PROPAGATING THROUGH A MEDIUM

GROSS-REFERENCE TO. RELATED APPLICATIONS

|0001j This application claims priorit to- U.S. Provisional Patent. Application Serial No.

62/53-8,933, entitled "METHODS OF GEOMETRIC ALTERATION TO ENABLE ACOUSTO- ELASTIC METAMATERIAL FUNCTIONALITY WITHIN ANTLTET.RACHIRAL LATTICE GEOMETRIES," to Martin, which. was filed on 31 My 2017 and is incorporated herein by reference,

FIELD OF THE INVENTION ^'

(0002] The present invention relates in general to articles of manufacture including heterogeneous -elastic composites as well as methods of manufacturing same, and relates more particularly to heterogeneous elastic composites that exhibit a yibro-aeonstie impedance match with other fluid and elastic materials as well as the method of manufacturing same,

BACKGROUND OF THE INVENTIO

00031 Truss-like lattice structures, where elastic beams are connected together at joints to form a regular lattice of geometries, support an extra degree of fie iiral motion due to the absence of an elastic boundary condition at the beams' outer surfaces. Chiral and anti-chiral lattice structures feature trass beams, termed "arms" for the purpose of this specification, which extend from joints with a specific rotational handedness to form a chiral geometry. The presence of truss beams in such lattices can produce a particularly low vibro-acoustie- stiffness when compared to the stiffness of their component materials due to this flexural degree of freedom. The low vibro-aeoustic stiffness in turn leads to low vibro-aeoustic wave speeds and short wavelengths, which are essential design features for applications that rely on vibro-aeoustic phase mitigation and resonance. While chiral and anti- ehirai lattices are known in die art, their use in applications: that mitigate vibm-acoustic wave propagation in other media has been limited to a narrow range of media with vibro-aeoustic impedance that approximately matches that of the chiral lattice structures. This limitation is due to the physical requirement that the vibro-aeoustic impedance of two media must be similar in order to exchange & significant amount of vibro-aeoustic energy between the media,

[0004] In the simpli fied case of a vibro-aeoustic wave propagating a t normal incidence to the interface between two media, the vibro-acoustie impedance 1 oc ^fCp of each medium is proportional to the square root of the medium ^' s vibro-aeoustic stiffness C and densit p. Here, C is the relevant stiffness tensor component for a particular elastic wave polarization in elastic media, while C is the bulk modulus for fluid media. For a given homogenous materia!,, both chiral and anti-chiral lattices made from that material can have lower vibro-acoustie stiffnesses than the .material itself, in accordance with the vibro-aeoustic impedance relationship,: the density of the lattices- ould have to increase in proportion to the decrease in stiffness in order to keep the impedance of the lattice matched to its component homogenous material . I an ^' embodiment with no density alteration, the ehirai and anii-chiral lattices would be impedance-matched to external media with lower vibro-aeoustic impedance.

[0005] Matching the ibro-acoustie impedance of such lattices is particularly challenging when the matching medium is similar t a dense fluid such as water. Many common elastic materials such as plastics, ceramics, metals, semiconductors* organic and biological matter have vibro-aeoustic impedances that are at least similar to and often higher than water. Taking water as an example, it is possible- to reduce the vibro-aeoustic stiffness of chiral ami and-ehira! lattices Blade irons plastic materials to achieve wave speeds of less than a tenth of water. The low stiffness and phase speed are achieved by rcnioving .material to form the chiral ^■ configuration of arms, but this removal of material ■simultaneously decreases the density of the plastic lattice, further reducing the. lattice's impedance compared to water. Although such low wave speeds are advantageous for phase mitigation and resonance applications, particularly those that require compact spatial designs, the accompanying low impedance compared with water makes these- lattices impractical for exchanging vibro-acoustic energy between the lattices and a volume of water.

BRIEF SUMMARY OF THE INVENTION

[1006] An embodiment of the inventio includes a device for use in a medium comprising a medium vtbro-aeoostic impedance. The device includes an elastic material including a plurality of unit cells. The plurality of unit cel ls includes a first unit cell. The first, uni cell includes a first unit- cell joint comprising a first unit-cell joint wall defining a first joint central void, a first unit-cell join inclusion located in the first joint central void, and at least two first unit-ceil arms connected to and extending away from the first unit-ceil joint. The elastic material includes an elastic-material vibro- acousiic impedance. The elastic-material vibro-acoustic impedance and the medium vibro-acoustic impedance are sufficiently vibro-aeoustieaily impedance-matched to couple- time-varying, propagating vibro-aeoustic fields between said elastic maierial and the medium.

{( ⁽ 007} An embodiment of the instant invention includes heterogeneous chiral and anii-ehiral lattices for use m m i tigating the propagation, of vibro-acoustic wa ve fields . An illustrative goal of the embodiment is to enable the phase manipulation of such wave fields when the wave fields ate reflected irons or transmitted through the lattices.

{00081 An embodiment of the invention includes heterogeneous elastic composites having a vibro-acoustic impedance match with the siinrounding or adjacent fluid and elastic materials. The impedance match enables the coupling of vibro-acousiic wave fields betwee the elastic composites and at least one extemal medium, where the vibro-acousiic wave propagation in the external mediom can. in turn be controlled and mitigated through the proper design of such composites. It finds particular application in conjunction with utilizing ehirai lattice structures, which can be designed to have low vibro-acou ic wave speeds compared to their underlying material components, and will be described with particular reference thereto. However it is to be appreciated that the present exemplary embodiments are also amenable to other like applications,

IO0O { Another embodiment of the invention includes the ehirai and/or aiiti-chital lattices selected to exhibit a low yibr -acoustic- stiftness, while simultaneously increasing the impedance - f the lattice. Thi s embodiment of the invention maintains the vibro-aeonstie impedance at. a value c lose to that of a particular medium, irrespective of the selection of differing vihro-acoust e wave speeds at different spatial locations within the lattice.

