Metamaterial structure, ventilated matrix member and method for ventilation and attenuating sound

Abstract

The application discloses a metamaterial structure for ventilation and sound attenuation in a first environment having an air circulation opening for ventilating the first environment. The metamaterial structure comprises an acoustic metamaterial portion comprising a plurality of metamaterial unit cells arranged to define a single air vent within the air circulation opening, wherein each metamaterial unit cell comprises a labyrinth channel defining an acoustic wave path having an acoustic wave inlet facing the single air vent and no acoustic wave outlet, at least a part of the metamaterial structure is configured to be releasably disposed in the air circulation opening, and the metamaterial structure has a metamaterial ventilation efficiency of at least 50%, and the air vent area is at least 50% of the total area of the metamaterial structure.

Description

[0001] METAMATERIAL STRUCTURE, VENTILATED MATRIX MEMBER AND METHOD FOR VENTILATION AND ATTENUATING SOUND TECHNICAL FIELD

[0002] The present invention relates to a metamaterial structure, ventilated matrix member and method for ventilation and attenuating sound in an environment.

[0003] BACKGROUND

[0004] Cooling techniques are central to ensuring proper function of electronic equipment and comfortable built environments for living and working. However, many standard cooling methods using energized devices such as fans or air conditioning units in homes and commercial buildings as well as exhaust fans for cooling electronic equipment through forced convection increase electricity consumption and contribute to fossil fuel combustion. As fossil fuels deplete and decarbonization efforts advance, there is a pressing need to explore passive cooling solutions. For example, in the built environment industry, more residential developments are being designed for natural ventilation instead of relying on mechanical ventilation using energized devices, there is a problem of undesired environmental sound.

[0005] In particular, in countries limited by land constraint, such residential developments are inevitably built closer to transportation infrastructure and thus impacted by traffic noise. Prolonged exposure to environmental noise in the urban environment may have negative impact on physical and mental health, such as increased stress and anxiety levels and sleep disruption. Traffic noise may be generated from traffic, such as vehicles on roads, trains on rail tracks, and air traffic. Another major source of noise is from building and construction sites. Such noise sources typically have a narrow bandwidth (dominant frequency).

[0006] Turning to cooling designs for electronic equipment, the incorporation of exhaust fans to cool such equipment generates noise in the industrial workplace. To incorporate a new panel solely for natural ventilation may add to additional material / part and increases material use.

[0007] In view of the above, materials and / or devices have been developed to enableattenuation of sound and allow ventilation concurrently. WO 2021 / 194419 A1 (“WO’419”) describes an acoustic attenuation panel with ventilation holes and array of attenuation sections to attenuate acoustic waves, and describes joining of the panels to form an enclosure to contain a machine or assembled to form a ventilation louver. While this is useful for the installation of new fittings, it does not allow for retrofitting of such panels to existing structures in the current built environment.

[0008] Therefore, there still exists a need for ventilation metamaterial structures that are capable of reducing undesirable sounds in an environment, while allowing thermal comfort in an interior space.

[0009] SUMMARY

[0010] According to a first aspect, there is provided a metamaterial structure for ventilation and sound attenuation in a first environment having an air circulation opening, wherein the metamaterial structure comprises: an acoustic metamaterial portion comprising a plurality of metamaterial unit cells arranged to define a single air vent ; wherein each metamaterial unit cell comprises a labyrinthine channel defining an acoustic wave path having an acoustic wave inlet facing the single air vent and no acoustic wave outlet; wherein at least a part of the metamaterial structure is configured to be releasably disposed in the air circulation opening; and wherein the metamaterial structure has a Metamaterial Ventilation Efficiency of at least 50%, the Metamaterial Ventilation Efficiency determined using formula (I) below:

[0011] Metamaterial Ventilation Efficiency = [P% x X] / [Y] x100% --(I)

[0012] where

[0013] P is a ventilation constant;

[0014] X is a floor area of the first environment; and

[0015] Y is a total area of the air circulation opening in the first environment.

[0016] The metamaterial structure has a total area C and the air vent has an air vent area V that may be determined using formula (II) below:

[0017] V = Metamaterial Ventilation Efficiency x C --(II)

[0018] and wherein V is at least 50% of C.

[0019] The acoustic metamaterial portion has an area MPA, and the ratio of V to MPAmay range from 1:1 to 2:1.

[0020] Each metamaterial unit cell is spaced apart from its adjacent metamaterial unit cell at a distance (d) of less than half a width of the metamaterial unit cell .

[0021] Each metamaterial unit cell may comprise a single labyrinthine channel.

[0022] The plurality of metamaterial unit cells may be integrally formed as a unitary piece.

[0023] The metamaterial structure may further comprise a plurality of T-shaped grooves formed in the metamaterial structure and a plurality of T-shaped protrusions projecting from the metamaterial structure, wherein one of the T-shaped protrusions on the metamaterial structure is configured to securely fit within one of the T-shaped grooves of another unit of the metamaterial structure thereby securely joining the metamaterial structure to the other unit of the metamaterial structure.

[0024] Each T-shaped groove may have straight interior sides, each T-shaped protrusion may have a curved top portion centrally provided on top of a straight post, and each T-shaped groove may be configured to be elastically deformed when fitted within one of the T-shaped grooves of another unit of the metamaterial structure.

[0025] The metamaterial structure may have a polygonal shape and the T-shaped grooves and T-shaped protrusions of the metamaterial structure may be provided adjacent the vertices of the polygonal shape.

[0026] The metamaterial structure may have a square shape, and the T-shaped grooves may be provided on first two adjacent sides of the metamaterial structure and the T-shaped protrusions may be provided on second two adjacent sides of the metamaterial structure.

[0027] The metamaterial structure may have a rectangular shape, wherein a first two adjacent sides of the metamaterial structure are each provided with a stepped edge and wherein a second two adjacent sides of the metamaterial structure are eachprovided with an overhanging edge, wherein one of the stepped edges of the metamaterial structure is configured to mate with one of the overhanging edges of another unit of the metamaterial structure to minimize air flow through any gap between the metamaterial structure and the other unit of the metamaterial structure.

[0028] Each metamaterial unit cell may be configured to fit within a rail guide disposed on the air circulation opening.

[0029] The plurality of metamaterial unit cells may be configured to be releasably connected to each other to form a grid of the plurality of metamaterial unit cells across the air circulation opening.

[0030] The first environment may comprise one of: an interior occupancy space of a built environment, an interior environment of a vehicle, an interior environment of an enclosure containing machinery, and an interior environment of an enclosure containing an engine.

