HYPERABSORPTION BY ACOUSTICALLY DARK METAMATERIAL CELLS

Inventor: Dwight W. Swett

FIELD OF THE DISCLOSURE

[0001] This disclosure relates to an acoustic attenuation system formed from at least one acoustic attenuator comprising a metamaterial matrix and a fluid in which the attenuator is at least partially immersed, and methods of making and using such acoustic attenuators, including in connection with treatments to vessel exteriors for stealth purposes.

BACKGROUND OF THE DISCLOSURE

[0002] Submarines can be detected acoustically via two main mechanisms: active detection in which an adversarial acoustic source emits an acoustic wave into the water and an adversarial receiver detects the reflected signal from encountered vessels (reflection signal strength is inversely proportionate to distance), and passive detection (an adversarial receiver detects latent submarine noise emitted into the water). The main acoustic stealth measures to counter detection can also be grouped into two main categories as well, passive (hull treatments) and active (acoustic reflection manipulation).

SUMMARY OF THE DISCLOSURE

[0003] Aspects of the present disclosure include apparatus, systems, and methods for enhancing passive stealth capabilities. Apparatus may include at least one acoustic attenuator comprising a metamaterial matrix having a plurality of cells and configured, upon at least a partial immersion in a fluid, to form an acoustic attenuation system including at least a portion of the matrix and the fluid, the acoustic attenuation system configured to acoustically attenuate acoustic signals incident on the attenuator from the fluid. At least one cell of the plurality of cells may comprise a plurality of sub-cells azimuthally arrayed about an axis of alignment, with at least one sub-cell of the plurality comprising a plurality of solid cell segments substantially oriented in alignment with a mapping geometry comprising an inversion of a canonical tangent circles mapping.

[0004] The at least one sub-cell may include a plurality of cell segments with at least a majority of cell segments of the plurality comprising at least one arcuate section and at least one radial finger. At least a majority of cell segments of the plurality may each comprise a plurality of arcuate sections. The at least one radial finger may comprise a resonant fork. The acoustic attenuation system may be configured to acoustically attenuate acoustic signals incident on the attenuator from the fluid by broad-band acoustic attenuation.

[0005] The canonical tangent circles mapping may provide focusing constant contours of eccentric circles with a common tangent point at the origin of Cartesian coordinates, and the inversion provides defocusing constant contours of the eccentric circles. The matrix may intrinsically damp incident acoustic waves. At least some of the at least one cell may focus incident acoustic waves to a cell interior where energy of the incident acoustic waves is dissipated by absorption. The absorption may be predominantly due to subwavelength wave scattering at metamaterial intracellular boundaries. The absorption may occur over a substantially unbounded attenuation frequency bandwidth.

[0006] The mapping may relate rectangular [x,y] Cartesian coordinates to [u,v] mapped coordinates by the relations:

[0007] The inversion may relate rectangular [x,y] Cartesian coordinates to [u,v] mapped coordinates by the relations:

[0008] At least some cells of the at least one cell may comprise a central elastomeric core. At least a majority of the cells may comprise at least one of: i) metal; ii) plastic; iii) composite. The fluid may be at least one of: i) seawater, ii) freshwater, iii) oil, iv) a hydrocarbon mixture, v) gas. The acoustic attenuation system may be configured to display a substantially unbounded attenuation frequency bandwidth with respect to absorption of incident acoustic energy waves. At least one absorption property of the acoustic attenuation system may be substantially independent of a pressure of the fluid.

[0009] Apparatus embodiments may include at least one acoustic atenuator comprising a metamaterial matrix having a plurality of cells and configured, upon immersion in a fluid, to form an acoustic attenuation system configured for absorption of incident acoustic signals, wherein the absorption occurs over a substantially unbounded atenuation frequency bandwidth. At least a portion of the absorption may be due to an unbounded hyperbolic spatial frequency dispersion.