BRIEF DESCRIPTION OF THE DRAWINGS

{0010] The following is a brief description of the drawings, which are presented for the purposes of illustrating the exemplary embodiments disclosed herein and not tor the purposes of limiting the same. [0021 J FIG. 1A is a schematic diagram of an. elastic material comprising a plurality of unit cells that form s ami-tetrachirai. lattice in accordance with the present invention;

(00123 FI .. IB is a schematic diagram of a sub-unit of an anli-ietrachiral unit cell in accordance with the present invention'

[0013] FIG. 2A is a schematic diagram of a unit cell having connecting arms that extend from the edge of the unit ceil joint wall in accordance with the present invention;

[0014] FIG. 2.B is a schematic diagram of a unit cell having connecting amis that extend from the center of the uni t cell joint, wai l in accordance with the present invention;

e015j FIG. 2G is a schematic diagram of a unit cell having connecting, arms that extend from a point between the edge and the center of the unit eel!, joint wail in accordance with the present invention;

{0016J F G- 2D is a schematic diagram of a unit cell with additional material added to the connecting; arms in accordance with, the present invention;

[0017] FIG. 3 A is a schematic diagram of a -plurality of unit cells that are functionally-grade in the vertical direction in accordance with the present invention ^*

[0018] FIG, 3B is a. schematic diagram of a plurality of unit cells that alternate their geomelry every other cell to form a supeilattice in accordance with the present invention;

[00191 FIG, 3C is a schematic diagram of a plurality of unit ceil that alternate- their composition ever other cell with a material thai is either homogenous or heterogenous in aeeordatice with the present invention;

[0020] FIG, 3D is a schematic diagram of a plurality of on.it cells having underlying unit cell geometries that are randoml configured in accordance with the present invention; {0021] FIG. A is a Sdiematic diagram of an anisotropic ^' unit cell with connecting arms lengthened in one spatial direction in accordance with the present invention;

(06223 FIG.. 4B is a schematic diagram of an anisotropic unit cell with, joint walls and joist central voids extended in one spatial direction in: accordance with the present invention;

fO023J FIG. 4C is a schematic diagram of an anisotropic unit cell with different materials filling- adjacent joint central voids in accordance with the present invention;

{0024] FIG. 4D is a schematic diagram of an anisotropic unit cell with joint walls and joint central voids composed of different geomeaie shapes in accordance with the present invention;

{0025} FIG. 4E is a schematic diagram, of a trichiral unit cell in accordance wit the present invention.;

[ 026] FIG. 4F is a schematic diagram of an anii-triehiral unit cell in accordance with the present, invention; _.

j O02?| FIG. 4 is a schematic di agram of a tetrachiral uni t cell in accordance with the present invention;

{0028] FIG. 4H is a- schematic diagram of three-dimensional anti -tetrachiral trait cell i accordance wit the present invention;

{0029] .FIG. 5 A. is a schematic diagram of the joining region between two adjacent anti- tetraehiral unit cells in the absence of joining region inclusions in accordance with the present invention;

{0036} FIG. 5B is a schematic diagram of the joining region between two adjacent anii- tetraehiral unit cells having identical joining region inclusions _, located at the joining interface in. accordance with the present invention; [8831] FIG. SC is a schematic diagram of the joining region between two adjacent anti- tetracMra! unit cells having joining region inclusions located at the joining interface that are different in geometry and composition in accordance with the present, invention;

[8832] FIG. SD is a schematic diagram of the joining region between two adjacent a tti- tetraehiral unit cells having inclusions set back from the joining interface i accordance with the present invention;

[0833] FIG. 5E is a schematic diagram of the joining regio between two adjacent anti- tetrachiral unit cell where joining region inclusions are used to directly connect ^" a joint wall on one side of the joining region to an arm on the other side in accordance with the present invention

[0834] FIG. 5F is a schematic diagram of the joining region between an anti-tetrachiral unit cell a different homogenous or heterogeneous material in accordance with the present invention;

[083S] FIG. 50 is a schematic diagram of the joining region between two adjacent anti- tetracMral unit cells that have rotated orientations and have as mmetric joining region, inclusions connecting the respective adjacent unit cell arms in accordance with the present invention;

[0836] FIG. 6A is a schematic diagram illustrating an aperture that alters vibro-acoustle propagating fields that are reflected from a surface in accordance with the present invention;

[083.7} .FIG. 6B is a schematic diagram illustrating an. aperture that alters vibro-acoustlc propagating fields that are reflected from and/or transmitted throug said aperture i accordance with, the present invention;

[0838] FIG. 6C is a. schematic diagram illustrating an aperture featuring negative refraction that alters vibro-acoustic propagating fields that are reflected from and'or transmitted through said aperture in accordance with the present invention; (0039] FIG. ΊΑ i a schematic diagram illustrating an aperture that alters vibrp-acoustic propagaiing fields that are incident on and/or emanating from a curved vibro-acoustie source and/or sensor in accordance with the present invention; and,

(0040) FIG. 7B is schematic diagram illustrating an. aperture that alters vibro-acoustie propagating fields thai are incident cm and/or emanatin from a dire lionally-dependent vibro- acoustic source and/or sensor in accordance with the present invention .

DETAILED DESCRIPTIO OF INVENTION

(0041 J A more complete understanding of devices, articles of manufacture, and/or processes disclosed herein can be obtained b reference to the accompanying figures. These figures are merely schematic representations based on -convenience and the ease of demonstrating the present invention, and are, therefore, not intended to indicate relative size and dimensions of the devices or components thereof and/or to limit the scope of the exemplary embodiments.

(0042) Although specific- terms are used .in the following descriptio for the sake of e-larity, these terms are intended to refer only to the particular structure of the embodiments selected for illustration in the drawings, and are not intended t limit the scope of the disclosure.

(9043) An objective of the instant invention is to create an elastic* material that couples propagating vibro-acoustie field from a first medkim that support the propagation of such fields to a second medium. In an embodiment of the invention, the second coupled ^' medium is the elastic material itself. For the purpose of the instant specification, the term ''propagating vibro-acoustie field** refers to a time-varying oscillation in the position of particles that make up a medium, which includes acoustic wave .fields in fluids and elastic wave fi elds solids. In some embodiments of the invention, when the elastic material is made up of an underlying lattice of chiral structures, the wave speed of the vibro~acoustic propagating fields in the lattice becomes significantly reduced compared to the characteristic eompressional wave speed of the base material used to form the lattice. In some embodiments of the invention, the wave speed in the lattice is significantly lower than One or more wa ve speeds in the coupled media. Lower wa ve speeds produce shorter wavelengths, which in. turn result in resonance phenomena at lower frequencies compared with a higher wave speed medium. Shorter wavelengths also improve the dissipation, of energy that is contained hi a propagating vibro- acoustie field when the field propagates across a particular spatial distance,

|(KI44J in one or more embodiments of the invention, low wa ve speeds in the elastic material are spatially dependent and advance or retard the phase of propagating vihro-aeoustie fields .in different amounts depending on the spatial location within the lattice. An. underlying goal of an embodiment of the invention is to maintain the coupling between a medium and the elastic material when the wave . ^' speed -and phase, modulation are spatially dependent.

