A dual-functional five-mode metamaterial structure with water-like and topological transmission characteristics

Abstract

The present invention discloses a dual-functional five-mode metamaterial structure with water-like and topological transmission characteristics, including a lattice unit. The lattice unit includes six metal arms, and an additional counterweight is provided on each of the six metal arms, with a total of six additional counterweights. The six additional counterweights are all in the shape of equilateral triangles, and are respectively four first additional counterweights, one second additional counterweight, and one third additional counterweight. The side length of the first additional counterweight is w, the side length of the second additional counterweight is w - dh, and the side length of the third additional counterweight is w + dh, where dh represents a set constant. By introducing structural perturbations in the PM, the present invention can open the Dirac point degeneracy at the K point to generate topological band inversion. By calculating the projected band structure of a supercell composed of two PMs with different topological valley phases, topological edge states are obtained, which have good robustness to defects such as bending and cavities.

Description

Technical Field

[0001] The present invention relates to the technical field of glass slide clamping mechanisms, and particularly relates to a dual-functional five-mode metamaterial structure with water-like and topological transmission characteristics. Background Art

[0002] In recent years, the emergence of acoustic metamaterials and phononic crystals has given a new life to the acoustic discipline and greatly promoted the development and progress of acoustic materials. Through special processing and combination designs of traditional materials, they have acquired extraordinary physical properties that natural materials do not possess. For example, special equivalent physical properties can be achieved in macroscopic systems: anisotropy, negative density, negative bulk modulus, negative refraction, etc. They have a unique "sub-wavelength" structure and can effectively control the transmission process of low-frequency sound waves in a small size, thus quickly becoming a research hotspot in the fields of modern acoustics and materials science.

[0003] As a new type of artificial acoustic metamaterial, the concept of five-mode metamaterial was initially proposed by Milton and Cherkaev in 1995. Since 5 out of 6 eigenvalues of its elastic coefficient matrix are zero, it is called five-mode metamaterial. Five-mode metamaterial has the unique property of having fluid properties in solid form and can achieve low scattering loss at the interface between fluid and five-mode metamaterial. When used underwater, it can diffract the detected sound waves within the single-mode frequency range, meaning that the five-mode metamaterial has an underwater acoustic stealth function. Subsequently, Muamer Kadic et al. improved the ideal structure proposed by Milton et al. to achieve small-size mutual contact between two cones, processed and fabricated the first five-mode metamaterial physical object, and analyzed the elastic properties of the five-mode metamaterial using numerical calculations, verifying that the five-mode metamaterial has good fluid characteristics. In 2015, our research group at Xi'an Jiaotong University proposed a narrow-diameter asymmetric double-cone five-mode metamaterial structure. The research results show that the narrow-diameter asymmetric double-cone five-mode metamaterial not only has a single-mode region that can maintain the transmission of compression waves while suppressing the transmission of shear waves, but also obtains a complete phononic bandgap. This means that this five-mode metamaterial can not only achieve the "fluid" property of the original five-mode metamaterial within the single-mode frequency range, but also prohibit the transmission of elastic waves in the complete phononic bandgap region. Subsequently, PM has also been applied to fields such as underwater acoustic lenses and underwater carpet cloaks.