[0010] Method embodiments in accordance with the present disclosure may include methods of reducing an acoustic signature of a vehicle at least partially immersed in a fluid from acoustic investigation. Methods may include positioning at least one acoustic atenuator on an exterior of the vehicle, the at least one acoustic atenuator comprising a metamaterial matrix having a plurality of cells configured for acoustic atenuation; allowing the at least one acoustic atenuator to be at least partially infiltrated with the fluid and thereby forming an acoustic atenuation system; and employing the acoustic atenuation system to mitigate reflected sound from the vehicle by absorbing at least one of: i) acoustic signals from the fluid; and ii) reflections of the acoustic signals from the vehicle. At least one cell of the plurality of cells may comprise a plurality of sub-cells azimuthally arrayed about an axis of alignment, with at least one sub-cell of the plurality comprising a plurality of solid cell segments substantially oriented in alignment with a mapping geometry comprising an inversion of a canonical tangent circles mapping. The vehicle may be a submarine and the acoustic signals may comprise at least one active SONAR transmission. [0011] Example features of the disclosure have been summarized rather broadly in order that the detailed description thereof that follows may be better understood and in order that the contributions they represent to the art may be appreciated.

BRIEF DESCRIPTION OF THE DRAWINGS

[0012] For a detailed understanding of the present disclosure, reference should be made to the following detailed description of the embodiments, taken in conjunction with the accompanying drawings, in which like elements have been given like numerals, wherein:

FIG. 1 shows curves representing reflection loss of anechoic tiles over a range of frequencies in accordance with the present disclosure;

FIGS. 2 A & 2B illustrate the mapping geometry of cells of a metamaterial in accordance with the present disclosure;

FIGS. 3A-3C illustrate example metamaterial cells with cell segments oriented in alignment with an inversion of a canonical tangent circles mapping for attenuating an acoustic wave in accordance with the present disclosure;

FIG. 3C & 3D illustrate one example of practical cell design compatible with conventional additive manufacturing technology;

FIG. 3E & 3F illustrate another example of practical cell design compatible with conventional additive manufacturing technology;

FIGS. 4 A & 4B illustrate an example metamaterial panel in accordance with embodiments of the present disclosure;

FIG. 5 illustrates a simulation model and boundary conditions for the metamaterial;

FIG. 6A shows absorption spectra for an ADM AlSilOMg metamaterial cell for a solid-finger sub-cell design and a resonant-fork sub-cell design;

FIG. 6B illustrates a harmonic response at 29 kHz for the resonant-fork sub-cell design response; FIG. 7A illustrates absorption spectra of two additional ADM materials with a dampening core;

FIG. 7B illustrates absorption spectra of steel in comparison to PLA plastic material fdled with 36% copper loading in the resonant-fork sub-cell configuration;

FIG. 7C illustrates absorption characteristics of the metamaterial for frequencies under 5 kHz;

FIG. 8 illustrates a simulation model and boundary conditions for the metamaterial;

FIGS. 9 A & 9B illustrate resulting refractive index response spectra;

FIGS. 10A & 10B illustrate equifrequency contours associated with the metamaterial frequency dispersion for wave propagations at 29 kHz;

FIGS. 11A & 11B illustrate an application of the hyperabsorption metamaterial to the reduction of acoustic signatures of naval vessels;

FIGS. 12 A & 12B shows a graphical illustration of the transient wave propagation response for the reference water case and the metamaterial case in accordance with embodiments of the disclosure;

FIG. 12C shows a comparison of the reflection frequency spectrum with the incident pulse frequency spectrum in accordance with embodiments of the disclosure;

FIG. 13 shows an echo reduction coefficient for the metamaterial using three conventional all-metal ADM materials and a copper-filled plastic filament;

FIGS. 14A & 14B show a transient reflection with and without the metamaterial. DETAILED DESCRIPTION

[0013] Aspects of the present disclosure include a broad-band acoustic atenuator comprising a metamaterial defining a plurality of cells. The cells of the metamaterial may intrinsically damp incident acoustic waves. Each cell may focus acoustic waves incident on the cell to an interior of the cell where energy of the acoustic waves is dissipated by absorption. Absorption frequency dispersion may exhibit a hyperbolic response and affect all (spatial) frequencies of propagation.

