NUM> dB, where dB is calculated as <NUM> log (input energy/output energy). In this example, the ratio of input energy to output energy is <NUM>/<NUM> = <NUM>, and <NUM> log (<NUM>) = <NUM> dB.

The examples in <FIG> are based on an acoustic plane wave incident on the upstream side <NUM> of the metamaterial silencer <NUM> with distinct acoustic properties.

It is assumed for these examples that the metamaterial silencer <NUM> has an axisymmetric configuration with respect to the X-axis with the thickness of t in which the first transmission region <NUM> (r < <NUM>) has an acoustic impedance of Z<NUM> and refractive index of n<NUM>, and the second transmission region <NUM> (<NUM> < r < <NUM>) has an acoustic impedance of Z2 and refractive index of n<NUM>. Note that the axisymmetric configuration is selected solely for the purpose of simplification and other configurations such as rectangular prism of honeycomb-like shape may be considered without a loss of generality. As described above, the interface between the first transmission region <NUM> and the second transmission region <NUM> (r = <NUM>) is considered as a hard boundary and the entire structure is assumed to be confined within a rigid, cylindrical (i.e., circular in cross-section) waveguide filled with a medium with sound speed of Co and density of p<NUM>, for the purposes of deriving the acoustic transmittance.

As the first step to derive the transmittance, the following definitions of acoustic pressure and velocity field at the interfaces (x = <NUM> and x = t) are employed to relieve the transverse variation of the fields. <MAT> <MAT> <MAT> <MAT> <MAT> <MAT> <MAT> <MAT>.

In which p and u are acoustic pressure and velocity field, respectively. P<NUM>,<NUM> and U<NUM>,<NUM> are averaged pressure and volume velocity at the first transmission region <NUM> and the second transmission region <NUM> interfaces. Next, considering that the regions are separated with a hard boundary, the transfer matrices relating the output pressure and velocity to the input condition, for first transmission region <NUM> and second transmission region <NUM>, may be written in a decoupled fashion. <MAT> <MAT>.

In which ko is the wave number associated with the medium within the duct, defined as ω/Co, n1 and n2 are the refractive indices of transmission regions <NUM> and <NUM>, respectively, t is the thickness, and Z<NUM> and Z<NUM> are the characteristic impedance values transmission regions <NUM> and <NUM>, respectively. Applying Green's function method, one may derive the following relationships. <MAT> <MAT> <MAT> <MAT>.

In which Green's functions are defined as: <MAT> <MAT>.

Where the eigenmodes are defined as ϕn (r)= J<NUM> (knr )/ J<NUM>(knr<NUM>) with the wavenumber kn as the solution of J'(knr<NUM>)= <NUM>.

By solving the foregoing equations, one may readily calculate the averaged pressures and volume velocities defined above, from which the acoustic transmittance may readily be derived as: <MAT>.

The transmittance from the bilayer metamaterial silencer <NUM> for different values of refractive index and acoustic impedance are illustrated in the graphs in <FIG>. In <FIG>, the effect of characteristic impedance ratio is depicted, for which the Q-factor (i.e., the "quality factor") of filtration may be tuned. In <FIG>, the effect of refractive index ratio is demonstrated for which filtration frequency regime can be adjusted.

In <FIG>, it is considered that n2/n1 =<NUM> and the transmittance is depicted versus the non-dimensional quantity n2t/λ (λ denotes the wavelength) for four different values of the impedance ratio. In <FIG>, the impedance ratio has been kept constant (Z2/Z1=<NUM>) and the transmittance is depicted for three different values of the refractive index ratio. Notably, for these examples, the background medium within the waveguide is considered air and it is assumed that the medium in transmission first transmission region <NUM> is identical to the background medium. Hence, the characteristic acoustic impedance of transmission first transmission region <NUM> may be derived as Zi = ρoco/πr<NUM><NUM> and the refractive index (n1) is equal to unity.