£01145] For an embodiment of the invention, FIGs. 1A and ^' I B .illustrate an elastic material including a plurality of unit cells 300, The plurality of unit cells 1.00 is also defined as a "lattice." in an embodiment of the invention such as shown in FIG. I A, the plurality of unit cells 100 is depicted as an anii-tetrachiral lattice. Although F G. 1 A shows a two-dimensional, lattice, in another embodiment of the invention, the number of unit cells in the lattice 100 Is extended in. the three orthogonal Cartesian directions to create a three -dimensional elastic material of size appropriate to a user's application, in another embodiment of the invention, the two-dimensional lattice 10 is extruded out of plane. F G. A shows an illustrative unit cell .102 as outlined by a rectangle with a dash-dot-styled border. Each unit cell 102 of the lattice is composed of least one sub-unit 1 10. FIG. 1 A shows an Illustrative sub-unit cell 1 10 as outlined b a rectangle with a dash-dash-styled border. For clarity, in FIG. iA, the rectangular border around writ cell 10:2 includes dots and dashes, and the rectangular border around sob-unit ceil J 10 includes dashes. Each sub-unit 1 10 includes a joint, which in tur includes an elastic joint wall .1 12 that encloses a joint central void 1 , Each joint wall 112 is connected to adjacent joint walls. y at least tw elastic connecting arms 1 16, 1 18, where the adjacent joint walls are in the same unit cell 102 or an adjacent unit cell. FIGs, 1 A. and 1 B show four connecting arms for ease of understanding. However , one of ordinary ski ll in the art ^' will readily appreciate that the number ^' of connecting amis depends on the user's application and -optionally includes two, three, or more than four connecting arms. FIGs. 1 A. and I B show connecting arms that extend straight without curvature for ease of understanding. However, one of ordinary skill in the art will readily appreciate that the curvature of the connecting arms depends on the user' s application and thai the amis optionally curve to connect two adjacent joint walls at varying locations,

j0046J The joint walls 1 12 and connecting arms 1 16, 1 18 are separated by gaps 104, 106.

Although only tw gaps are shown in FIGs, I A and I B, one of Qui a _, skill, in the art will readily appreciate that the number of gaps depends on the user's application and optionally includes one, three, or more gaps. The gaps 104, 106 are filled with a standard material that allows the connecting arms 1.1.6, 1 18 to fle out of plane, where one of the vectors thai defines the fiexural plane is parallel to the direction of the connecting arm's extension .between - the joint walls. In a embodiment of t.be in ven tion, the ^' material comprising the gaps 104, 106 includes a standard low-viscosity material, such as a standard .fluid. In. another embodiment of the invention, the gaps 104, 106 are left, vacant, thereb enclosing a vacuum or air. In still another embodiment, the gaps 104, 106 are filled with a standard elastic material with a bulk modulus, shear .modulus, and density that does not .tally suppress the propagation of vibro-acoustic waves along the connecting arm ^' s 1 16, i. 18.

(00 73 In the exemplary embodiment shown in FIGs. I A and I B, the unit cell 102 of the lattice has connecting arms 1.1.6, 1 I S oriented in an. anti-ehiral geometry, in some embodiments of the invention, the unit ceil 102 has connecting arms 1 16, 118 oriented in a chrraS geometry, hi other embodiments of the invention, the plurality of unit cells 100 include an and-txiehlrai lattice, a trichiral lattice, or & tetrachiral lattice.

|Qd48] An illustrative goal of the instant invention is to create a material that couples ^' time- varying, propagating vibro-aeoustie fields between the lattice 1.00 and an exterior medium when the exterior medium is brought into mechanical contact with the lattice. The term "coupling" is defined herein as the act of bringing the exterior medium into mechanical contact with the lattice 100 such that, some fraction of energ contained in a propagating vibro-acoustie field transfers between the two media, hi an embodiment of the invention., the exterior medium is, for example, a standard fluid or standard elastic materia!, and the exterior medium is,, for example, a standard homogenous material or a standard heterogeneous material, in another embodiment of the invention, the aforementioned heterogeneous material includes another lattice.. In order to achieve sufficient coupling between the exterior medium and the lattice, the material composition, of the joint central void 1 14 is chose such that the plurality of unit cells 100 as a whole are approximately vifero-acoustkally impedance-matched to the exterior medium. For the purpose of the present specification, an "appro mate' ^' ' impedance match is defined as a vibro-acoostic impedance contrast between the lattice 1.00 and the exterior medium that is sufficiently small such that the transferred portion of the propagating vibro-acousiic field's energy achieves the goal of an application-specific embodiment of the invention under consideration.

The primary purpose of selecting the material composition of the joint central voids 114 is to achieve -a predetermined dynamic composi te density of the plurality of unit cells 100 as a whole. The "dynamic composite density" is defined herein as the density that the lattice appears to have if the lattice were assumed to be a homogenous medium at a given frequency of vibro-acoustic oscillation. The dynamic composite density has also been termed an "effective density" in the relevant literature. Seleeting the material composition of the joint central voids 114 in this way determines the den sity of the lattice without signi ficantly impacting the vibro-acoustic and mechanical stiffnesses of the plurality of unit ceils 100. Furthermore, the freedom to select the composite density of the plurality of unit cells 100, while leaving the composite -vibro-acoustic. stiffness only slightly perturbed, provides a means of selecting the vibro-acoustic wave speed of the lattice while maintainin approximately the same stiffness. m an embodiment ^" of the invention, the joint central voids 1 1-4 are, for example, filled wit a standard acoustic fluid or a standard elastic material and the central voids 114 are, for example,, filled with a standard homogenous .or a standard heterogeneous material, hi another embodiment of the invention, the central voids 11 are, for example, tilled with a combination, of such standard materials.