[0014] Detection of vehicles in the water, including stealth vehicles

(e.g., submarines), is based on active and passive SONAR techniques. Targets are ensonified by transient acoustic signals. Echoes from targets are interpreted to detect presence, location information, and the like. See for example, U.S. Patent No. 4,847,817 to Whitlow granted July 11, 1989; U.S. Patent No. 5,930,201 to Cray granted January 27, 1998; U.S. Patent No. 7,206,258 to Fisher granted April 17, 2005, each herein incorporated by reference in their entirety.

[0015] Conventional passive stealth techniques for water vehicles

(e.g., submarines) are based on the use of anechoic tiles. These tiles are composed of elastomeric materials with embedded voids and/or gas-filled cavities that act to absorb incident sound intensity and thereby reduce the strength of the reflected acoustic wave. Reduction of the intensity of the hull acoustic reflection reduces the active sound ranging and the terminal acquisition range of active sonar that may be used, such as, for example, by torpedoes. The technology of anechoic tiles was pioneered by the Kriegsmarine in World War II. The material was nonhomogeneous with embedded air cavities that degraded the reflection of active sonar. The coating reduced acoustic reflection intensity by about 85% in the 10 to 18 kHz range (matching the operating range of the early active sonar used by the Allies).

[0016] The modem materials for acoustic tiles consist of a number of elastomeric layers embedded with different size gas-filled cavities. Each cavity size may be designed for a specific acoustic frequency range at a range of depths. Some of the most advanced stealth technology tiles include hollow microspheres that are more pressure resistant than the conventional tile technologies. In addition, other materials are sometimes used in different areas of the submarine to better absorb specific frequencies associated with machinery at that location inside the hull. Unfortunately, major problems associated with adhesion and degradation of the acoustic absorption performance with diving depth still remain a challenge for state-of-the-art acoustic tile technologies.

[0017] FIG. 1 illustrates the endemic degradation in reflection loss with increasing water pressure. FIG. 1 shows curves 101, 102, 103 representing reflection loss of anechoic Expancel ^® tiles, designed and fabricated by QinetiQ Ltd, UK, over a range of frequencies. Each curve corresponds to a particular pressure. Curve 101 represents reflection loss at 0.1 Mpa. Curve 102 represents reflection loss at 0.7 Mpa. Curve 103 represents reflection loss at 1.4 Mpa. The parameter‘Reflection Loss’ shown in FIG. 1 includes other dissipative effects such as tile edge scattering and transmission loss through the tile and does not equate to conventional‘Echo Reduction’ experiments extracted from measurements of strictly plane waves with sound hard acoustic waveguide experiments.

[0018] Aspects of the present disclosure include apparatus for enhanced broad-band acoustic attenuation. Aspects of the present disclosure include an acoustic metamaterial cell which may be used in bulk production of anechoic materials for undersea acoustic stealth applications. The metamaterial cell may be composed of solid metal material, plastic, or composite that can be easily fabricated from conventional 3D additive manufacturing (ADM) techniques and then attached mechanically to the vessel hull. In other examples, additive manufacturing or a combination of manufacturing techniques may be employed to make hull plates or other vehicle structures incorporating metamaterial cells. The metamaterial absorption characteristics may be water pressure independent and remain consistent over a full operational range of diving depths. The metamaterial may intrinsically develop broad-band acoustic echo reduction properties by absorption of incident acoustic energy.

[0019] Techniques are disclosed herein for acoustic attenuation using a metamaterial comprised of cells comprising a plurality of sub-cells. The metamaterial cell design is investigated analytically herein to with respect to the acoustic absorption characteristics of the material over a broad frequency range (0-100 kHz) of incident acoustic radiation that is of specific interest for military naval stealth applications. The dissipation of the energy of incident acoustic radiation by the metamaterial may be due to macroscopic cell boundary scattering analogous to intrinsic damping in solid metals developed by microscopic grain boundary scattering. The absorption frequency dispersion may exhibit a hyperbolic response and may affect all (spatial) frequencies of propagation.