From <FIG>, it may be observed that for different values of Z<NUM> and n2, given the differing acoustic properties of transmission region <NUM> transmission region <NUM>, an asymmetric transmission profile is obtained in which destructive interference may result in zero transmittance due to Fano-like interference. The destructive interference emerges where n2t ≈ λ/<NUM> which is the resonating state of the second transmission region <NUM>. Given the contrast in refractive indices (n1 and n2) of the two regions, the first transmission region <NUM> will remain in a continuum state and, consequently, a Fano-like interference occurs. During this state, the portion of the acoustic wave traveling through the second transmission region <NUM> interacts with resonance-induced localized modes in this region, resulting in an out-of-phase condition after traveling through this region. The portion of the incident acoustic wave traveling through region <NUM> will pass the metamaterial <NUM> with negligible phase shift and, consequently, a resultant destructive interference occurs on the transmission side of the metamaterial. Of note, the destructive interference initially occurs at n2t ≈ λ/<NUM> which is the first resonance mode of region <NUM>, but will also occur at higher resonance modes when n2t ≈ Nλ/<NUM> for integers of N.

From <FIG>, by comparing the transmittance for different values of the impedance ratio, it can be understood that by increasing the contrast between the characteristic acoustic impedances of the two regions, the quality factor (Q factor) of the attenuation performance is increased. This attribute provides a degree of freedom and, by adjusting the impedance contrast, the desired filtration bandwidth may be realized. Of interest, when the characteristic impedance ratio yields a very large number (Z<NUM> /Z<NUM>=∞), the filtration performance is suppressed, given its marked narrowband character, and an orifice-like behavior is realized. However, the orifice structure with a similar open area geometry results in a relatively poor sound filtration performance, leading to only minor reductions in attenuation of the transmitted acoustic wave.

<FIG> demonstrates the effect of refractive index contrast between the two media on transmittance and illustrating that high degrees of filtration are obtained when n2t ≈ λ/<NUM>. Thusly, the inventors have discovered that by adjusting the refractive indices in the proposed structure, high performance sound attenuation may be realized at any desired frequency.

As shown in <FIG>, the transmittance of the acoustic signal, at the target frequency is at or near zero. Thus it may be said that the destructive interference dampens sound wave at the target frequency, to reduce transmission of the sound wave silencer <NUM> by at least <NUM>%.

It should be noted that the metamaterial silencer <NUM> is a passive device in that it does not require a supply of energy, and instead operates using only the energy in an impinging signal.

From the foregoing disclosure, and in view of examples provided below, it can be understood that the properties of a metamaterial silencer <NUM> can be specified by selection of its parameters, such as physical dimensions (radiuses, thickness, helix angle) and other properties (Z1, Z2, n1, n2). For example, by informed selection of such parameters, a designer can specify the target frequency of a metamaterial silencer <NUM> (the frequency at which its dampening effect is most pronounced), its bandwidth at that target frequency, and its openness ratio. Moreover, by specification of physical dimensions, the first transmission region <NUM> of a metamaterial silencer <NUM> may be configured such that a wave propagating through that first transmission region <NUM> remains in a continuum state (e.g., the first transmission region does not resonate at the target frequency) (such a first transmission region may be described as maintaining, or remaining in, a continuum state), and the second transmission region <NUM> may be configured such that it resonates at the target frequency.

<FIG> schematically illustrates a front view of an embodiment (<NUM>) of a cylindrical bilayer metamaterial silencer <NUM>. <FIG> schematically illustrates a side cutaway view of the cylindrical bilayer metamaterial silencer <NUM>, and <FIG> schematically illustrates a rear view of the cylindrical bilayer metamaterial silencer <NUM>.

The metamaterial silencer <NUM> in <FIG> has a cylindrical shape, and includes an outer ring <NUM> with an outer surface <NUM>. The outer ring <NUM> defines an interior space that includes the two transmission regions (or "layers") <NUM> and <NUM>.

The first transmission region <NUM> in this embodiment includes an inner ring <NUM>, and is defined by an inner radius <NUM>.

In preferred embodiments, the inner ring <NUM> acoustically isolates the first transmission region <NUM> from the second transmission region <NUM> by substantially preventing the transmission of gas and acoustic energy from a gas within the first transmission region <NUM> to the second transmission region <NUM>, and by substantially preventing the transmission of gas and acoustic energy from a gas within the second transmission region <NUM> to the first transmission region <NUM>. The inner ring <NUM> may be referred to as an "acoustically rigid spacer. " In illustrative embodiments, the inner ring <NUM> is made of acrylonitrile butadiene styrene plastic.