[0050J Another illustrative goal of this invention is to create a material that has a geometrically-iunable vibro-acoustic wave speed, but. that simultaneously maintains the coupling of propagating vibro-acoustic fields between the plurality of unit cells 100 and. a -exterior medium or media, hi order to accomplish this goal, a second mechanism is required to select the dynamic composite stiffness of the- lurality of unit cells as a whole without significantly modifyin the density of the lattice. The "dynamic composite stiffness" is defined herein as the stiffness that the lattice appears to have if the lattice were assumed to be a homogenous medium at a given frequency o vibro- acoustic oscillation. The dynamic composite stiffness has also been termed an "effective stiffness" in the relevant literature. The second mechanism is to select the position and orientation of the connecting arms 1 16, 118, As illustrated tor the embodiment of an anti-tetrac ral unit cell 102, 202, 204, 206 in FIGs. 2A.-2D, the position of the connecting ami s can be ^" located at the edge 1 16, 1 18 of the joint wall 112 (e.g., as shown in FIG. 2A), at the center 216, 218 of the joint wall (e.g., as shown in FIG, 2B), or in between the edge and center 226, 228 of the joint wail (e.g., as shown in FIG, 2C), in each case without c hanging the directi on of extension of the connecting arms . The embodimen t of the invention shown by way of illustration in FIG. 2B represents the special case where the chirai asymmetry of the unit cell is lost. An embodiment of the invention, shown by way of illustration in FIG. 2 A, represents the geometric configuration of the unit cell 102 with the lowest stiffness, while the embodiment of the invention, shown by way of illustration in PIG, 2B, represents the highest stiffness configuration. One of ordinary skill, in the art will readily appreciate that positioning of the connecting arras between these two extremes allows for the selec tion of a stiffness appropriate for the user's application. By simultaneously selecting ^' the geometric position of the connecting amis 1 16, 118, 216, 218, 226, 228 and the material composition of the central joint voids 114, both the.vib.ro- acousttc wave speed and impedance of the lattice can be independently selected. In this way, the vibro-aeoustic wave speed of the lattice can be selected to have a plurality of values while preserving an approximate impedance match with an exterior medium.

\ 0051 J In some embodiments of the invention, the connecting anus 116, 1.18 do not have a uniforftT thickness acros their ex tensions. In other embodiments, of the invention, such as that shown in FIG. 2D, additional material or materials 208, 209 are added to the connecting arms 1 16, .1 18 and serve to provide an additional means of selecting the dynamic ^' composite density and stiffness of the lattice. The additional materials 208, 209 include standard heterogeneous or standard homogeneous elastic materials, and their geometry (or geometries) with respect to the connecting am s 1 16. 1 18 can be selected to meet the requirements of the specific user's application; the geometries of the additional materials 208, 209 are, for example, standard shapes such as circles, squares, and triangles. The additional material 208 need not be the same as the additional material 209 iocaied in a different part of the unit cell 206, and their respective geometries need not be the same.

|(KI52J The. material composition of the joint walls 112, the connecting ami 1 1 , 1 18, the joint central voids 1 4, the gaps 104, 106, and the additional materials 208, 209 added to the connecting arms depend on the user's intended application. For example, in an illustrative embodiment the joint wall and connecting amis are made from a standard -semiconductor, a siandar metal, a standard metal alloy, a standard polymer, a standard foam, a standard gel, a standard rubber, a standard elastic composite, and or a standard ceramic that is amenable to manufacturing usin a standard three-dimensional additive build process. Examples of- such a. metal include steel and titanium, an example of such a ceramic is alumina, and an example of such a polymer is acrylomtrile butadiene styrene. In some embodiments of the invention, the polymers used in -an additive build process are standard plasties. After manufacturing the joint walls and connecting, arms, the joint central voids and gaps are optionally filled in with other standard materials. Examples -of such fi lling materials are standard fluids, standard foams, standard gels, and other standard solids,

{0053] In an illustrative embodiment that is intended to be impedance-matched, with the exterior medium of water, the joint walk and connecting arms are manuf ctu ed out of acrylonitrile butadiene styrene using a standard additive, build process. The joint central voids are filled with tungsten, where the tungsten is inserted using rods that have the same cross-sectional, geometry as the joint central voids. The gaps are -filled- with air. In the aforementioned embodiment of the invention, th compressiona! wave speed of the lattice can be reduced to 1/10* that of water while maintaining a vibro-acoustic impedance match with water. Tungsten increases the- .dynamic composite density of the lattice to -simultaneously reduce the vibro-acoustic wave speed and to increase, the impedance of the lattice. Although tungsten is used to fill, the joint central voids in this embodiment of the invention, one of ordiiiary skill in the art will readily appreciate that any sta dard material that is much denser than water can he used to fill the joint central voids. For example, in other embodiments of the invention, the tungsten is exchanged with another dense material such as steel, gold, or lead,

[0054] in some embodiments of the invention, one or more components of the unit cell are manufactured out of a standard piezoelectric ceramic, such as lead zirconate tiiaiiate, or a standard electro- or magneto-rheoiog-ic material, such as a standard polymer composite containing ferromagnetic -particles, in order to introduce an active forcing component that .generates vibro- acoustic fields within the lattice through, the application of an electric or magnetic field,