[0020] In some implementations, each cell comprises a plurality of sub-cells azimuthally arrayed about an axis of alignment. One example described herein is that of using a canonical tangent circles transformation in which a canonical tangent circles mapping forms the sub-cell geometry. The mapping focuses constant contours of eccentric circles with a common tangent point at the origin of Cartesian coordinates. Each sub-cell comprises a plurality of cell segments with each cell segment of the plurality comprising at least one arcuate section and at least one radial finger, wherein the cell segments of each sub-cell are oriented in alignment with a mapping geometry comprising an inversion of a canonical tangent circles mapping in a plane transverse to the axis of alignment.

[0021] The rectangular |x v| Cartesian coordinates may be related to the [u,v\ mapped coordinates by the relations:

Eq. (1)

The inversion relates rectangular [x,y\ Cartesian coordinates to \u v| mapped coordinates by the relations:

Eq. (2)

[0022] FIG. 1 shows curves 101, 102, 103 representing reflection loss of anechoic tiles over a range of frequencies. FIGS. 2A & 2B illustrate the mapping geometry. FIG. 2A shows tangent circles curvilinear contours. FIG. 2B shows inverted tangent circles curvilinear contours. Eq. (1) develops focusing constant contours of eccentric circles with a common tangent point at the origin of Cartesian coordinates as shown in FIG. 2A. The inversion of this mapping according to the relations of Eq. (2) is used to obtain the defocusing constant contours of eccentric circles, shown in FIG. 2B. The physical cell design is developed with the inversion constant coordinate contours in FIG. 2B as a sub-cell template for octagonal symmetry in the sub-cell geometry.

[0023] General embodiments include an acoustic metamaterial cell used in metamaterials having“dark” acoustic reflection loss characteristics, e.g., a phenomenon where a material develops broad-band acoustic attenuation characteristics by absorption of incident acoustic energy waves. Aspects of the present disclosure relate to advanced stealth hull treatment for military submarines, unmanned underwater vehicles, and surface vessels.

[0024] In contrast to other novel cells of other acoustic systems, such as the cells used in vibrational isolation, aspects of the present disclosure include cells comprising a solid material (such as a metal) arrayed in a fluid background resulting from the immersion of the cell in the fluid medium conveying the vehicle.

[0025] The absorption characteristics may be brought about by energy transfer within the material to dissipate acoustic energy. Both 2D acoustical simulations and frequency dispersion analyses concluded that the attenuation mechanism is related to absorption behavior as opposed to simple reflection. The energy of an incident acoustic wave appears to be focused to the interior of the cell structure and dissipated there by absorption created from macroscopic cell boundary scattering. The absorption frequency dispersion was determined to exhibit a hyperbolic response and affected all (spatial) frequencies of propagation. In aspects, additive manufacturing processes may be employed to embed the material intrinsically within a tool or tool components with inherent hyperabsorption characteristics. See also, Patent Cooperation Treaty application filed as U.S. Patent Application Ser. No. 2015/044467 to Weisman et al filed August 10, 2014, and published as WO 2016025388 Al.

[0026] For the manufacture of metal-based materials, additive manufacturing powder bed systems (such as selective laser melting (SLM), metal 3D printing, laser cusing, electron beam melting (EBM), and direct metal laser sintering (DMLS)) or powder fed systems (such as laser cladding, directed energy deposition, and laser metal deposition) may be employed. Example commercial systems which are suitable for manufacture include the Laser Engineered Net Shaping (LENS) powder delivery system from Optomec, and Studio System+ from Desktop Metal of Burlington, Massachusetts. For plastic materials, filament-based 3D printing techniques, such as fused deposition modeling, may be employed in manufacture. 3D printer filaments may include PLA and ABS and may contain metal powder.

[0027] FIGS. 3A-3C illustrate example metamaterial cells with cell segments oriented in alignment with an inversion of a canonical tangent circles mapping for attenuating an acoustic wave in accordance with the present disclosure. FIG. 3A shows sub-cell inversion of tangents mapping contours. FIG. 3B shows isotropic cell geometry.