[0031] The first environment may be a room in a building and the air circulation opening may be a window in the room.

[0032] Each metamaterial unit cell may be configured to attenuate sound emitted by at least one vehicle outside the first environment.

[0033] The first environment may be the interior environment of an enclosure containing machinery or the interior environment of the enclosure containing the engine and wherein each metamaterial unit cell is configured to attenuate sound emitted within the first environment.

[0034] The metamaterial structure may further comprise a permeable substrate provided over each acoustic wave inlet and configured to prevent foreign matter from entering the labyrinthine channel.

[0035] The metamaterial structure may further comprise a mounting portion operably attachable to the acoustic metamaterial portion for releasably attaching themetamaterial structure to the air circulation opening.

[0036] The portion may have a releasable attachment comprising at least one of: a snap-fit, a clip, a flange, and peg-spring clipping.

[0037] The acoustic metamaterial portion may comprise a stepped outer surface configured to mate with a stepped inner surface of the mounting portion for slidable releasable attachment of the acoustic metamaterial portion to the mounting portion.

[0038] The mounting portion may be made of a material comprising at least one of: plastics material, elastomeric material, metal, and wood.

[0039] Sound attenuation may be determined from Ventilation Ratio (VR) according to formula (III) below:

[0040] Sound attenuation = 33.5 - 0.52698VR + 0.001587VR2-(III)

[0041] wherein VR = V / C X 100%

[0042] According to a second aspect, there is provided a ventilated matrix assembly (90, 600) configured to fit within an air circulation opening of a first environment for ventilation and sound attenuation in the first environment, the matrix assembly comprising: a plurality of units of the metamaterial structure according to the first aspect; wherein an aggregate air vent area of the individual air vent areas of each unit of the metamaterial structure is determined using formula (IV) below:

[0043] Aggregate Air Vent Area = Metamaterial Ventilation Efficiency x Total Ventilation Area -(IV),

[0044] wherein

[0045] Aggregate Air Vent Area = t iviar|d Total Ventilation Area = La x Wawhere

[0046] M is the total number of air vents

[0047] La is a length of the air circulation opening;

[0048] Wais a length of the air circulation opening;V is one air vent area;

[0049] wherein the Aggregate Air Vent Area is at least 50% of the Total Ventilation Area.

[0050] The matrix assembly may further comprise a matrix support comprising horizontal segments joined to vertical segments to define a grid having a plurality of matrix openings, wherein the plurality of units of metamaterial structures are disposed adjacent to the plurality of matrix openings, wherein the matrix support is a window grill.

[0051] BRIEF DESCRIPTION OF THE DRAWINGS

[0052] While the specification concludes with the claims particularly pointing out and distinctly claiming the invention, it is believed that the present invention will be better understood from the following description taken in conjunction with the accompanying drawings in which:

[0053] FIG. 1 A is a front sectional view of a metamaterial structure;

[0054] FIG. 1 B is a section A-A view of the metamaterial structure of FIG. 1 A;

[0055] FIG. 2 is a front schematic view of an array of metamaterial structures of FIG.

[0056] 1 A configured and arranged to form a ventilated matrix member;

[0057] FIG. 3 is a perspective view of a rail guide for receiving a plurality of metamaterial unit cells at their periphery to form a ventilated matrix member;

[0058] FIG. 4Ais a perspective sectional view of an alternative metamaterial structure according to the present invention;

[0059] Fig 4B is a front view of the metamaterial structure of FIG. 4A;

[0060] FIG. 4C is a section B-B view of the metamaterial structure of FIG. 4A;

[0061] FIG. 5 is an exploded assembly view of another alternative metamaterial structure with a releasable attachment;

[0062] FIG. 6A and 6B are the perspective views of the assembled metamaterial structure of FIG. 5;

[0063] Fig 7 is a front view of a matrix support for mounting one or more metamaterial structures;

[0064] FIG. 8 is a front view of a ventilated matrix member;

[0065] FIG. 9 is a front interior view of a labyrinthine channel design according to the prior art for use in a metamaterial structure;FIG. 10 is a front view of an experimental set up for Example 1 ; and FIG. 11 is a graph plotting the attenuation of Inventive Sample A as a function of frequency (Hz) (Inventive Sample A).

[0066] FIG. 12 is a graph plotting attenuation of Inventive Sample A as a function of Ventilation Ratio (%).

[0067] FIG. 13 is a schematic close-up view of first two connected identical metamaterial structures before their connection with second two connected identical metamaterial structures.

[0068] FIG. 14 is a schematic close-up view of the first two connected identical metamaterial structures connected to the second two connected identical metamaterial structures of FIG.14.

[0069] FIG. 15 is a schematic illustration of one of the metamaterial structures of FIG.

[0070] 13.

[0071] FIG. 16(a) is a schematic close-up side view of stepped and overhanging edges of two units of metamaterial structures before mating.

[0072] FIG. 16(B) is a schematic close-up side view of stepped and overhanging edges of two units of metamaterial structures before mating.

[0073] DETAILED DESCRIPTION

[0074] This specification discloses a metamaterial structure for ventilation and attenuating sound. The metamaterial structure is suitable for the purposes of sound attenuation and providing natural ventilation.

[0075] Specifically, the metamaterial structure comprises an acoustic metamaterial portion comprising a plurality of metamaterial unit cells arranged to define a single air vent within an air circulation opening of a first environment. Each of the plurality of metamaterial unit cells comprises a labyrinthine channel having an acoustic wave inlet facing the single air vent, and a channel inner surface extending from the acoustic wave inlet along a distance of the channel to define an acoustic wave path, wherein the acoustic wave path is substantially free of an acoustic wave outlet. At least a part of the metamaterial structure is configured to be releasably disposed in the air circulation opening, wherein the metamaterial structure comprises a Metamaterial Ventilation Efficiency of at least 40%.The Metamaterial Ventilation Efficiency is determined based on Formula (I): Metamaterial Ventilation Efficiency = [P% x X] / [Y] x100% (I)

[0076] wherein

[0077] P = Ventilation Constant (%)

[0078] X = a floor area in a first environment;

[0079] Y = a total area of the air circulation opening in the first environment based on X.

[0080] According to the Building Construction Authority (BCA), a Singapore statutory board that establishes requirements for the bult environment such as buildings, the Ventilation Constant, P is 5%. Natural ventilation shall be provided by means of openable windows with an aggregate area of not less than (P=5%) of the floor area of the room or space.