[0004] On the other hand, the emergence of the quantum Hall effect, quantum spin Hall effect, and quantum valley Hall effect in condensed matter physical systems has greatly promoted the development and progress of basic disciplines and frontier technology fields. A topological insulator is a material that is insulating inside but allows charge movement at the interface. Inside a topological insulator, the electronic band structure is similar to that of a conventional insulator, and its Fermi level lies between the conduction band and the valence band. However, there are some special quantum states on the surface of a topological insulator. These quantum states are located within the bandgap of the bulk band structure and can conduct electricity. Its topologically protected edge state mode brings feasibility to the realization and design of disruptive materials and devices that break through the limits of traditional technologies, making it potentially applicable in fields such as spintronics and quantum computing. Currently, the research on topologically protected edge states has been extended to photonics and phononics. The emergence of topological phononic crystals has completely subverted people's understanding of traditional acoustic materials and quickly become a research hotspot in the fields of materials science and information engineering technology. In 2014, Romain Fleury et al. proposed a method to break time-reversal symmetry using an annular flow velocity field and constructed an acoustic circulator. This discovery provided the possibility to achieve the acoustic analogue of the quantum Hall effect. The characteristics of the quantum Hall phase are that electrons are confined in the bulk but transported unidirectionally along the boundary. The breaking of time-reversal symmetry makes the transport of the boundary state chiral, so even if there are disorders and defects on the boundary, the boundary state will not produce backscattering. In addition to the quantum Hall effect that requires breaking time-reversal symmetry, the state - quantum spin Hall effect that does not require breaking time-reversal symmetry has also been studied. Cheng He et al. demonstrated in detail how the acoustic analogue of the quantum spin Hall effect based on accidental degeneracy is realized in a honeycomb lattice composed of steel rods in air. By reducing the filling rate of the steel rods in air, two pairs of dipole modes and quadrupole modes separated by a bandgap will shift in frequency and exchange positions (i.e., the so-called band inversion). Between them, there is a point where the bandgap closes, and the two pairs of particles accidentally come into contact to form a doubly degenerate Dirac cone (essentially different from the zone folding mechanism). This process of bandgap opening - closing - reopening leads to a topological transition from a topologically trivial state to a topologically non-trivial state, and the transition point is the double Dirac point. The discrete valley degree of freedom, as a label for the quantum state of energy extremum in momentum space, has received increasing attention because of its role as a novel spin-like information carrier. Subsequently, theoretical predictions and experimental observations of the valley Hall effect and the corresponding valley-protected edge states were carried out in two-dimensional acoustic systems. Lu et al. first introduced the concept of valley states into acoustic phononic crystals. In a two-dimensional waveguide, the scatterers in the hexagonal primitive cell of the phononic crystal are triangular rods, and its symmetry can be characterized by the rotation angle. As the rotation angle changes, the Dirac point is opened, and the edge state caused by the quantum valley Hall effect is also very robust to bending defects. Subsequently, different structural types of topological metamaterials have also been studied.

[0005] However, current research on the topological properties of phononic crystals mainly focuses on the field of air acoustics, and there is a relative lack of research on topological states in underwater elastic wave systems, which to a certain extent limits the practical application scope of topological acoustic metamaterials. In addition, using the topological protected acoustic properties of phononic crystals to regulate elastic wave transmission has important theoretical and practical guiding significance in underwater acoustic fields such as acoustic cloaking and underwater acoustic lenses. Summary of the Invention

[0006] Aiming at these above-mentioned drawbacks, the present invention provides a dual-functional five-mode metamaterial structure with water-like and topological transmission characteristics. By introducing structural perturbations in the PM, the Dirac point degeneracy at the K point can be opened to generate topological band inversion. By calculating the projected band structure of the supercell composed of two PMs with different topological valley phases, topological edge states are obtained, which have good robustness against defects such as bending and cavities. In addition, the supercell also has water-like acoustic properties in a relatively wide frequency range. When used as an underwater waveguide, it will have both good transmission efficiency and acoustic cloaking performance. The dual-functional metamaterial proposed by the present invention provides theoretical guidance for designing underwater stealth acoustic waveguides.

[0007] In order to achieve the above object, the present invention provides a dual-functional five-mode metamaterial structure with water-like and topological transmission characteristics, and the technical solution adopted is as follows:

[0008] A dual-functional five-mode metamaterial structure with water-like and topological transmission characteristics, including a lattice unit. The lattice unit includes six metal arms, and an additional counterweight is provided on each of the six metal arms, with a total of six additional counterweights. The six additional counterweights are all equilateral triangle shapes, and are respectively four first additional counterweights, one second additional counterweight, and one third additional counterweight. The side length of the first additional counterweight is w, the side length of the second additional counterweight is w - dh, and the side length of the third additional counterweight is w + dh, where dh represents a set constant.

[0009] Further, the value of dh is -0.5 mm.

[0010] Further, the value of dh is 0.5 mm.

[0011] Further, a plurality of the lattice units are provided, and in the plurality of lattice units, the value of dh in at least one lattice unit is -0.5 mm and the value of dh in at least one lattice unit is 0.5 mm.

[0012] Further, the interior of the lattice unit is provided with a hollow, and the hollow is filled with air.

[0013] Further, the lattice unit is a regular hexagonal honeycomb shape.

[0014] Further, the side length of the lattice unit is 6 mm, and the width is 0.126 mm.

[0015] Further, the value of the side length w of the first additional counterweight is 2.17 mm.

[0016] Further, the metal arm is made of titanium metal.

[0017] Compared with the prior art, the present invention has at least the following beneficial effects:

[0018] 1) By changing dh, the present invention can open the Dirac cone at the K-point and achieve the inversion of the energy band.

[0019] 2) Two lattice unit structures constructed based on different dh values form a topological phononic crystal, and numerical simulations are carried out on the topologically protected boundary sound transmission. It is found that its energy is mainly concentrated at the interface between the two structures and decays exponentially into the body. This boundary state has good robustness to defects such as bending and cavities.