[0028] FIG. 3B illustrates the cell 310. The cell 310 has two opposing planar surfaces that are parallel. As illustrated, the visible planar surface 313 is parallel with the paper. The distance between the two surfaces, or thickness, may be in the range of 1 millimeter to 1000 millimeters. The diameter of a circle enclosing the cell 310 may be in the range of 1 millimeter to 100 millimeters. These dimensions are generally selected to allow phenomena such as resonances to have a measurable influence on the behavior of the cell 310 and affect wave manipulation in the particular frequency ranges of interest. The cells, such as cell 310, of the present disclosure may be made up of a solid, e.g., metals or non-metals. Suitable metals include, but are not limited to, steel, platinum, tungsten, gold, and exotic options such as iridium, with the important material property for acoustic wave attenuation being the mass density of the metal.

[0029] The cell 310 may be comprised of a plurality of sub-cells 320.

As shown in FIG. 3B, the cell 310 includes eight sub-cells 320. Although sub cells are depicted as identical, in some applications, each sub-cell may be unique. In some implementations, one or more sub-cells may depart from the canonical mapping for cost, ease of manufacture, and so on. The curvilinear geometry of the segments 304 of cell 310 may be constructed from the set of sub-cell inversion of tangents mapping contours 301 with [x, y] coordinates located within an eight sub-cell cell of the Cartesian frame such that for each sub-cell the segments 304 align with the set of contours 301. FIG. 3A illustrates the set 391 of contours 301. See P. Moon and D. E. Spencer, Field Theory Handbook, New York: Springer- Verlag, 1971.

[0030] The cells of the metamaterial intrinsically damp incident acoustic waves. Each cell focuses acoustic waves incident on the cell to an interior of the cell where energy of the acoustic waves is dissipated by absorption. This absorption may be predominantly due to subwavelength wave scattering at metamaterial intracellular boundaries.

[0031] The dissipation phenomena may display some similarities to damping from grain boundary scattering in conventional metals, except that the metamaterial absorption behaves with a hyperbolic frequency dispersion that develops an almost unbounded ultrasonic attenuation spatial frequency bandwidth; in other words, with“hyperabsorption.”

[0032] The segments 304 of the plurality may be an arcuate segment

350 comprising a curve corresponding to a contour line. The arcuate segments 350 may have offshoot segments, or fingers. These fingers may be radial fingers 351 perpendicular to the tangent of the curve. The fingers may be substantially rectangular, or may also have a curvature, which may also comport with the canonical mapping. Radial fingers 351 and other offshoot segments may also have effects such as chamfering, bullnosing, or the like. The surfaces of the fingers may also be individually curved, textured, split, or the like. Other embodiments may include other types of segments in some or all of the sub-cells, for some or all of the cells, in dependence upon the particular application or design considerations, such as cost, ease of manufacture, and so on.

[0033] The resonances and anti-resonances within the cell 310 are affected by the interaction of the various structural features. Thus, the number, size, shape, and orientation of features influence where and to what extent resonances and anti-resonances occur and how they complement or negate one another in affecting manipulation and control of the incident acoustic wave. Any number of segments may be used. Configuration may be carried out by building the cell - that is, iteratively adding design elements to the mapping.

[0034] FIG. 3C & 3D illustrate one example of practical cell design compatible with conventional additive manufacturing technology. The cell may be comprised of metallic material and arrayed in a fluid background (e.g., seawater) to produce hyperabsorption characteristics and enhanced reflection loss performance for undersea stealth applications.

[0035] FIG. 3E & 3F illustrate an example of practical cell design compatible with conventional additive manufacturing technology and including the addition of comer fillet radii 380 and resonant fork fingers 390 that enhance the broadband absorption characteristics of the metamaterial.