0055Ϊ In some embodiments o f the invention, the components of the unit cell are east wi thin a standard mold using a standard casting process. The casting process and moid components depend on the application. In embodiments that utilize high-temperature metal casting, for example, illustrative casting materials include- standard -metal- -alloys, .such a■ gallium-indium alloys, and brass. In embodiments that utilize the lower-temperature casting of standard polymers, for example, illustrative casting materials include polycarbonate and poiydimethySsiloxane, hi. some embodiments of the invention, the pre-manufactiired joint walk and connecting arms ^' act as -molds for the easting of materials into the joint central voids and gaps. In oilier embodiments of the invention, the pre- mahufectured joint central voids and gaps act as molds for the easti ng of materi als into the joint walls and eonneetin amis,

fWI56] in one or more embodiments of the invention, the ^' components of the unit cell are manufactured out of standard foams that have high porosity, in some embodiment of the invention, the base material of the foams includes standard polymers, such as polystyrene, in other embodiments of the invention, the base material of the foams includes standard metals, such as aluminum or copper, O057] In one or more embodiments of the invention, the components of the unit cell are etched out of a standard semiconducting material using a standard etching process. For example, standard semiconducting wafer etching is used to produce lattice structures consistent with embodiments of the invention. Examples of such semiconducting material s include silicon, gallium arsenide, or gallium nitride. For example, in an illustrative embodiment of the invention where the joint wails and connecting arms are etched at the surface, of a semiconducting wafer, the joint central voids and gaps are then filled with other materials. through stand rd mask and deposition techniques. Illustrative semiconductor applications include the production of delay lines that function using surface acoustic waves or other coupled elastic waves,

f(H!58| in one or more embodiments of the invention, the lattice. ^' unit .cells are manufactured with characteristic scale that is important to the propagation of .phonons and the transport of heat through a medium. In such embodiments of the invention, the unit cell geometries are optimized for the purpose of controlling thermal or phonon transport, through the elastic material

{0059] In one or more embodiments of the invention, the materials making, up. the unit cell components are standard composite materials such as standard, carbon fiber epoxy or standard nylon fiber/epoxy compos tes. In other embodiments, the materials making up the unit cell components ate standard rubbers such as butyl rubber or natural rubber.

¾! one or more embodiments of the invention where multiple gaps axe present, the materials filling the gaps 104 and 106 are not the same materials; in other words, gap 104 and gap .106 have respective materials.

[11061 } in one or more embodiments of the invention, the plurality of unit cells 100 produce band gaps at certain vibro-aeoustie oscillation frequencies that suppress the propagation of vibro- acoustie waves. A "band gap" is defined herein as a band of frequencies where there are no modes of p ropagating vibiO-aco ustie fie lds in the latti ce, in such embodimen ts of the invention, the material composition of the joint central voids 1 14 and or the location of the connecting arras 1 16, 1 18 determine the range of vibro-acoustic frequencies at which these band gaps occur. In some embodiments of the invention, the range in frequency of the band gaps is determined solely by selecting the materi al composition of the joint, central void 1 14 ,

[0062] In one or more embodiments of the invention, the plural ity of unit cells 100 produce a band of propagating vibro-acoustic oscillation frequencies where the lattice vibrates at only one vibrational mode, in such embodiments of the invention, the single vibrational mode has a polarization defined by compressional, shear, or a mi of compressional. and shear motion. The material composition of the joint central voids 1. 1.4 and the location of connecting arms 11.6, 1 18 is deiemiined in order to select in turn the ra ge of vibro-aeotistic frequencies at which these single vibrational modes occur. An illustrative embodiment of the invention that produces single modes .of propagation is an. anii-tetoae!iiral lattice where the joint walls 112 and connecting arms 1 1.6, 1 18 of the unit cell 102 are composed of acrylon iirile butadiene styrene. In an embodiment of the in vention where the joint central voids 114 are filled with air, the band of single-mode -propagation is broken up by complete band gaps. In an embodiment of the in vention where the joint wall 1 12 is seleeted to be thicker, thereby filling in the joint central void 1 14 with acrylonitrile butadiene styrene, the band, gaps forms at higher frequencies:, while the bands of single-mode propagation ref ms at lower frequencies. In. an embodiment of the invention where th connecting arms 226, 228 of the unit cell 204 are selected to be between the center and the edge of the joint wall 1 12, the band of single-mode propagation forms at a higher frequen cy compared to an embodi ment of the i nvention wh erein a unit celt 102 includes connecting arms 1 16, 1 18 at the edge of the joint wall,

|(NH»3J Another illustrative goal of this invention is to create a material that has a spatiall heterogeneous distribution of vibro-acoustic wave speeds. In accordance with some aspects of the present invention, FIGs, 3Α-3Ϊ) illustrate alternate embodiments of the invention, showing standard anisotropic and standard disordered heterogeneous elastic materials with a plurality of unit cells 300, 302, 304, 306. The erm "heterogeneous elastic materia!" as used for the purpose of the instant specification refers to an elastic material with a plurality of unit cells, . but where at least one of the unit cells is not identical to the others. Each unit cell 102, 312, 314, 3 6, 318 does no necessarily have the same geometry as its adjacent unit cells. In some embodiments, of the invention _* such as that shown in FKL 3 A, the. unit ceils 12 have timetionally-graded geometries, wherein the unit cells have one or more geometric features that diffe from cell to cell in at least, one spatial direction. Alternatively, in other embodiments of the invention, the unit cells 312 have functionally-graded geometries, wherein the unit cells have one or more geometric features thai differ from plurality of unit cells to plurality of unit cells i at least one spatial direction. Alternatively, in other embodiments of the invention, the unit cells 3.12 have functionally-graded geometries, wherein the unit cells have one or more geometric features that differ between interfaces, i.e., between layers of like unit cells, in at least one spatial direction. In some embodiments of the invention, sue as tha shown in FIG. 3B, the unit cells 102, 314 alternate back and forth between at least two different: unit cell geometries in at least one Spatial direction. The geometries of such embodiments are often referred to as a "superlattice" in the literature and for the purpose, of this specification. The lattices shown in. FIGs, 3A. and 3B are described as "multi-component lattices, ^" " which for the purpose of this specification are lattices that have more than one type of unit cell but that repeat in a regular order in at least one spatial direction.

|(Ki64J in one or more embodiments of the invention, such as that shown in FIG. 3C, the unit cells 1.02 alternate with other types of material geometries 308, 309 in at least one spatial direction. The alternate material geometries 308 and. 309 are a heterogeneous geometry or a homogeneous geometry, and need no t be composed of the same material. The term "homogeneous geometry" refers herein to a geometry composed of a single material, T he term, "heterogeneous geometry" refers herein to a -geometry composed of more than one material and/or geometry. Heterogeneous geometries can be disordered heterogeneous geometries or lattice geometries. The term "disordered heterogeneous geometry" refers herein to a geometry composed of multiple component geometries that do not repeat in space with a regular order. The term "lattice, geometry" refers herein to a .geometry with an underlying unit cell thai repeats in space with a .regular order. Disordered heterogeneous geometries are either lattice-free, wherein there are no lattice geometries found in any component geometries, or disordered heterogeneous geometries, which contain component geometries that form a lattice locally, but that do not repeat in space beyond a confined region. [0065} in one or more embodiments of the invention,, such as that shown in FIG, 3D, the unit cells 3.16, 318 have geometries that do not repeat i a tegular order and have randomized configurations, hut nevertheless preserve an underlying regular spatial repetition. In one or more embodiments of the invention, the rotational orientation of each unit cell 102, 312, 314, 316, 318 is not preserved between adjacent -unit cells, causing functionally graded or random rotational orientations across the entire plurality of unit cel ls 300, 302, 304, 306.