[0020] 3) The present invention has water-like characteristics in a relatively wide frequency range. When used underwater, it can have good acoustic stealth performance from 1 kHz to 25 kHz and acoustic topological transmission characteristics from 74.4 kHz to 84.4 kHz. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for the description of the specific embodiments or the prior art. In all the drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, the elements or parts do not necessarily draw to actual scale.

[0022] Figure 1 Shows the structure and energy band diagram of a slide box of a dual-functional five-mode metamaterial structure with water-like and topological transmission characteristics according to an embodiment of the present invention, where (a) is a schematic diagram of the PM structure, and (b) is the energy band diagram of the S2 structure.

[0023] Figure 2 Shows the energy band diagram and mechanical energy flow distribution diagram of the structure according to an embodiment of the present invention, where (a) is the energy band diagram of the S1 structure, (b) is the energy band diagram of the S3 structure, and (c) is the mechanical energy flow distribution diagram of the valley state at the K point.

[0024] Figure 3 Shows the schematic diagram of the evolution of the eigenfrequency corresponding to the valley state at K with dh according to an embodiment of the present invention.

[0025] Figure 4Shows a schematic diagram of the supercell structure, projected energy band, supercell valley edge state and its displacement amplitude distribution according to an embodiment of the present invention, where (a) is a schematic diagram of the supercell structure, (b) is a projected energy band diagram, and (c) is the supercell valley edge state and its displacement amplitude distribution.

[0026] Figure 5 Shows the experimental results diagram of the topological refraction and robust transmission of the valley edge state according to an embodiment of the present invention, where (a) is a schematic diagram of the bent - angle defect supercell composed of S1 - S3; (b) is a schematic diagram of the edge - state displacement field excited by a point source with a frequency of 80 kHz; (c) is a schematic diagram of the displacement field distribution of the edge state after introducing a cavity, and the inset part is an enlarged view of the interface structure, and the circle is the cavity part.

[0027] Figure 6 Shows the full - wave simulation of the PMW structure under the action of a 6 kHz plane wave according to an embodiment of the present invention, where (a) is the contour map of the total sound pressure field of the PMW at 6 kHz, and (b) is the TSCS spectrum of the PMW.

[0028] In the figure, 100 is a lattice unit, 101 is a metal arm, 102 is an additional counterweight, 1021 is the first additional counterweight, 1022 is the second additional counterweight, 1023 is the third additional counterweight, and 103 is a hollow. Detailed implementation manners

[0029] The following uses specific specific examples to illustrate the implementation manners of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific implementation manners, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that, without conflict, the following embodiments and the features in the embodiments can be combined with each other.

[0030] In the description of the present invention, unless otherwise stated, "a plurality of" means two or more; the terms "upper", "lower", "left", "right", "inner", "outer", "front end", "rear end", "head", "tail", etc. indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation of the present invention. In addition, the terms "first", "second", "third", etc. are only used for descriptive purposes and cannot be understood as indicating or implying relative importance.

[0031] In the description of the present invention, it should be noted that unless otherwise clearly specified and defined, the terms "connected" and "connected" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be directly connected or indirectly connected through an intermediate medium. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0032] The following will further describe in detail the specific embodiments of the present invention with reference to the accompanying drawings and embodiments.

[0033] Embodiment 1: A dual-functional five-mode metamaterial structure with water-like and topological transmission characteristics

[0034] The embodiment of the present invention provides a dual-functional five-mode metamaterial structure with water-like and topological transmission characteristics, as Figure 1 shown. The dual-functional five-mode metamaterial structure with water-like and topological transmission characteristics includes a lattice unit 100. The lattice unit 100 includes six metal arms 101, and an additional weight 102 is respectively arranged on each of the six metal arms 101. There are a total of six additional weights 102. The six additional weights 102 are all equilateral triangle shapes, and are respectively four first additional weights 1021, one second additional weight 1022, and one third additional weight 1023. The side length of the first additional weight 1021 is w, the side length of the second additional weight 1022 is w - dh, and the side length of the third additional weight 1023 is w + dh, where dh represents a set constant.