[0036] FIGS. 4 A & 4B illustrate an example metamaterial panel in accordance with embodiments of the present disclosure. The metamaterial panel 400 may comprise a series of connected cells. The panel may be coupled to the hull plate 401 of the vessel with an attachment lug 402. The panel may be configured such that when installed on the vessel surface, an axis of alignment 403 for the cells is orthogonal to an incident acoustic wave 405 normal to the surface. The axis of alignment 403 may be normal to the plane formed by cell axes 411 and 413.

[0037] FIG. 5 illustrates a simulation model and boundary conditions for the metamaterial. To understand the fundamental acoustic attenuation characteristics of the cell design a series of detailed multi-physics finite element analyses were conducted. The acoustic absorption properties of the proposed metamaterial design are analyzed using an analytical model 500 simulating a perfect waveguide with incident plane wave radiation 502 at the inlet port 501 of the waveguide and a hard sound boundary 590 at the terminal port of the waveguide. The analysis is conducted using the Comsol ^® MultiPhysics software package. An array 511 having three solid metamaterial cells 510 along the propagation direction and one cell transverse is placed at the terminal port just inside the hard sound boundary. The fluid background is inviscid water 520. The elastomeric dampening core 599 in both cell designs is a centrally located elliptical geometry having major and minor dimensions of 13 mm and 9 mm, respectively.

[0038] Three all-metal cell materials are considered in the below analyses based on conventional 3D additive manufacturing (ADM) options available, (i) steel, (ii) Ti6Al4V alloy, and (iii) AlSilOMg alloy. In addition, a PLA plastic with 36% copper loading was also considered. The material properties for the analysis materials are summarized in Table 1.

[0039] The absorption analysis may be conducted in the form of a steady-state harmonic frequency response. The absorption spectrum is calculated by first extracting the complex reflection coefficient R at each frequency for the section as denoted for the reflected wave in FIG. 5 :

^R = j - 1 Eq· ¹ where Pi is the incident pressure and P is the average complex pressure at the section. The frequency dependent absorption coefficient is then calculated as: and represents the ratio of the absorbed acoustic energy to the incident acoustic energy.

[0040] FIG. 6A shows absorption spectra for the ADM AlSilOMg metamaterial cell for the solid-finger sub-cell design, represented by curve 602, and the resonant-fork sub-cell design, represented by curve 601. The spectrum for the solid-finger sub-cell design exhibits near 100% absorption over multiple bandwidths with most frequency ranges remaining above 60% absorption, with the exception of mixed degrees of absorption below 30 kHz. This absorption phenomena is unusual considering the minimal damping assumed for the AlSilOMg material (x = 1 percent), suggesting that absorption is created by macroscopic artificial cell boundary scattering. The introduction of the resonant-fork sub-cell design broadens the high absorption bandwidths over the entire frequency range. FIG. 6B illustrates the harmonic response at 29 kHz for the resonant-fork sub-cell design response.

[0041] FIG. 7 A illustrates absorption spectra of two additional ADM materials with a dampening core. FIG. 7A shows absorption spectra for steel, represented by curve 701, Ti6Al4V, represented by curve 702, and AlSilOMg, represented by curve 703. The absorption properties of the metamaterial cell design appear to be moderately affected by cell material change, predominantly with respect to local absorption. The AlSilOMg resonant-fork sub-cell design exhibits more absorption generally over the lower frequency (0-20 kHz) of the bandwidth analyzed. The steel cell material has broader absorption bandwidth at 30 kHz than the other all-metal materials considered.

[0042] FIG. 7B illustrates absorption spectra of steel (represented by curve 711) in comparison to PLA plastic material filled with 36% copper loading (represented by curve 712) in the resonant-fork sub-cell configuration. The material is utilized in 3D additive fabrication machines in the form of a filament and is manufactured under the tradename CopperFill ^® . The CopperFill ^® material absorption spectrum is much broader bandwidth than any of the all-metal material spectra and exhibits very broadband absorption of almost 100% above 20 kHz. [0043] FIG. 7C illustrates absorption characteristics of the metamaterial design for frequencies under 5 kHz. The metamaterial design has also moderate acoustic intensity absorption of energy transmitted to a free fluid medium, such as when internal vessel noise or vibration are transmitted into the water through the vessel hull plate. The frequency content of this type noise and vibration is typically confined below 5 kHz.