The second transmission region <NUM> in this embodiment is defined by the outer radius <NUM> and the inner radius <NUM>. As shown in <FIG> and <FIG>, the second transmission region <NUM> has an upstream face <NUM> on a first side, and a downstream face <NUM> on the side opposite the first side.

The second transmission region <NUM> includes a set of helical channels <NUM>, <NUM>, <NUM>, <NUM>, <NUM>. Each helical channel <NUM>-<NUM> of the set of helical channels has a corresponding channel inlet aperture (<NUM>-<NUM>, respectively) opening to the upstream face <NUM>, and a corresponding channel outlet aperture (<NUM>-<NUM>, respectively) opening to the downstream face <NUM>.

The upstream face <NUM> of the first transmission region <NUM> has an area (A1) defined as the square of the inner radius <NUM> times pi. As shown, the second transmission region <NUM> includes a set of helical channels <NUM>-<NUM>. Each of those helical channels <NUM>-<NUM> has a radial height defined as the distance between the inner ring <NUM> and the outer ring <NUM> (or the inner radius <NUM> and the outer radius <NUM>). Consequently, when viewed in cross-section (<FIG>, along the X axis of <FIG>), the set of channels presents a cross-section having an area (A2) of two pi time the square of the difference between the inner radius <NUM> and the outer radius <NUM>. In other words, the second transmission region <NUM> of the metamaterial silencer <NUM> of <FIG> is annular in shape, and has an area of two pi times the square of outer radius (<NUM>) minus two pi times the square of the inner radius (<NUM>) [i.e., <NUM>π(R<NUM><NUM> - R<NUM><NUM>), where R<NUM> is the inner radius <NUM> and R<NUM> is the outer radius <NUM>)]. In fact, the second transmission region <NUM> would have the same area (A2) even if the metamaterial silencer <NUM> of <FIG> had only a single helical channel (e.g., <NUM>) because even that single helical channel would, when viewed in cross-section, present a cross-section having an area (A2) of two pi time the square of the difference between the inner radius <NUM> and the outer radius <NUM>.

The helical channels <NUM>-<NUM> may be referred to as "resonator channels" because, in operation, one or more frequency components (each a "target frequency") of an acoustic wave impinging on the upstream face <NUM> will resonate in one or more of the helical channels <NUM>-<NUM>.

Each helical channel <NUM>-<NUM> of the set of helical channels has a helical axis, and in illustrative embodiments the helical channels <NUM>-<NUM> have the same helical axis.

Each helical channel <NUM>-<NUM> of the set of helical channels has a helix angle <NUM>. In the embodiment of <FIG>, each the helix angle <NUM> for each helical channel <NUM>-<NUM> is the same, but in some embodiments, any one or more of the helical channels <NUM>-<NUM> may have a helix angle <NUM> that is different from the helix angle <NUM> of one or more of the other helical channels in the set.

Each helical channel <NUM>-<NUM> of the set of helical channels also has a channel length, the length of a given helix channel being the distance, along the helix axis, between its corresponding channel inlet aperture and corresponding channel outlet aperture. In illustrative embodiments, each helical channel <NUM>-<NUM> of the set of helical channels is a sub-wavelength structure, in that its channel length is less that the wavelength of the frequency for which the channel acts as a silencer. Moreover, in some illustrative embodiments, the channel length of each channel <NUM>-<NUM> is one half (<NUM>/<NUM>) of the wavelength of the frequency for which the channel acts as a silencer, and in preferred embodiments is less than one half (<NUM>/<NUM>) (but more than ¼) of such a wavelength.

The operation, and certain characteristics, of a bilateral metamaterial silencer <NUM> configured to have a target frequency of <NUM>, are described below, with the understanding that the operation and characteristics of a metamaterial silencer <NUM> generally are not limited to that specific embodiment. The embodiment of the metamaterial silencer <NUM> used to produce these characteristics had a thickness (t) <NUM> of <NUM>; an inner radius <NUM> of <NUM>, and outer radius <NUM> of <NUM>, and a helix angle <NUM> of <NUM> degrees. The impedance ratio Z2/Z1 was <NUM>, and the refractive index ratio n2/n1 was <NUM>.