[0081] For example, where the first environment comprises a bedroom having a floor area, X of 14m2, and an air circulation opening (window). A total area of the window having a length and width of 1.4m by 1m, Y is 1.4m2. Based on Formula (I), a Metamaterial Ventilation Efficiency may be determined as follows:

[0082] Metamaterial Ventilation Efficiency = [5% of 14m2] / 1.4 m2= 50%.

[0083] Without wishing to be bound by theory, a metamaterial structure according to the present invention comprising a Metamaterial Ventilation Efficiency of at least 50% enables attenuation of sound while enabling natural ventilation. X and Y may vary based on a respective floor area and a total area of the air circulation opening. However, as long as the metamaterial structure comprises the Metamaterial Ventilation Efficiency of at least 50%, the sound is attenuated effectively at the specified frequency as shown in the results of Inventive Sample A described hereinafter.

[0084] The Ventilation Constant P refers to a minimum air circulation opening of P square meters for every 100 square meters of floor area required to allow adequate air movement. P may be determined by authorities or regulatory bodies, or a pre-set parameter in order to achieve a suitable Metamaterial Ventilation Efficiency.As the metamaterial structure is configured to be releasably disposed in the air circulation opening, this enables a highly reconfigurable way of providing customized metamaterial structures for use in both commercial and DIY applications.

[0085] In the following description, the metamaterial structure described is a metamaterial structure for use in a built environment such as in an interior space such as rooms in household and commercial establishments. However, it is contemplated that the metamaterial structure may be configured for use in a variety of applications to provide passive ventilation and sound attenuation.

[0086] Prior to describing the present invention in detail, the following terms are defined for clarity. Terms not defined should be given their ordinary meaning as understood by a skilled person in the relevant art.

[0087] “Sound” as used herein refers to any sound, noise or acoustic frequency.

[0088] “Ventilation” as used herein refers to allowing air to enter and exit and circulate freely.

[0089] “Attenuating” as used herein refers to reducing or lowering the volume of sound.

[0090] “Labyrinthine” as used herein refers to maze-like, winding structures.

[0091] “releasably disposed” or “releasably attached”, “releasable attachment” as used herein refers to removable securing, joining, connecting, attaching, or fitting the metamaterial structure to the matrix member or ventilation opening.

[0092] “Permeable substrate” as used herein refers to materials that are permeable and allow movement of air, but impermeable to water and larger objects, such as insects. Water may include rainwater.

[0093] “Environment” as used herein refers to any space including indoor and outdoor environments. In some embodiments, the first environment may be an interior environment and the second environment may be an exterior environment. In other embodiments, the first environment may be an exterior environment and the secondenvironment may be an interior environment. Interior environment includes, but is not limited to, an interior occupancy space of a built environment, such as a room in a building, an interior environment of a transportation vehicle, an interior environment of an enclosure containing machinery, and an interior environment of an enclosure containing engines.

[0094] For the purposes of illustrating the present invention in detail, the invention below is described as a metamaterial structure configured to be releasably disposed within a window of a room in a built environment. However, the metamaterial structure may be configured for use with a housing for machinery or equipment attenuate sound where the sound source is the machinery or equipment.

[0095] FIG. 1A is a front view of a metamaterial structure 100 for ventilation and attenuating sound according to the present invention. FIG. 1B is a section A-A view of the metamaterial structure 100 of FIG. 1A. The metamaterial structure 100 comprises an acoustic metamaterial portion 102 comprising a plurality of metamaterial unit cells 104. The metamaterial unit cells 104 are arranged within an air circulation opening to define a single air vent 106 to allow for ventilating a first environment 10. Each metamaterial unit cell 104 comprises at least one labyrinthine channel 108, preferably a single labyrinthine channel.

[0096] Without wishing to be bound by theory, an advantage of a metamaterial structure having a metamaterial unit cell comprising a single labyrinthine channel according to the present invention is that the metamaterial structure can be optimized to balance an acoustic attenuation effect with ventilation requirements. If there are more than one channel, then the size of the unit cell will increase, and the air vent area may be reduced. As such, a metamaterial structure comprising a metamaterial unit cell with a single labyrinthine channel will result in an overall smaller size, convenient to stack adjacently to form a metamaterial structure 100. Smaller metamaterial unit cells make it easier to configure a metamaterial structure that conforms to air circulation openings or window grills of different shapes.

[0097] The labyrinthine channel 108 includes an acoustic wave inlet 110 and a closed end 111 facing the single air vent 106 to receive and channel acoustic waves travellingthrough the air vent 106 into an acoustic wave path 114. The acoustic wave path 114 is defined by a channel inner surface 112 of the labyrinthine which extends from the acoustic wave inlet 110 along a distance of the labyrinthine channel 108. The acoustic wave path 114 is substantially free of an acoustic wave outlet as the labyrinthine channel 108 ends in a closed end.

[0098] As shown in FIG. 1 B, each metamaterial unit cell 104 is enclosed by walls 118a and 118b on both sides so that there is no acoustic wave outlet or leakage of acoustic wave from the acoustic wave path 114. When the acoustic wave is directed into the acoustic wave path 114, the acoustic wave is required to travel along a long distance created by the acoustic wave path 114, thereby reducing its acoustic energy transmitted. In addition, by directing acoustic wave into the acoustic wave path 114, less acoustic wave is channelled into the first environment. The combined effect is attenuation of acoustic waves entering the first environment.

[0099] Further, the metamaterial unit cells 104 may be spaced apart by spacers 120. The distance, d, of the spacers 120 may be of different lengths but are less than 14 of a width, x, of the metamaterial unit cell 104. An advantage of this configuration maximises the number of metamaterial unit cells that can be placed around the air vent which optimises attenuation of acoustic waves and ventilation. Specifically, a maximum number of metamaterial unit cells may be disposed around the air vent using a minimum number of spacers.

[0100] Referring to FIG. 1A, the single air vent 106 may be characterised by a length, L2 and a width, W2, to define an air vent area, V.

[0101] Referring to FIG. 1A and FIG. 1B, the metamaterial structure 100 may be characterised by a length, Li, a width, W1, and a thickness or depth of T, wherein a total area of the metamaterial structure, C is determined based on Formula (IV):

[0102] C = Lix W1 (IV).