[0066] i accordance with some aspects of the present invention, FiGs, 4A-4M illustrates alternate embodiments of the unit cells that make up the lattice- structures depicted in FK3s. IA-3. In one or more embodiments of the invention, such as shown in FIG. 4A, the connecting arms 404 of the unit cell 400 are lengthened in at least one direction when compared to connecting arms 406 in orthogonal directions in order to produce an anisotropic geometry, and thereby produce anisotropic vibro-acoostic material properties. In one or more embodiments of the invention, such as show in FIG. 4B, die size and geometry of the elastic joint walls 416 of the unit cell. 4 1 are extended or contracted in at least one direction compared to other orthogonal directions, thereby creating anisotropic vibro-acoustie material properties. In one- or more embodiments, such as shown in FIG. 4C, the material composition of one joint central void 408 of the unit cell 402 differs from that of at least- one adjacent joint central, void 41.0, thereby creating amsotropie vibro-acoostic material properties. In one or more embodiments of the invention., such as shown -in FIG. 4I>, the geometric shape of the elastic joint walls 420, 422, 424, 426 are selected to - impose alternative symmetries and asymmetries to the unit cell.403, In such embodiments of the invention, the geometry of one particular elastic joint wall 420 is the same or different from the joint wails of adjacent sub-units. In one or more embodiments of the Invention, such as shown in FIG. 4D, the elastic joint wait includes a standard shap such as a ^' standard rectangle 420, a standard oval ^' 422, a standard triangle 424, or a standard diamond 426. In one or more embodiments of the invention, the axes of symmetry of the geometry defining the elastic joint walls ^' 420, 422, 24, 426 is rotated with respect to the direction of extension of the connecting arms 418, which is exemplified by the rotated oval 422 in the upper left of the unit cell in FiO. 4 .

[0067] in one or more embodiments, of the invention, the amsotropy introduced by appropriately selecting the geometry of the unit cells 400, 40 i, 402, 403 i at least one principal directio creates directional band gaps in at least one principal direction compared to other orthogonal directions. In some embodiments of the invention, the directional band gap creates a hyperbolic band structure over a range of vibro-aeoustic oscillation frequencies, in. such embodiments of the invention, the range of frequencies tha t feature the directional and/or hyperbol ic bands are determined by appropriate selection of the geometric ami material composition of the connecting arms 404, 406, 4.1.8, the join walls 416, 420, 422, 424, 426, and the joini central voids 408 and 410.

[0068] in one or more embodiment., of the invention, snob as. shown in FIGs. 4B, 4F, and 4G, the lattice unit cell is configured as a trichirai symmetry 412, an anti-trichiral symmetry 413, or a telrachiral symmetry respectively 414, In one or more embodiments of the invention, the unit cells such as shown in FIGs. lA-3 and 4A-G are extruded out of the plane to form a three-dimensional honeycomb-like lattice. In other embodiments of the invention, such as a three-dimensioaal. anti- tetrachiral unit cell shown in FIG. 4H, the lattice unit cell 415 is the fl ree-dimensional embodiment of any unit cell consistent with this specification, in embodiments of the invention, the unit cells 412, 413, 414, 415 take on any geometric modifications consisten with this disclosure. |80 ^' 69] In one or more embodiments of the instant mvention, the vibro-acoustic bands approach a B ouiri mm boundary with a linear slope, In. such embodiments of the invention, the frequency at which the vibro-aconstic and crosses: the Brillouin zone boundary is selected by •selecting the geometric and/or material composition of the connecting aims, the joint wails, and/or the joint central voids. For example _* when, compared with the selection of locating the connecting arms 1 6, } I S at the edge of the joint walls 1 12 In FIG. 2A, if instead the connecting amis 226, 228 are located between the edge and the center of the joint walls 112, the dynamic composite stillness of the unit cell increases, whicli in turn increases the frequency at which a linear crossing occurs. In another illustrative embodiment of the invention, the f equency at which a linearly-sloping band crosses the BriSlouin zone boundary is selected by selecting the scale of the unit cell

[ 070] In one or more embodiments of the invention where different unit cells are coupled together, for example as show in FIGs. 3A-3D, a subset of such embodmieBis requires a modification of the joinin regions where the unit cells 102, 312, 31.4, 316, 318 are coupled to other adjacent unit eel Is. For the illustrative joining region 500 shown in FIG. 5 A, no modification of the joining region is required to couple two identical unit cells 02 because the connecting arm 521 to the left of the joining region meets the connecting awn 522 lo the right of the joining region in the same spatial location. For the illustrative joining region 510 shown in FIG..5B, some embodiments of the invention include joining region inclusions 503, 505 to couple the connecting arm 521 to the left of the joining region with the connecting ami 532 to the righ of the joining region because the two connecting arras 521, 532 do not meet in the same spatial location. Such a joining region, inclusion is, for example, important for embodiments of the invention wherei the materia! filling the gaps 534, 536 around the connecting arms has a substantially different vibro-acoustic impedance when compared with, the material composition of the connecting arms. For example, for an. embodiment of the invention where the connecting amis 521, 532 include a standard, metal and the gaps 534, 536 are filled with air, there is significantly degraded vibro-aconstie coupling between the connecting amis and the gap because of the high vibro-aeousiic impedance contrast etwe n -metals and air. In such embodiments, the joining region inclusions 503, 505 are selected to be composed of an appropriate standard material, such as the same metal, to provide improved coupling between adjacent unit cells.