In illustrative embodiments of operation, a metamaterial silencer <NUM> is disposed in the path of an acoustic signal propagating in a gas. Specifically, the metamaterial silencer <NUM> is disposed such that the acoustic signal impinges on, and enters, the first transmission region <NUM> and the second transmission region <NUM> (in this example, the channel inlet apertures <NUM>-<NUM> of the helical channels <NUM>-<NUM>). A portion of the wave propagating in the first transmission region <NUM> may be referred-to as a first wave, and the portion of the signal propagating in the second transmission region <NUM> may be referred to as a second wave. It should be noted that acoustic energy from the acoustic signal may enter the channel inlet apertures <NUM>-<NUM> without first entering the cylinder of the first transmission region <NUM>.

The gas itself may be moving in a direction along the gas flow axis <NUM>. Such a direction may be referred to as the "downstream" direction. The acoustic signal may have a spectrum that includes a plurality of frequency components. In illustrative embodiments, the metamaterial silencer <NUM> is configured to allow the gas to pass through the first transmission region <NUM>, while dampening or silencing at least one frequency (the "target frequency) of the acoustic signal spectrum.

As previously noted, the helical channels <NUM>-<NUM> may be referred to as "resonator channels" because, in operation, one or more frequency components of the acoustic wave impinging on the upstream face <NUM> resonates in one or more of the helical channels <NUM>-<NUM>. Simultaneously, the acoustic signal propagates through the first transmission region <NUM> without resonating (i.e., in a "continuum state"). Moreover, if the gas is moving, it may pass through the first transmission region <NUM> substantially unimpeded.

Acoustic energy from the helical channels <NUM>-<NUM> exits the metamaterial silencer <NUM> at the channel outlet apertures <NUM>-<NUM>. Specifically, the acoustic energy exits from the downstream face <NUM> of the metamaterial silencer <NUM> into the unbounded space <NUM> disposed in the downstream direction from the metamaterial silencer <NUM>. Moreover, in illustrative embodiments, the acoustic energy exits from the second channel <NUM> of the metamaterial silencer <NUM> in a tangential direction. The tangential direction is defined as a direction tangential to a radius (<NUM>, <NUM>) extending from a center of the metamaterial device <NUM>, and substantially parallel to downstream face <NUM>. The direction of energy exit from the second channel <NUM> of the metamaterial silencer <NUM> may still be described as axial (or axially-oriented), however, at least in that it is not in a radial direction.

The acoustic energy from each helical channel <NUM>-<NUM> has a frequency equal to the resonant frequency of the channel from which it exits, and through FANO interference, cancels acoustic energy at that frequency in the gas from the first transmission region <NUM>.

In order to visualize the silencing performance of an embodiment of a metamaterial silencer <NUM>, <FIG> schematically illustrate sound transmission through the metamaterial silencer <NUM>. <FIG> show cutaway views of the metamaterial silencer <NUM>. In other words, in these figures, a cut plane is used to demonstrate the resultant pressure and velocity fields in two dimensions (2D).

<FIG> is a graph illustrating transmission of a first frequency of a plane wave incident on a bilateral metamaterial silencer. <FIG> is a graph illustrating transmission of a second frequency (a "target" frequency) of a plane wave incident on a bilateral metamaterial silencer. In <FIG>, the background color represents the absolute value of the pressure field normalized by the amplitude of the incident wave, and the white lines reflect the stream and orientation of the local velocity field.

Demonstrated in <FIG> is a plane wave with frequency of <NUM> incident on the metamaterial silencer <NUM> from the left side as shown with black arrows. In accordance with the analytically and experimentally expected behaviors of the metamaterial silencer <NUM> structure, in the frequency regime of <NUM>, highpressure transmission results.

At this state, given the fact that the helical portion <NUM> of the metamaterial silencer <NUM> structure possesses a markedly larger acoustic impedance (Z2) in comparison with the acoustic impedance (Z1) of the open portion <NUM> in the center, the incident wave will predominately travel through the central open portion <NUM> of the metamaterial silencer <NUM>. This behavior may be visually confirmed with the local velocity field stream shown in <FIG> where both preceding and beyond the metamaterial silencer <NUM> structure, the velocity field exhibits minimal disturbance save for the change in cross-sectional area.

In <FIG>, a similar case of a plane wave incident from the left side is demonstrated but with a frequency of <NUM>. Based on the theoretical and experimental results obtained above, it is expected that at this frequency, the wave transmitted through the helical portion <NUM> of the metamaterial silencer <NUM> will become out of phase with the transmitted wave traveling through the central open portion <NUM> of the metamaterial silencer <NUM>. The results obtained herein demonstrate that the destructive interference on the transmission side (right side in these figures) of the metamaterial silencer <NUM> has resulted in dampening wave transmission in the unbounded space <NUM>.