[0103] The metamaterial unit cells 104 and spacers 120 may be arranged in an alternating manner with each other around the air vent 106 such that there is an equal number of acoustic wave inlets 110 disposed on opposing sides facing the air vent 106 along alength L2 or a width W2 of the air vent 106. FIG. 1A shows three metamaterial unit cells 104 disposed along the length L2 and on each opposing side such that respective acoustic wave inlets 110s, 11 Or, 110q on a side and respective acoustic wave inlets 110g, 110h, 110i on an opposite side face the air vent 106 but do not face each other. For example, acoustic wave inlet 110s is diagonally opposite to acoustic wave inlet 110g. Similarly, six metamaterial unit cells 104 are disposed along the width W2 of the air vent 106 and on each opposing side such that respective acoustic wave inlets 110a, 110b, 110c, 110d, 110e, 110f on a side and acoustic wave inlets 110j, 110k, 1101, 110m, 11 On, 11 Op face the air vent 106 but do not face each other.

[0104] Without wishing to be bound by theory, an advantage of having such a configuration enable balanced sound attenuation through acoustic waves entering the metamaterial unit cells 104 in an evenly distributed manner around the air vent 106 resulting in optimal attenuation of acoustic waves.

[0105] According to the present invention, the air vent area, V, should be at least 50% of the total area of the metamaterial structure, C. In other words, a ventilation ratio, VR, of V to C in percentage should be at least 50%, wherein VR = V / C X 100%. Ventilation is necessary for the built environment suitable for human living. An advantage of allowing the air vent area V to be at least 50% of the total area of the metamaterial structure C is to achieve natural ventilation to make the interior environment habitable. Providing a metamaterial structure 100 in a housing for machinery or engines may also allow heat or fumes to dissipate through the air vent 106 of the metamaterial structure 100. As the metamaterial structure 100 enables passive ventilation in the housing for machinery or engines, this enables reduced use of mechanical ventilation means such as exhaust fans for thermal management or dissipation of fumes, thereby reducing energy consumption.

[0106] The area of the acoustic metamaterial portion 102 may be characterised by an area MPA. MPA may be calculated by taking the difference between the area of the metamaterial structure, C, and the air vent area, V. The ratio of the air vent area V, to the area of the acoustic metamaterial portion, MPA, may be from 1 :1 to 2:1 , preferably from 1 :1 to less than 2:1 , more preferably 1:1.The metamaterial unit cells 104 and spacers 120 may be configured to fit within a rail guide 20 of a plurality of rail guides 20 disposed around the air circulation opening 12.

[0107] FIG. 2 is a front schematic view of an array of metamaterial structures 100 of FIG.

[0108] 1A configured and arranged to form a ventilated matrix member 90 according to the present invention. Each of the metamaterial unit cells 104 and spacers 120, 130 may be configured to be releasably connected to each other to form a grid layout across the air circulation opening 12. The spacers 120, 130 may be made of a same material, a different material, or a material similar to the metamaterial structure as long as there are no gaps within the ventilated matrix member 90 except for a total ventilation area. As the ventilated matrix member 90 comprises a plurality of metamaterial structures 100, the aggregate air vent area is defined as the sum of the individual air vent areas (i.e. Vi + V2 +... + Vn ). The metamaterial unit cells 104 and spacers 120, 130 may be connected to each other by mechanical means such as dovetail joints or chemical means such as adhesives or combinations of mechanical and chemical means known to the skilled person.

[0109] FIG. 3 illustrates a partial perspective view of a rail guide 20 for use in a metamaterial structure 100 of FIG. 1A. Specifically, each of the metamaterial unit cells 104 may be characterized by a length, a width and a depth sized to correspond to the internal dimensions of the rail guide 20.

[0110] The rail guide 20 may be a metal channel widely used in both commercial and DIY applications by a person skilled in the art. The metal channel may be made up of a single piece formed to a substantially U or C shape. The metal channel may be made of aluminium, stainless steel or galvanized steel. The metal channel may be configured for cutting to size based on the air circulation opening. The rail guide 20 may be a metal channel comprising a substantially U-shape and comprising a square edge profile 22 and an open side 24 extending along a length of the rail guide 20. The square edge profile 22 makes the channel 20 strong and thereby making it suitable for fabrications and use in construction applications.

[0111] Such rail guides may be obtained from commercially available metal channels, forexample, provided by RS Components or custom made based on the air circulation opening. Other than rail guides, it will be appreciated that any channel / column / strut for receiving components can also be used for receiving the metamaterial unit cells as long as the outer profile and dimensions fit. The metamaterial unit cells 104 may comprise an outer profile corresponding to a shape of the square edge profile 22 of the rail guide 20. The metamaterial unit cells 104 may be received or slotted into the rail guide such that the acoustic wave inlet 110 of each of the metamaterial unit cells 104 faces the air vent 106 through the open side 24 of the rail guide 20.

[0112] FIG. 4A, 4B, 4C shows different views of a metamaterial structure 200 according to the present invention. FIG. 4A is a perspective view of the metamaterial structure 200, FIG. 4B is a front view of the metamaterial structure 200. The metamaterial structure 200 of FIG. 4A - 4C comprises substantially similar features of the metamaterial structure 100 and varies in the number of metamaterial unit cells and wherein the plurality of metamaterial unit cells 204 form a unitary piece.

[0113] The metamaterial structure 200 comprises an acoustic metamaterial portion 202 comprising a plurality of metamaterial unit cells 204, arranged to define a single air vent 206. An advantage of the air vent 206 is to ventilate a first environment. Each of the metamaterial unit cells 204 comprises a single labyrinthine channel 208 having an acoustic wave inlet 210. Similar to the metamaterial structure 100 in FIG. 1Aand 1B, the acoustic wave inlet 210 faces the air vent 206 to receive and channel acoustic waves travelling through the air vent into an acoustic wave path 214. The acoustic wave path 214 is defined by a channel inner surface 212 which extends from the acoustic wave inlet 210 along a distance of the channel. The acoustic wave path 214 is substantially free of an acoustic wave outlet as it ends in a closed end.

[0114] Referring to FIG. 4B, the unitary piece is enclosed by panels or walls, 218a and 218b, on both sides and leaving only the acoustic wave inlet 210 open so that there is a single point of entry for acoustic waves, and there is no acoustic wave outlet or leakage of acoustic wave from the acoustic wave path 214. The mechanism by which acoustic wave is attenuated by the acoustic wave path is substantially similar to that described for FIG. 1Aand 1B.Referring to FIG. 4B, the metamaterial structure 200 is characterized by a length, Ls and a width, W3 and comprises an air vent area, V which is characterized by a length, l_4, and a width, W4. It will be appreciated by a person skilled in the art that a shape and / or dimensions of the metamaterial structure according to the present invention may have any configured according to the size of the air circulation opening, as long as the Metamaterial Ventilation Efficiency is at least 50%.