[0071 _. 1 in one or more embodiments of the invention, such as shown in FIG. 5B, the joining region inclusions 503, 505. 506, 507 have the same geometry and material composition, and are symmetric about the joining region 10, in other embodiments of the invention, the joining region inclusions 504, 505, 07, 08 do not have the same geometry, material composition, and/or symmetry of location about the unit cell, for the illustrative- example shown hi FIG 5C, the joining region inclusion 504 i selected to have a different geometry from the inclusion 505, and the joining region inclusion 50 is selected to have a different material composition from, the inclusion 507.

[ 72] In one or more embodim en ts of the invention , such as shown in FIG. 5D,. the joining region inclusions 524, 525, 526, 527 are located at a position offset from the joining regio location 530, When offset by some distance from the joining region 530, some embodiments of the inventio will have. joining -regio inclusions 524, 525 that. are selected to have the same geometry, material composition, and symmetry. Other embodiments of the invention will have the joining region inclusions- 526, 527 that are selected, t have different geometry, material composition, and/or symmetry.. |0©73J in one or more embodiments of the invention, such as show in FIG. 5E the connecting arms 536, 537 of a single unit cell 202 are connected directly to the joint walls 1 12, 538 of an adjacent unit ceil 102 using joining region inclusions 51 1 , 512.

10074] in one or more embodiments of the invention, such as shown in FIG. 5F, a unit cell

102 is coupled to a homogenous or heterogenous geometry 528 by attaching the connecting arms 54 , 542 to the geometry 528 at the joining region 550. In one or more embodiments of the invention, the homogenous or heterogenous · geometry 528 fills the gaps 544 on the other side of the joining regioo 550.

[WI5\ in one or more embodiments of the invention, such as shown in FIG. 5G, where adjacent unit cells 102 and 204 have a rotated orientation with respect to one-another, joining region inclusions 513, 514, 515, 516 are used to couple the connecting arms of these two unit cells together. The joining region inclusions 513, 514, 515, 516 are extended to bridge the additional space 546 introduced by the rotated orientations. The additional space 546 is filled, for example, with any material consistent with thi s di sclosure, or is evacuated. In some embodiments of the invention, the material filling the additional space 546 is selected to be the same as the materia! selected to fill the gaps 548; in other embodiments of the invention, the materials filling the additional space and gaps differ .from, each other,

|i}®76j Another illustrative goal of this Invention i to create wave-steering material that can alter the propagation of vibro-acoustic fields within an exterior medium as the field propagates away from its source, in order to alter the propagation of such fields, the vibro-acoustic fields must be coupled into the wave-steering material, hi one or more embodiments of the invention, such as depicted In .FIGS. 6A-6C, exterior media 600, 614, 616 are coupled to lattices 602, 61.0, 622, In one or more embodiments of the invention, such as shown in FIG. 6A, the lattice 602 is resting on a surface ^' 604 that primarily reflects incoming vibro»acoustie propagating fields 606. in such embodiments of t e invention, the exterior media 600, . 14, 16 include standard heterogeneous media or standard homogeneous media, and include acoustic or elastic media, in such, embodiments f the invention, the lattices 602, 610, 622 include a plurality of unit cells with composition that is consistent with the instant invention as described herein, A purpose of the embodiment depicted in F IG, 6A is to use the vibro-acousiic coupling with the lattice 602 to preserve or modify the outgoing reflected vibro-acoustic propagating field 608. In one or more embodiments of the invention, the exterior medium 600 is water.

{0077] fn some embodiments of the invention, the lattice 602 has a funefional!y-graded vibro- acoustic wave speed such that the ou t-going vibro-acoustic field 60S propagates away from the lattice at a different reflection angel & _$ than the incident angle & _f of the incident vibro-acoustic field 606, in some embodiments of the invention, the out-going vibro-acoustic field 60S is focused and Intensified within a finite spatial region within the exterior medium 600, In some embodiments of the invention, the amplitude of the out-going vibro-a.cou.siic field 60S is minimized due to finite absolution in the lattice 602, In some embodiments of the invention the out-going vibro-acoustic field 608 is dispersed in random directions. In other embodiments of the invention, the out-going vibro-acoustic ^■ field 608 mimics the radiated spatial and temporal vibro-acoustic field pattem. that would have been, generated by at least one vibro-acoustic source situated on the reflecting surface 604.

{00781 hi one or more embodiments of the invention, such as depicted in FIG. 6B, the lattice

610 transfers an incident vibro-acoustic propagating field 606 from a source medium 614 to a destination medium 616. In some embodiments of the invention, the source me ium 61 and destination medium. 61 are composed of the same standard material; in other embodiments of the invention, the source medium and the destination medium are composed of different standard materials, A purpose of the embodiment of the invention depicted in FIG. 6 is to use the vibro- aeoustic coupling with the lattice 610 to preserve or modify both the vibro-aeoustic field 608 reflected from flie lattice and the vibro-acoustic field 620 transmitted through the lattice. In some embodiments of the invention, the lattice 610 has a. functionally-graded vibro-aeoustic wave speed such that at least one of the out-going vibro-acoustic fields reflected 608 and transmitted 620 by the lattice propagates with a different reflection angle .& _s and transmission angle # _r< respectively, compared with that of the incident angle B _f . In one or more embodiments of the invention, at least one of the out-going vibro-aeoustic fields reflected 608 and transmitted 620 by the lattiee is fbcused and intensified within a finite spatial region within at least one of the exterior media 614 and 616, In some embodiments of the invention, the amplitude of at least, one of the out-going, vibro-acoustic fields bolh- reflected 608 and transmitted 620 by the lattice 61,0 is mininiixed due t finite absorption in the lattice, in other embodiments of the invention, at least one of the out-goin vibro-acoustic fields reflected 608 and transmitted 620 by the lattice is dispersed in random directions,

(0079] In one or more embodiments of the invention; the amplitude of the reflected vibro- acoustic field 608 is minimized due to an approximate vibro-acoustic impedance match between the lattice 610 and the exterior media 614 and 61 , In other embodiments of the invention where the vibro-aeoustic; impedance of the source medium 614 differs from that of the destination medium 616, the amplitude of the reflected vibro-aeoustic field 608 is minimized using a funeiionaliy-graded vibro- acoustic impedance in the lattice 1 . [0080] In one or more embodiments of the invention, the lattices 602 -and 610 are used to exchange the primary polarization of the incident vibro-acoustie wave 606. in such embodiments of th invention, the lattices 602 and 610 transform eompressional polarization to shear polarization or transform the shear polarization to com ression^ polarization.