Notably, the out-of-phase transmission through the two regions <NUM>, <NUM> of the metamaterial silencer <NUM> may be further understood by reference to the velocity profile shown in <FIG> with white lines. It may be readily observed that the local acoustic velocities of the transmitted wave from the two regions <NUM>, <NUM> of the metamaterial silencer <NUM> are in opposite directions, resulting in a marked curvature of the velocity stream and diminished far-field radiation. It should be mentioned that, with the presence of the destructive interference due to Fano-like interference, the metamaterial structure <NUM> mimics the case of an open-end acoustic termination in which near-zero effective acoustic impedance results in a predominant reflection of the incident wave.

In other words, in <FIG>, the absolute pressure value normalized by the incident wave magnitude resulting from a plane wave with a frequency of <NUM> and incident on the metamaterial silencer <NUM> from the left-hand side is shown using a color map. The local velocity stream is shown with the white lines. At this frequency, the transmission coefficient (which is the ratio of the transmitted pressure over incident pressure) is about <NUM>, hence, approximately <NUM>% of the acoustic wave energy is transmitted.

In <FIG>, the pressure and velocity profile is depicted with an incident plane wave of the same amplitude as the incident wave described in <FIG>, but having a frequency of <NUM>. At this frequency, due to Fano-like interference, the transmitted wave has a markedly decreased amplitude, and the wave has been effectively silenced. In this embodiment, the phase difference between the transmitted waves from the two regions <NUM>, <NUM> of the metamaterial silencer <NUM> has resulted in a curvature of the wave velocity field and has diminished the far-field radiation.

<FIG> is a graph illustrating the normalized amount of acoustic energy transmitted and the amount of acoustic energy reflected by a bilayer metamaterial silencer <NUM>. As shown, at the target frequency of <NUM>, very little acoustic energy is transmitted by the metamaterial silencer <NUM> (approximately less than <NUM>%), while most of the acoustic energy is reflected by the metamaterial silencer <NUM> (approximately <NUM>% or more).

<FIG> is a graph illustrating acoustic transmittance through bilayer metamaterial silencers <NUM> with different degrees of structure openness. Transmittance has been analytically derived using the Green's function method. Notably, bilayer metamaterial silencer structures considered herein feature identical refractive index ratios in their transverse bilayer metamaterial model but have different impedance ratios.

According to illustrative embodiments, openness percentage is correlated with the acoustic impedance ratio, and even with very high openness percentage, silencing can be realized within the scope of the presented embodiments. For example, as shown in <FIG>, even for bilayer metamaterial silencers <NUM> with a very high percentage of open area (approaching nearly complete open area where openness approximates <NUM> or <NUM>%), the silencing functionality remains present, although with a resultant decrease in the silenced frequency bandwidth. The following table presents relationships between openness (open area/total area; in the column captioned "open:") and acoustic transmission (transmittance) at a variety of frequencies, as shown in <FIG>.

Although the foregoing figures illustrate an embodiment of a silencer <NUM> with a target frequency of <NUM>, embodiment are not limited to silencers with that target frequency. As described above, the target frequency of a silencer <NUM> may be established by specification of the silencer's parameters.

<FIG> schematically illustrate another embodiment (<NUM>) of a metamaterial silencer <NUM>. In this embodiment, the helical channels <NUM>-<NUM> in the second transmission region <NUM> do not have identical physical dimensions. For example, some helical channels are longer than others. To accommodate different channel lengths, the channel inlets <NUM>-<NUM> for the helical channels <NUM>-<NUM> are not uniformly distributed around the upstream face <NUM>. Alternatively, or in addition, the channel outlets <NUM>-<NUM> are non-uniformly distributed around the downstream face <NUM>. Moreover, the six channels <NUM>-<NUM> have different helix angles <NUM>. In this design, given the different frontal angles of the channels, both effective length (and consequently refractive index, n) and cross sections (and consequently impedances, Z) are different. Therefore, this model of silencer may be designed to simultaneously target multiple frequencies with different silencing bandwidth.