[0115] The metamaterial structure 200 may be characterized by an area, C, and the acoustic metamaterial portion may be characterized by an area, MPA. MPA may be calculated by taking the difference between the area of the metamaterial structure, C and the air vent area, V. A ratio of the air vent area, V to the area of the acoustic metamaterial portion, MPA, may be from 1:1 to 2:1, preferably 1:1. A technical effect of the ratio of from 1:1 to 2: 1 is that the benefits of air ventilation and sound attenuation may be optimized at levels which enable cooling comfort and minimizing noise in the first environment. When the ratio of V:MPA is greater than 2:1, there is a reduced attenuation effect, albeit having an increased ventilation effect. On the other hand, when V:MPA is less than 1:1, the air vent area is reduced, and consequently a ventilation effect may be reduced.

[0116] The metamaterial unit cells 204 may be spaced apart on the unitary piece by spacers 220. The distance, d, of the spacers may be of different lengths but are less than Vi of a width, x, of the metamaterial unit cell. An advantage of this configuration maximises the number of metamaterial unit cells that can be placed in the unitary piece. As explained above with reference to the metamaterial structure 100 of FIG. 1A, using a maximum number of metamaterial unit cells optimises attenuation of acoustic waves and ventilation. Hence, a maximum number of metamaterial unit cells should be disposed around the periphery of the air circulation opening with a minimum number of spacers.

[0117] The metamaterial structure 200 may further comprise a mounting portion 302 operably attachable to the acoustic metamaterial portion 202 for releasably attaching the metamaterial structure 200 to an interior surface in the first environment. The acoustic metamaterial portion 202 may comprise a stepped outer surface configured to mate with a stepped inner surface of the mounting portion 302 for slidable releasableattachment of the acoustic metamaterial portion 202 to the mounting portion 302. However, it will be appreciated that other well-known mating features for releasably attaching two different parts, such as catches, may also be used, and will not be further described. The mounting portion 302 may comprise a releasable attachment selected from the group comprising of: a snap-fit, clip, flange, peg-spring clipping and combinations thereof.

[0118] The mounting portion may be made of a material selected from the group consisting of plastic, elastomeric material, metal, wood and combinations thereof.

[0119] Other than allowing the metamaterial structure to be releasably attached to the air circulation opening, the releasable attachment may be configured for sealing of the labyrinthine channels to prevent leakage of the acoustic waves in the acoustic wave path from the metamaterial unit cell.

[0120] The releasable attachment may be configured in a variety of ways known to a person skilled in the art to enable the metamaterial structure according to the present invention to be retrofit onto existing ventilation openings such as window grills of existing built environment. For example, the releasable attachment may be configured to allow the metamaterial structure to ride on the structural strength of existing window grills. As such, the metamaterial structure does not need to be made of a structural material for loading in built environments. In particular, the acoustic metamaterial portion may be made from a material selected from the group consisting of: thermoplastic, light weight metals, wood and combinations thereof, preferably the light weight metal is oxidant resistant, preferably aluminium, stainless steel.

[0121] The releasable attachment may be sized and shaped to allow the metamaterial structure to fit into the ventilation opening of an enclosure containing machinery or engines.

[0122] FIG. 5 is an exploded assembly view showing components of a metamaterial structure 400 according to the present invention. FIG. 5 illustrates an exemplary example of a releasable attachment 302, wherein the releasable attachment 302 is a flange 302. The flange 302 may be characterized by a depth corresponding to a thickness of a matrix support to which the metamaterial structure 400 is mounted to. The flange 302 may comprise a profile 304 that is shaped to correspond to an outerprofile of a matrix opening of the matrix support.

[0123] The releasable attachment 302 may be assembled to the acoustic metamaterial portion 202 to form a metamaterial structure 400 as shown in FIG. 5A and FIG. 5B. For example, if the matrix support is characterized by a thickness of 20 mm, the flange 302 may have a depth of 20 mm. As the acoustic metamaterial portion 202 may have a depth of 15 mm, the metamaterial structure 400 may have a total depth of 35mm (20 mm + 15 mm) upon assembly.

[0124] FIG. 6A and 6B are perspective views of the assembled metamaterial structure 400, wherein the mounting portion 302 and the acoustic metamaterial portion are assembled. The acoustic wave inlet 110 faces the airvent 106 to receive and channel acoustic waves travelling through the air vent into an acoustic wave path.

[0125] FIG. 7 is a front view of a matrix support 502 comprising horizontal segments 506 joined to vertical segments 508 to define a grid having a plurality of matrix openings 504. While FIG. 7 depicts a matrix support with forty-nine (49) matrix openings 504, it will be appreciated by a person skilled in the art that the matrix support 502 may be configured with any number of matrix openings 504 based on a desired ventilation. In particular, the matrix support 502 may comprise any number of matrix openings as required, depending on the size of the air circulation opening and size of matrix openings required.

[0126] FIG. 8 is a front view of a ventilated matrix member 600 configured to fit within an air circulation opening 12. The ventilated matrix member 600 comprises the matrix support 502. In this example of the matrix support, there are nine (9) matrix openings 504. The ventilated matrix member 600 may comprise a plurality of metamaterial structures 400 of Figs. 6Aand 6B disposed adjacent to the plurality of matrix openings 504. There are a few configurations for disposing the metamaterial structures 400 adjacent to the matrix openings 504. In one example, the metamaterial structure 500 may be stacked on the matrix support such that the metamaterial structure protrudes into either the first or second environment. In another example, the acoustic metamaterial portion sits within the matrix opening while the releasable attachment of the mounting portion sits on the matrix support.Although one metamaterial structure is shown in FIG. 8, however, it is understood by a person skilled in the art that to obtain a desired acoustic attenuation, metamaterial structures 400 may be disposed in all the matrix openings. The metamaterial structure 400 may be releasably attached to the matrix support 502 via the mounting portion 302.

[0127] Similar to FIG. 1Aand 2B, the metamaterial structure 400 of FIG. 8 comprises an air vent characterised by a length, l_4, and a width, W4, to define an air vent area, V. As the ventilated matrix member comprises a plurality of metamaterial structures, the aggregate air vent area is defined as the sum of the individual air vent areas (i.e. Vi + V2 +... + Vn ). Also similar to FIG. 1A and 2B, the metamaterial structure is characterised by a length, Li, and width, W1, to define a total area of metamaterial structure, C. As the ventilated matrix member comprises a plurality of metamaterial structures affixed on the matrix support, the total ventilation area is defined by the sum of the individual metamaterial structures (i.e. Ci + C2 + ... + CN). According to the present invention, the aggregate air vent area of the individual air vent areas of the plurality of metamaterial structures is at least 50% of a total ventilation area.