[0044] FIG. 8 illustrates a simulation model and boundary conditions for the metamaterial. To understand the fundamental acoustic attenuation characteristics of the cell design a series of detailed multi-physics finite element analyses were conducted to calculate the transmission frequency response spectra of a classic acoustical T-R waveguide problem. The waveguide background material has the acoustic properties of water and the cell material has solid elastic properties of steel. The center core in each cell has solid elastic properties of an elastomeric dampening material as described in Error! Reference source not found.. The waveguide longitudinal edges are constrained with Bloch periodic symmetry boundary conditions to simulate the effect of placement in a perfectly reflecting waveguide. An incident harmonic acoustic plane wave propagates from the bohom edge boundary of the waveguide and a perfectly matched layer is placed at the top of the waveguide to eliminate all reflections. The transmission and reflection coefficients are retrieved over a frequency range of 0-100 kHz, and the effective acoustic Pentamode properties are extracted to calculate the effective frequency response spectra.

[0045] FIGS. 9 A & 9B illustrate resulting refractive index response spectra. The spectra (represented by curves 901, 902, 911, 912) indicate multiple bands of backward propagating sound speed as evidenced by the negative real parts of the refractive indices. The multiple bands of non-zero imaginary part of the indices are an indication of bandwidths containing significant energy absorption.

[0046] FIGS. 10A & 10B illustrate the equifrequency contours associated with the metamaterial frequency dispersion for wave propagations at 29 kHz. These equifrequency contours show that the imaginary absorptive component of the wavenumber dominates all spatial frequency propagation modes and exhibits a hyperbolic dispersion that continues to increase in the higher spatial frequency modes. This unusual hyperabsorption phenomena is evident for wave propagation in both the cellular‘ 1’ propagation direction as well as the transverse cellular ‘2’ propagation direction. The unusual broadband and significant magnitude of energy absorption shown above can thus be understood as phenomena associated with hyperbolic frequency dispersion affecting all modes of wave propagation through the metamaterial.

[0047] FIGS. 11 A & 11B illustrate an application of the hyperabsorption metamaterial to the reduction of acoustic signatures of naval vessels. The implications are to reduce the targeting range of undersea and surface vessels by enemy active sonar systems through the enhancement of the acoustic echo reduction characteristics of the vessel hull. FIG. 11 A illustrates a 2D acoustic waveguide Comsol ^® Multiphysics simulation model of an array of the metamaterial cells in a water medium used to evaluate the transient echo properties of the metamaterial. FIG. 11B illustrates an incident pressure pulse. The Multiphysics simulation model includes waveguide boundary conditions that develop Bloch periodicity in the finite dimension metamaterial array to approximate a large extent cellular array in the geometry directions lateral to the waveguide propagation direction. The terminal wall of the waveguide behind the metamaterial array is modeled as a perfect reflector so that any reduction in reflection would be known to be attributable to the hyperabsorption properties of the metamaterial. The simulation is conducted by applying a plane wave incident pressure pulse at the entry port of the waveguide propagating towards the metamaterial array.

[0048] Referring to FIG. 11B, the transient pressure pulse is a short

Gaussian waveform having a center frequency of 20 kHz and bandwidth of 40 kHz to capture the reflection loss characteristics over the spectral frequency range of primary interest for submarine stealth applications (1 - 35 kHz). The metamaterial cells are modeled as solids having metal properties typically achievable with conventional 3D additive manufacturing (ADM) technology with a conservative damping coefficient x =1%. The water medium was modeled as a fluid having density of 1.0 g/cc and sound speed c=l500 m/sec. [0049] The waveguide transient simulations were conducted using pure water. To determine the echo reduction properties, spectral characteristics of the transient reflection waveforms are calculated using the FFT algorithm with no zero padding and 1500 microsecond transient response windows. The echo reduction coefficient is calculated in the frequency domain as:

where the pressures P _r , Pi are the average values taken over the entry port section.