<FIG> schematically illustrate another embodiment (<NUM>) of a metamaterial silencer <NUM>. In this embodiment, the helical channels <NUM>-<NUM> in the second transmission region <NUM> include individual channel wrapped around an inner ring <NUM>. Each individual channel <NUM>, <NUM> has a top panel <NUM> and two side panels <NUM>, <NUM>. Each of the two side panels extends radially outward from the inner ring <NUM>, and the top panel <NUM> extends between the radially outward ends of the two side panels <NUM>, <NUM>, to form a helical channel having a rectangular cross-section. The helical channels <NUM>, <NUM> may be identical, or may have differing helix angles, and/or helix lengths, and/or different areas in cross-section. This embodiment may be desirable when the minimizing pressure loss in the central channel <NUM> is a goal. In this case, the channel inlet aperture <NUM>, <NUM> and channel outlet apertures <NUM>, <NUM>, are arranged radially, and the silencer features two channels <NUM>, <NUM> with different lengths (channel <NUM> has <NUM> revolution) (channel <NUM> has <NUM> revolutions). By adjusting the length of the channels and cross section of the channels the desired silencing, either multiband or single band with proper bandwidth may be realized.

<FIG> schematically illustrates a stack <NUM> of a plurality of metamaterial silencers <NUM>, such as those illustrated in <FIG>. Each metamaterial silencer <NUM> may be configured to dampen a frequency different from the other two metamaterial silencers <NUM>. The plurality of metamaterial silencers <NUM> in the stack <NUM> exhibit a synergy, such that the stack <NUM> is configured to dampen transmission of a plurality of target frequencies.

<FIG> schematically illustrate another embodiment (<NUM>) of a metamaterial silencer <NUM>. This embodiment includes a second transmission region <NUM>, and a first transmission region <NUM> disposed radially outward of the second transmission region <NUM>. The first transmission region <NUM> is bounded by an outer ring <NUM> and defines a non-resonating passage around the second transmission region <NUM>. In this embodiment, the second transmission region <NUM> is a hub suspended from the outer ring <NUM> by one or more spars <NUM>.

Although embodiments described above (<NUM>; <NUM>; <NUM>; <NUM>; <NUM>) are un-ducted, and require an outer casing to produce the described performance and obtain the described results, illustrative embodiments may be disposed and used within a casing, as described in connection with <FIG>.

<FIG> schematically illustrates an embodiment of a metamaterial silencer <NUM> disposed within a tube <NUM>. The metamaterial silencer <NUM> may be any of the cylindrical silencers disclosed herein. <FIG> is a graph showing the silencing effect of a metamaterial silencer <NUM> within a tube <NUM>.

The tube <NUM> is a cylinder with two openings <NUM> and <NUM> at its ends. For purposes of illustration for this embodiment, a sound source (e.g., a loudspeaker) <NUM> is disposed at a first end <NUM> of the tube <NUM> such that a sound signal produced by the sound source <NUM> is directed into the tube <NUM> through the first opening, and then propagates down the tube <NUM> toward the second opening <NUM> at the other end of the tube <NUM>. The sound signal in this embodiment has a spectrum that covers a range of frequencies, including the target frequency of the metamaterial silencer <NUM>. An acoustic load <NUM> (which may be a cap, for example) is disposed in or over the aperture <NUM>.

A metamaterial silencer <NUM> is disposed within the tube <NUM> with its upstream face <NUM> facing the sound source <NUM>. The metamaterial silencer <NUM> in this embodiment has a target frequency of <NUM>.

In <FIG>, the tube <NUM> is fitted with several microphones <NUM>-<NUM> disposed to measure the intensity of the sound signal at various points within the tube <NUM>. Microphones <NUM>, <NUM> and <NUM> are disposed upstream from the metamaterial silencer <NUM>, and microphones <NUM>, and <NUM> are disposed downstream from the metamaterial silencer <NUM>. As shown in <FIG>, the metamaterial silencer <NUM> substantially dampens the sound signal at the target frequency (<NUM>), downstream from the metamaterial silencer. Specifically, the metamaterial silencer <NUM> transmits approximately <NUM>% of the acoustic energy of the sound signal at frequencies below the target frequency, and transmits approximately <NUM>% of the acoustic energy of the sound signal at frequencies above the target frequency, but transmits almost none (at or about zero percent) of the acoustic energy of the sound signal at the target frequency, and less than <NUM>% of the acoustic energy of the sound signal in a band around the target frequency. Consequently, <FIG> illustrate that the metamaterial silencer <NUM> operates well even when its downstream face <NUM> is in bounded space instead of free space or unbounded space. For example, the operation of the metamaterial silencer <NUM> in unbounded space <NUM>, as illustrated above, is also valid for operation in bounded space, such as inside the tube <NUM>.