[0128] The above illustrates a non-limiting example where the aggregate area of the acoustic metamaterial portion, MPA, is approximately equivalent to the area occupied by the matrix support. In another example, the dimensions of the horizontal segments and vertical segments of the matrix support may be larger such that MPA may be less than the area occupied by the matrix support. In this case, the total ventilation area is characterised by the area defined by length of the air circulation opening, La, and width of the air circulation opening, Wa. Nevertheless, the aggregate air vent area of the individual air vent areas of the plurality of metamaterial structures is still at least 50% of the total ventilation area.

[0129] This formula to calculate area includes the following scenarios:

[0130] Scenario 1: when the aggregate area of the acoustic metamaterial portion, MPA, is equivalent to the area of the matrix support 502 (i.e. the matrix support 502 is fully covered by the acoustic metamaterial portion), the total ventilation area may be defined by the formula

[0131]

[0132] and

[0133] Scenario 2: when the MPA is less than the area of the matrix support 502, wherein the vertical and / or horizontal segments of the matrix support 502 is not fully covered by the acoustic metamaterial portion 202, the total ventilation area may be defined by La X Wa.

[0134] An example of the matrix support is a window grill. The window may be a window of a building, or a window of an enclosure containing machinery, motors or engines.

[0135] The metamaterial structure attenuates sound travelling from the exterior environment to the interior environment or vice versa. To attenuate sound travelling from the exterior environment to the interior environment, the metamaterial structure may be assembled into the ventilation opening by facing the labyrinth units towards the exterior environment, where the acoustic wave path receives the acoustic waves from the exterior environment. This enables the reduction of sound from traffic, trains, airplanes, construction from entering the interior environment.

[0136] To attenuate sound travelling from the interior environment to the exterior environment, the metamaterial structure may be assembled into the ventilation opening by facing the labyrinth units towards the interior environment, where the acoustic wave path receives the acoustic waves from the interior environment. This enables the reduction of sounds from machinery or engines from escaping into the exterior environment.

[0137] The plurality of metamaterial unit cells is configured to attenuate sound frequencies emitted by a transportation means. Transportation means include vehicle transportation by air, road, rail and or sea. Preferably, the transportation means include vehicles.

[0138] As the metamaterial structure is fitted at interfaces between exterior and interior environments, it is expected that the structure will be exposed to the elements of weather and insects. The metamaterial structure may be configured to prevent entry of insects and water. For example, the metamaterial structure may include a permeable substrate provided over each acoustic wave opening, the permeable substrate being permeable to acoustic waves but impermeable to foreign matter suchas water and insects. The permeable substrate may include but is not limited to cling wrap, food wrap, polyethylene wrap, polyvinylidene chloride wrap and / or repellent wool.

[0139] The metamaterial structures may be attached permanently to the matrix support, wherein the matrix support comprising the metamaterial structures is subsequently installed in a ventilation opening. This is particularly useful for allowing ventilation and attenuation of sound in a new building or caged machinery or engine where the desired acoustic frequency and attenuation level does not change.

[0140] Alternatively, the metamaterial structures may be releasably attached to the matrix support. There are a few advantages with releasable attachment. Firstly, it allows for cleaning and maintenance of the metamaterial unit cells of the metamaterial structures. Secondly, it allows for tuning the attenuating frequencies and attenuation levels by attaching metamaterial unit cells having labyrinthine channels configured with different width, height, path length and / or number of labyrinthine channels. This is particularly useful for environments where the frequency of sounds and levels to be attenuated changes. Thirdly, releasable attachment allows for retrofitting the metamaterial structures onto existing ventilation openings and / or matrix support. Existing buildings that may require attenuation of sound in their interior environments may be able to do so by installing the metamaterial structures. Fourth, releasable attachment allows the user to balance the desired sound attenuation effectiveness of the metamaterial to the desired open ventilation.

[0141] The following examples are intended to more fully illustrated the present invention and are not to be construed as limitations of the present invention since many variations thereof are possible without departing from the scope of the present invention.

[0142] TEST EQUIPMENT / MATERIALS

[0143] Equipment and materials used for each of the Example(s) set forth herein are listed in Table 1 below.

[0144] Table 1

[0145]

[0146] Table 2 shows an example of a metamaterial structure according to the present invention.

[0147] Table 2 - Parameters of Inventive Sample A

[0148]

[0149]

[0150] Based on the parameters of the inventive metamaterial structure in the above Table 2, the ratio of the air vent area, V to the area of the acoustic metamaterial portion, C is 1.04 or 51 %, wherein A = 10,000 sqmm, B = 9, 600 sqmm.

[0151] The design of the labyrinthine channel 208 fora metamaterial unit cell for Inventive Sample A is based on the specification of a design described in the prior art WO’ 419 and reproduced in FIG. 9. However, it will be appreciated that the labyrinthine channel 208 can be configured in various ways known to the person skilled in the art as long as the frequency to be attenuated is specified.

[0152] The specifications of the labyrinthine channel design shown in FIG. 9 is reproduced in Table 3 below.

[0153] Table 3

[0154]

[0155] TEST METHOD(S)

[0156] METHOD OF MANUFACTUREInventive Sample A was manufactured according to the following steps:

[0157] (a) creating a CAD drawing based on the details above in Table 2 using SolidWorks (b) using Cura software to convert the CAD drawing from SolidWorks, customise the infill density of 10% and infill pattern as Triangles;

[0158] (c) using a dual nozzle UltiMaker 3D printer and polylactide as the material (d) printing a metamaterial structure comprising an acoustic metamaterial portion having a plurality of metamaterial unit cells (Inventive Sample A).

[0159] To maximise the number of metamaterial unit cells in the metamaterial structure for maximum benefit of sound attenuations, four metamaterial unit cells were printed on each side of the acoustic metamaterial portion, with one metamaterial unit cell flushed to each corner of the frame to define a substantially square shape as shown in FIG. 4B. An advantage is that there is no wastage of metamaterial used in the manufacture of the acoustic metamaterial. An advantage of having a square shape is for ease of manufacture.