[0050] FIGS. 12A & 12B illustrates a graphical illustration of the transient wave propagation response for the reference water case and the metamaterial case. The reflected wave is shown in two dimensions as lighter with increasing amplitude. FIG. 12C shows a comparison of the reflection frequency spectrum (1202) with the incident pulse frequency spectrum (1201). As can be seen, pressure is drastically reduced over entire range of frequencies, so that very little acoustic signature remains.

[0051] FIG. 13 shows the echo reduction coefficient for the metamaterial using three conventional all-metal ADM materials (Steel, Ti6Al4V, and AlSilOMg) and the copper-filled plastic filament, each with a dampening core. The curve 1301 represents echo reduction for cells manufactured using copper-filled plastic filament. The curve 1302 represents echo reduction for cells manufactured using steel. The curve 1303 represents echo reduction for cells manufactured using AlSilOMg. The curve 1304 represents echo reduction for cells manufactured using Ti6Al4V. Narrow band amplifications in echo reduction vary among the all-metal cell material options, with the overall echo reduction spectra extending from about 20 dB below 1 kHz and increasing asymptotically to about 26 dB above 15 kHz. The echo reduction spectrum for the CopperFill ^® is similar over the lower frequency range below 15 kHz but exhibits more extensive narrowband attenuation regions than the all-metal spectra.

[0052] FIGS. 14 A & 14B show a transient reflection with and without the metamaterial. FIGS. 14 A & 14B illustrate that a reflection of the incident pressure pulse from the metamaterial is not only significantly reduced in amplitude but the incident signature is distorted in the reflection as well. The degree of distortion in the echo returned from the metamaterial decreases the signature correlation with the incident waveform thus increasing the difficulty in detection by devices such as comparative receivers. For naval undersea applications, the CopperFill ^® filament may be preferable for the cell material due to the more significant energy absorption properties and the resulting lightweight metamaterial (0.933 g/cc anechoic panel). However, various materials may be suitable for individual applications, in dependence upon a variety of factors, such as cost, durability, availability, detectability via non acoustic means, ease of manufacture, and so on. Materials and overall design may be tailored to different types of vehicles, or vehicles used for different purposes.

[0053] In some implementations, combinations of materials may be used for an individual panel, for cells in a panel, sub-cells in a cell, segments in a sub-cell, and so on. Subsequent panels, cells, sub-cells, and/or segments of an installation may be made of different materials or combinations of materials, or with different configurations, such as, for example, alternating cell size, segment design, mapping, and the like. The cell design of a panel may be layered, or panels themselves may be installed in layers, or different portions of the vehicle may correspond with panels having a different configuration. In some implementations, a panel, or other form of the metamaterial, may be manufactured integral with vessel structures, such as, for example, hull plates, such that integrated structure in its entirety comprises the acoustic attenuator. An acoustic attenuator may also be manufactured or assembled to include structural components, including fastening, welding, adhering, or otherwise coupling the matrix to one or more components.

[0054] A metamaterial is a material engineered to have a property that is not found in nature.“Conformal mapping geometry,” as used herein, refers to an arrangement of cell segments within the cell such that the contour lines from a non-Cartesian coordinate system are mapped onto a surface. Herein the surface may be a flat base from which each cell projects in a cantilever fashion. “Unbounded” as used herein describes a frequency range including normal operating frequencies for downhole ultrasonic (e.g., less than lMHz). “Non-solid” as defined herein refers to a liquid, gas, vacuum, dissolved and/or suspended particulate matter, mixtures, solutions, emulsions, suspensions, or combinations of these.

[0055] The present disclosure is susceptible to embodiments of different forms. There are shown in the drawings, and herein are described in detail, specific embodiments of the present disclosure with the understanding that the present disclosure is to be considered an exemplification of the principles of the disclosure and is not intended to limit the disclosure to that illustrated and described herein. While the foregoing disclosure is directed to the one mode embodiments of the disclosure, various modifications will be apparent to those skilled in the art. It is intended that all variations be embraced by the foregoing disclosure.