<FIG> schematically illustrate practical applications of various embodiments of a metamaterial silencer <NUM> (e.g., <NUM>; <NUM>; <NUM>; <NUM>). <FIG> schematically illustrates a metamaterial silencer <NUM> disposed at an outlet <NUM> of a tube <NUM>. The tube <NUM> may be, or include, a sound source. For example, the tube <NUM> may be an exhaust pipe of a motor vehicle, or a jet engine, to name but a few examples. The metamaterial silencer <NUM> operates as described above to dampen noise exiting the tube <NUM>, yet allows the flow of gas (e.g., exhaust gas; jet blast) out of the tube <NUM>.

<FIG> schematically illustrates a sound barrier <NUM> having a set of metamaterial silencers <NUM> (e.g., <NUM>; <NUM>; <NUM>; <NUM>). Each such metamaterial silencer <NUM> operates as described above to dampen noise impinging on the barrier <NUM>, yet allows the flow of gas through the barrier <NUM>. In some embodiments, a set of metamaterial silencers <NUM> is placed near ground level, so that animals may pass through the metamaterial silencers <NUM>.

<FIG> schematically illustrate another embodiment of a metamaterial silencer <NUM>. This embodiment includes an outer ring <NUM> has an inner radial face <NUM>, which defines an interior region <NUM>. An arc-resonator <NUM> is disposed on the inner radial face <NUM>, and includes one or more serpentine resonating channels <NUM>. In this illustrative embodiment, a single channel <NUM> is wrapped in the are-resonator <NUM>. The arc-resonator <NUM> subtends and angle <NUM> at the center at the outer ring <NUM>, which angle in this embodiment is approximately <NUM> degrees. In other embodiments, the angle <NUM> may be greater or less than <NUM> degrees, for example <NUM> degrees, <NUM> degrees, <NUM> degrees, or <NUM> degrees.

In operation, acoustic energy enters the channels <NUM> and resonates within those channels. The acoustic energy then exits the arc-resonator <NUM> and dampens acoustic energy within the interior region <NUM>.

One application for such an embodiment is within the wheel of a motor vehicle. To that end, <FIG> illustrates noise pressure within a sealed automobile wheel <NUM>. In this embodiment, a metamaterial silencer having three arc-resonators <NUM> is disposed within the wheel <NUM>.

<FIG> is a graph <NUM> that shows the pressure within the wheel, normalized to the pressure when the wheel does not have a metamaterial silencer <NUM> of <FIG>. Trace <NUM> shows that normalized pressure without the inclusion within the wheel <NUM> of a metamaterial silencer <NUM> of <FIG>. In contrast, trace <NUM> shows the normalized pressure within the wheel <NUM> when the metamaterial silencer <NUM> of <FIG> is included within the wheel <NUM>, as schematically illustrated in <FIG>. As shown, inclusion within the wheel <NUM> of the metamaterial silencer <NUM> reduces acoustic pressure by approximately <NUM> percent.

<FIG> schematically illustrates an embodiment of a wheel <NUM> having an arc-resonator <NUM> disposed on its wheel hub <NUM> and within a tire <NUM> mounted to the hub.

Claim 1:
A sound silencing apparatus comprising:
a first channel (<NUM>) open to propagation of a first wave at a target frequency therethrough, and having a first inlet and a first outlet, wherein the first channel (<NUM>) is configured due to its dimensions to remain in a continuum state in the presence of a wave at the target frequency;
one or more second channels (<NUM>), each open to propagation of a second wave at the target frequency therethrough and configured, by specification of physical dimensions, to resonate at the target frequency, and each having a second inlet and a second outlet;
wherein each of the one or more second channels (<NUM>) is disposed, relative to the first channel (<NUM>), such that the second wave at the target frequency exiting the one or more second outlets (<NUM>) is capable of destructively interfering with the first wave at the target frequency exiting the first channel (<NUM>).