[0160] EXAMPLE

[0161] This example illustrates the effectiveness of the metamaterial structure of Inventive Sample Abased on FIG. 4B according to the present invention to attenuate sound.

[0162] To accurately measure the attenuation level and frequency, the metamaterial structures were configured to fit snugly in the ventilation opening. As such, a 1m by 1m window grid (as shown in FIG. 7) was made to fit in the ventilation opening of the Source Room. The metamaterial structures are releasably attached to the matrix support 502 as shown in FIG. 10. The matrix support 502 may be a window grid.

[0163] White noise was used as a source, produced from the Source Room. The sound travelled from the Source Room through the ventilation opening to the Receiving Room where sound pressure levels were collected. Nor 150 was used to collect data in a linear frequency scale, mounted on a tripod and placed in the Receiving Room at four different angles and orientation to simulate revolution of the boom. All openings in the Source Room and the Receiving Room were sealed. Plasticine was also stuffed around the perimeter of the window grid to prevent sound leakage.

[0164] Experiments were conducted to obtain:1) a comparison of attenuation levels between a set up without a metamaterial structure (See FIG. 7) and a set up with metamaterial structures according to the present invention (See FIG. 10);

[0165] 2) Effectiveness of attenuation at a specific frequency.

[0166] FIG. 11 is a plot of attenuation (dB) vs frequencies between 630Hz and 1.6kHz with a set up (without the metamaterial structure) and a set up with the metamaterial structure of Inventive Sample A. It is appreciated that for this specific dimensions of metamaterial structure, attenuation in the frequency range of around 860Hz to 1 kHz is achieved. In particular, peak attenuation of 5.7dB is achieved between around 923Hz and 926Hz. As these frequency ranges mirror that of traffic or transportation, the metamaterial structure according to the present invention effectively attenuates these sounds in the built environment.

[0167] Inventive Sample A has a ventilation ratio, VR, of approximately 51%. This was used as a central benchmark in determining higher and lower configurations. The findings from publication “Kumar, S., Xiang, T. B., & Lee, H. P. (2019), Ventilated acoustic metamaterial window panels for simultaneous noise shielding and air circulation, Applied Acoustics, 159, 107088” indicated optimal trade-offs between acoustic attenuation and ventilation at three key ventilation ratios: 17%, 34% and 45%. Using the attenuation at these ventilation ratios, a fitted polynomial curve representing the theoretical relationship between the VR and attenuation was obtained as shown in FIG. 12, from which sound attenuation can be determined from Ventilation Ratio (VR) according to formula (V) below:

[0168] Sound attenuation = 33.5 - 0.52698VR + 0.001587VR2-(V)

[0169] To facilitate forming a grid comprising a plurality of identical metamaterial structures 200 (with or without a matrix support), each metamaterial structure 200 may comprise a plurality of T-shaped grooves 31 formed in the metamaterial structure 200 and a plurality of T-shaped protrusions 32 projecting from the metamaterial structure 200. This is shown in FIG. 13 which depicts a close-up view of two already connected metamaterial structures 200-1 , 200-2 before their connection with another two already connected metamaterial structures 200-3, 200-4, and in FIG. 14 which shows the fourmetamaterial structures 200 connected together. As can be seen, one of the T-shaped protrusions 32 on the metamaterial structure 200 is configured to securely fit within one of the T-shaped grooves 31 of another unit of the metamaterial structure 200 thereby securely joining one metamaterial structure 200 to the other unit of the metamaterial structure 200.

[0170] Preferably, as shown in FIG. 13, each T-shaped groove 31 has straight interior sides and each T-shaped protrusion 32 has a curved top portion 32T centrally provided on top of a straight post 32P, so that each T-shaped protrusion 32 is elastically deformed when fitted within one of the T-shaped grooves 31 of another unit of the metamaterial structure 200.

[0171] Preferably, the metamaterial structure 200 has a polygonal shape (such as a rectangle which includes a square) and the T-shaped grooves 31 and T-shaped protrusions 32 of the metamaterial structure 200 are provided adjacent the vertices of the polygonal shape, for example, adjacent the exterior corners of the rectangular metamaterial structures 200 shown in FIGS. 13 and 14. In alternative embodiments (not shown), the metamaterial structure may have a hexagonal shape, for example.

[0172] In embodiments where the metamaterial structure 200 has a rectangular shape including that of a square, the T-shaped grooves 31 may be provided on first two adjacent sides S1 of the metamaterial structure 200 and the T-shaped protrusions 32 may be provided on second two adjacent sides S2 of the metamaterial structure 200 as shown in FIG. 15.

[0173] To minimize air flow through any gap between two adjacent and identical metamaterial structures 200 when each metamaterial structure 200 has a rectangular shape, a first two adjacent sides of each metamaterial structure 200 are preferably each provided with a stepped edge 41 and a second two adjacent sides of the metamaterial structure 200 are each provided with an overhanging edge 42. As shown in FIG. 16, one of the stepped edges 41 of one unit of the metamaterial structure 200-1 is configured to mate with one of the overhanging edges 42 of another unit of the metamaterial structure 200-2, thereby minimizing air flow through any possible gap 43 between the two units of metamaterial structures 200.While embodiments and examples of the present invention have been shown and described, it would be obvious to a person skilled in the art that various other changes and modifications can be made without departing from the spirit and scope of the invention. It is therefore intended to cover in the claims, all such changes and modifications that are within the scope of this invention.

[0174] The dimensions and values disclosed herein are not to be understood as being strictly limited to the exact numerical values recited. Instead, unless otherwise specified, each such dimension is intended to mean both the recited value and a functionally equivalent range surrounding that value. For example, a dimension discloses as “40 mm” is intended to mean “about 40 mm”.

Claims

CLAIMS1. A metamaterial structure (100, 200) for ventilation and sound attenuation in a first environment (10) having an air circulation opening, wherein the metamaterial structure (100, 200) comprises:an acoustic metamaterial portion (102, 202) comprising a plurality of metamaterial unit cells (104, 204) arranged to define a single air vent (106, 206);wherein each metamaterial unit cell (104, 204) comprises a labyrinthine channel (108, 208) defining an acoustic wave path (114, 214) having an acoustic wave inlet (110, 210) facing the single air vent (106, 206) and no acoustic wave outlet;wherein at least a part of the metamaterial structure (100, 200) is configured to be releasably disposed in the air circulation opening; andwherein the metamaterial structure has a Metamaterial Ventilation Efficiency of at least 50%, the Metamaterial Ventilation Efficiency determined using formula (I) below:Metamaterial Ventilation Efficiency = [P% x X] / [Y] x100% --(I)whereP is a ventilation constant;X is a floor area of the first environment; andY is a total area of the air circulation opening in the first environment.