f dSl] In one or more embodiments of the invention, the source media 600, 6.14 and destination medium 616 are water. In other embodiments of the invention, the source medium 614 is a standard elastic material that contains a standard vibro-acoustie source, while the destination medium 616 is the body of an animal or the body of a human, in other embodiments of the invention, the source medium 614 is a standard elastic material that contains a standard vih -aeoustic source, while the destination, medium 61 is a standard elastic medium thai is the target of ^' non-destructive testing,

19082] In one or more embodiments of the inventi on, the thickness of the lattices 602 and 610 i s much smaller than the vibro-acoustie. wa velength of propagation in at least one of the source medi a 600, 14 and the destination medium 1 . In such embodiments of the invention, ihe lattices 602 and 610 are defined as * netasnrl¾ees" for the purpose of the instant specification, hi one or more embodiments of the invention, the purpose of coupling to such meiasuriaee lattices 602. ami 610 is to create vibro-acoustie resonances in the meiasuriaee lattices, ! some embodiments of the invention, the lattices 602 and 61.0 delay the phase of a propagating yibro-aeoustic Held over sub-wavelength path length by up to and including 360 degrees.

{9083} In one or more embodiments of the invention, the lattices 602 and 610 are used to focus a vibro-acoustie field into a spatial region that is sub-wavelength in. size and smaller than the virbo-aeoastic diffraction limit Such a embodiment functions as a *'superlens" for the purpose of the instant specification. s that term is used in the relevant literature. When the sub-wavelength focusing occurs due to an interaction with a hyperbolic band structure, such an embodiment functions as a ^M hyperie«s ^t> for th purpose of the instant specification as that term is used in the relevant literature. In such embodiments of the invention, it is possible to focus the near-field components of a vibro-acoustic wave.

[01184} in one or more embodiments of the invention, such a tot shown hi FIG. 5C, the lattice

622 creates negative refraction and/or backward reflection. Backward reflection occurs when the outgoing, reflected ^■ vibro-acoustic field 624 propagates in a direction that is back toward the incident field 606 on the same side of the line 628 norma! to the surface interfacin with the lattice 622,. Negative refraction occurs when the out-going, transmitted vibro-acoustic field 630 propagates away i a direction tha is on the same side of the line 629 norma! to the surface interfacing with the lattice 622.

jOOSSj in. one or more embodiments of the in vention, such as that, shown in FSGs. 7A-7B, the lattices 706, 71.2 are wrapped around vibro-acoustic field sources .and/or sensors 708, 7.1.4, which are situated in exterior media 700, 01. The purpose of such embodiments of the invention is to preserve or modify the spatial and/or temporal content of the propagating vibro-acoustic fields as they leave the source or are recei ved by the sensor. One of ord inary skill in the art will, readily appreciate that a component that cat* be used- as a vibro-acoustic field source can also .be used to sense such fields. In such embodiments of the invention, the exterior media 700, 701 include/standard heterogeneous or standard, .homogeneous media, and are standard acoustic or standard elastic media,, in such embodiments of the invention, _, the lattices 706, 712 have a plurality of unit cells with composition that is consistent with the instant invention as described herein, in some embodiments of the invention, the vibto-acoustic field source and/of sensor 708, 714 include a group of multiple standard sources and/ or standard sensors.

{00861 ¾! one or more embodiments of the invention, .such as that shown in FIG. 7A, the vib.ro- aeoustic field source 708 propagates vibro-acoustie fields 702, 704 outward in an omni-directional pattern with .spherical or cylindrical symmetry. In suelremhodiments of the invention, the lattice 706 maintains -or changes the temporal and/or spatial content of the propagating vibro-acoustie fields 702, 704 such that the spherical or cylindrical symmetry is preserved or is broken. Similarly, when the vibro-acoustie field source is used to sense incoming vibro-aeoustic fields 710, the spherical or cylindrical symmetry of the sensor's spatial -temporal sensitivity is preserved or broken,

{0087] in one or more embodi ments of the invention, such as that shown in FIG. 7B, the vibro- acoustie field source. 714 propagates vibro-acoustie fields 703, 705 outward in a directed beam pattern. In soch embodiments of the invention, the lattice 712 maintains or changes the temporal and/or spatial content of the propagating vibro-aeoiistie fields 703, 705 such that the beam shape and/or it directivity is preserved, or is altered. Similarly, when the vibro-acoustie field source is used to sense incoming vibro-acoustie fields 71 i, the sensor's spatial-temporal sensitivit is preserved or altered.

(0088] in one or more embodiments of the invention, the lattices 706 and 712 are used to exchange the primary polarization of the outgoin vibro-acoustie fields 702, 703, 704, 705. In such embodiments of the invention, the lattices 706, 712 transform compressions! polarization to shear polarization or transform, the shear polarization to corapressional polarization. A transformation to shear polarization Is possible when the exterior media 700, 701 are standard elastic solids. Similarly, in other embodiments of the^ invention, the lattices 706 and 712 are used to exchange the primary polarization of the incoming vibro-acou&tk .fields 710, 71 1. hi such embodim n s of l ve invention, the exterior media 700, 701 are standard fluids or standard elastic solids,

{00891 Although a particular ^' feature of the disclosure may have been illustrated and/or described with respect to-only one o several implementations, such feature may be combined ^' with one or more other features o f the o ther implementations as may be des ired and advantageous for any given or particular application. Also, to the extent that the terms "including", "includes", "having", "has", Vith", or variants thereof are used in the detailed description and/or in ihe claims, such terms are intended to be inclusive in a manner similar to the term "comprising".

10090! This written description, sets forth the best mode of the invention and provides examples to describe the invention and to enable a person of ordinary skill i the art to make and use the in vention. This written description does not limit the invention to the precise tenns set forth. Thus, while the invention has been described in detail with reference to the examples set forth above, those of ordinary skill in the art may elTeci alterati ons, modifications and variation s to the examples without departin from, the scope of the invention.

{0091! These and other implementations are within the scope of the following claims,