2. The metamaterial structure (100, 200) according to claim 1, wherein the metamaterial structure has a total area C and the air vent (106, 206) has an air vent area V determined using formula (II) below:V = Metamaterial Ventilation Efficiency x C --(II)and wherein V is at least 50% of C.

3. The metamaterial structure (100, 200) according to claim 2, wherein the acoustic metamaterial portion has an area MPA, and wherein the ratio of V to MPA ranges from 1:1 to 2:1.

4. The metamaterial structure (100, 200) according to any one of claims 1 to 3, wherein each metamaterial unit cell (104) is spaced apart from its adjacent metamaterialunit cell at a distance (d) of less than half a width of the metamaterial unit cell (104).

5. The metamaterial structure (100, 200) according to any one of claims 1 to 4, wherein each metamaterial unit cell (104, 204) comprises a single labyrinthine channel.

6. The metamaterial structure (200) according to any one of claims 1 to 5, wherein the plurality of metamaterial unit cells (204) are integrally formed as a unitary piece.

7. The metamaterial structure (200) according to claim 6, further comprising a plurality of T-shaped grooves formed in the metamaterial structure and a plurality of T-shaped protrusions projecting from the metamaterial structure, wherein one of the T-shaped protrusions on the metamaterial structure is configured to securely fit within one of the T-shaped grooves of another unit of the metamaterial structure thereby securely joining the metamaterial structure to the other unit of the metamaterial structure.

8. The metamaterial structure (200) according to claim 7, wherein each T-shaped groove has straight interior sides and wherein each T-shaped protrusion has a curved top portion centrally provided on top of a straight post, and wherein each T-shaped groove is configured to be elastically deformed when fitted within one of the T-shaped grooves of another unit of the metamaterial structure.

9. The metamaterial structure (200) according to claim 7 or 8, wherein the metamaterial structure has a polygonal shape and the T-shaped grooves and T-shaped protrusions of the metamaterial structure are provided adjacent the vertices of the polygonal shape.

10. The metamaterial structure (200) according to claim 9, wherein the metamaterial structure has a square shape, and wherein the T-shaped grooves are provided on first two adjacent sides of the metamaterial structure and the T-shaped protrusions are provided on second two adjacent sides of the metamaterial structure.

11. The metamaterial structure (200) according to any one of the preceding claims, wherein the metamaterial structure has a rectangular shape, wherein a first twoadjacent sides of the metamaterial structure are each provided with a stepped edge and wherein a second two adjacent sides of the metamaterial structure are each provided with an overhanging edge, wherein one of the stepped edges of the metamaterial structure is configured to mate with one of the overhanging edges of another unit of the metamaterial structure to minimize air flow through any gap between the metamaterial structure and the other unit of the metamaterial structure.

12. The metamaterial structure (100) according to any one of claims 1 to 5, wherein each metamaterial unit cell is configured to fit within a rail guide disposed on the air circulation opening.

13. The metamaterial structure (100) according to claim 12, wherein the plurality of metamaterial unit cells are configured to be releasably connected to each other to form a grid of the plurality of metamaterial unit cells across the air circulation opening.

14. The metamaterial structure (100, 200) according to any one of the preceding claims, wherein the first environment comprises one of: an interior occupancy space of a built environment, an interior environment of a vehicle, an interior environment of an enclosure containing machinery, and an interior environment of an enclosure containing an engine.

15. The metamaterial structure (100, 200) according to claim 12, wherein the first environment is a room in a building and the air circulation opening is a window in the room.

16. The metamaterial structure (100, 200) according to claim 15, wherein each metamaterial unit cell is configured to attenuate sound emitted by at least one vehicle outside the first environment.

17. The metamaterial structure (100, 200) according to claim 14, wherein the first environment is the interior environment of an enclosure containing machinery or the interior environment of the enclosure containing the engine and wherein each metamaterial unit cell is configured to attenuate sound emitted within the first environment.

18. The metamaterial structure (100, 200) according to any one of the preceding claims, further comprising a permeable substrate provided over each acoustic wave inlet and configured to prevent foreign matter from entering the labyrinthine channel.

19. The metamaterial structure (200) according to claim 6, further comprising a mounting portion (302) operably attachable to the acoustic metamaterial portion (202) for releasably attaching the metamaterial structure (200) to the air circulation opening.

20. The metamaterial structure (200) according to claim 19, wherein the mounting portion (302) has a releasable attachment (304) comprising at least one of: a snap-fit, a clip, a flange, and peg-spring clipping.

21. The metamaterial structure (200) according to claim 19, wherein the acoustic metamaterial portion (202) comprises a stepped outer surface configured to mate with a stepped inner surface of the mounting portion (302) for slidable releasable attachment of the acoustic metamaterial portion (202) to the mounting portion (302).

22. The metamaterial structure (200) according to any one of claims 19 to 21, wherein the mounting portion is made of a material comprising at least one of: plastics material, elastomeric material, metal, and wood.

23. The metamaterial structure according to any one of the preceding claims, wherein sound attenuation can be determined from Ventilation Ratio (VR) according to formula (III) below:Sound attenuation = 33.5 - 0.52698VR + 0.001587VR2-(III)wherein VR = V / C X 100%24. A ventilated matrix assembly (90, 600) configured to fit within an air circulation opening (12) of a first environment for ventilation and sound attenuation in the first environment, the matrix assembly (600) comprising:a plurality of units of the metamaterial structure (100, 200) according to any one of claims 1 to 23;wherein an aggregate air vent area of the individual air vent areas of each unit of the metamaterial structure (100, 200) is determined using formula (IV) below:Aggregate Air Vent Area = Metamaterial Ventilation Efficiency x Total Ventilation Area --(IV),whereinAggregate Air Vent Area = t iviar|d Total Ventilation Area = La x WawhereM is the total number of air ventsLa is a length of the air circulation opening;Wais a length of the air circulation opening;V is one air vent area;wherein the Aggregate Air Vent Area is at least 50% of the Total Ventilation Area.

25. The matrix assembly (600) according to claim 24, further comprising a matrix support (502) comprising horizontal segments joined to vertical segments to define a grid having a plurality of matrix openings, wherein the plurality of units of metamaterial structures (100, 200) are disposed adjacent to the plurality of matrix openings, wherein the matrix support (502) is a window grill.

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