[0035] In this embodiment, multiple lattice units 100 can be set. The multiple lattice units 100 can be connected in the manner shown in (a) in Figure 1 . The lattice unit 100 is a regular hexagonal honeycomb lattice composed of six metal arms 101 (the side length a = 6 mm and the width t = 0.126 mm). The six additional weights 102 (the equilateral triangle regions with side lengths w, w1, and w2 surrounded by dotted lines in the figure) are located at the vertices of the hexagon. Among them, w = 2.17 mm, w1 = w - dh, w2 = w + dh, and the lattice constant a s = sqrt(3)*a. Figure 1 The gray part in Ti is titanium metal (density r 3 , Young's modulus E Ti = 108 GPa, Poisson's ratio c Ti = 0.34), and the internal white hollow 103 is filled with air (density r air = 1.21 kg / m 3 , sound speed c air= 343 m / s). The density and the sound speed of the background water are ρ water = 1000 kg / m 3 and c water = 1500 m / s. The solid mechanics module of COMSOL Multiphysics is used to calculate the band structure and displacement field distribution of the PM. When solving the bulk (edge) band dispersion relation, Floquet periodic boundary conditions are applied on the periodic surface of the unit cell (supercell), and obtained by scanning the first Brillouin zone. When dh = 0, the corresponding PM structure is denoted as S2, which satisfies the spatial C 3v symmetry. At this time, there is band degeneracy at the high-symmetry points. As shown in Figure 1 (b), there is a Dirac cone with a frequency of 79.0 kHz at the K point in the Brillouin zone.

[0036] Example 2: Valley Band Inversion Experiment

[0037] Based on the material structure described in Example 1 and the topological defect theory, two different PM structures, denoted as S1 and S3, are studied by changing dh. Specifically, S1 corresponds to dh = -0.5 mm, and S3 corresponds to dh = 0.5 mm. The dispersion curves corresponding to the above two structures are shown in Figure 2 (a) and (b), respectively. It can be clearly seen from the figure that due to the lack of mirror symmetry, the Dirac cone in the band structure is opened to form a complete bandgap, and the corresponding frequency range is from 73.7 kHz to 83.7 kHz. A pair of extreme points, that is, valley states, are formed on both sides of the bandgap. Since the K and K' points can be converted by time-reversal operation, the displacement field distribution corresponding to the valley state at the K point can be mainly studied. After the bandgap is opened, two pairs of inequivalent valley states are generated at the K point, and the total displacement field distributions corresponding to the eigenmodes of the four valley states are shown in Figure 2 (c). Similar to the valley states in the electronic system, the valley states in the elastic solid also have chirality, and this valley vortex property is usually characterized by the time-averaged mechanical energy flow distribution at the valley, that is, I j = -s ij v j , where s ij and v j represent the stress tensor and the velocity vector, respectively. According to the energy flow arrows in the figure, it can be observed that the two structures have different vortex energy flow directions at the K valley point, which are marked as K + and K - , respectively, where "+" and "-" represent the counterclockwise and clockwise rotation of the energy flow, respectively. The vortex chirality of the valley states corresponding to the K point in the two structures is reversed. Therefore, the above results indicate that during the change from the S1 to the S3 structure, topological band inversion and topological phase transition occur.

[0038] Figure 3 shows the evolution of the eigenfrequency corresponding to the valley state at the high-symmetry point K in the first Brillouin zone of the PM with respect to dh, where the red and blue curves represent the edge states of the bandgap. It can be clearly seen from the figure that as the value of dh increases, the bandgap experiences a process of closing and reopening, and the vortex characteristics are exchanged at dh = 0 mm. The above band inversion means that an elastic valley Hall phase transition occurs during the geometric change, forming two PMs with different topological properties, and the regions with different topological properties are distinguished by different colors. In addition, different valley Hall phases can also be characterized by the effective mass . It can be observed from the figure that when -2 mm < dh < 0 mm, the valley states K + and K - are located above and below the bandgap respectively, that is the corresponding effective mass m > 0. When 0 mm < dh < 2 mm, the valley state K + is located below K - , that is the corresponding effective mass m < 0. Therefore, according to the band inversion of the valley state, the acoustic valley Hall phase transition can be characterized. According to the bulk-boundary correspondence, there will be topological valley projection boundary modes on the boundaries with opposite signs of the equivalent mass at both ends.

[0039] Example 3: Valley topological edge state experiment

[0040] To verify the existence of topological valley edge states of elastic waves in the PM, a ribbon supercell composed of two structures, S1 and S3, was constructed, as shown in Figure 4 (a). Bloch continuous periodic boundary conditions were applied to the left and right boundaries of the supercell, and the projected band structure of the supercell along the G-K direction was calculated, as shown in Figure 4 (b). An additional mode with a frequency of 74.4 kHz - 84.4 kHz appears in the bandgap range, which is represented by a red solid line. This mode corresponds to the edge state mode of the S1-S3 phase structure, and the light red region in the band diagram is the edge state region. Figure 4 (c) shows the in-plane total displacement distribution corresponding to the two topological edge state eigenmodes when the wave vector is k x = 0.8′p / a s . It can be clearly seen that the displacement energy is mainly concentrated at the interface between the two structures and decays exponentially into the body, indicating that the topological edge state can be well localized on the interface, confirming the existence of the interface state. In addition, from the normalized displacement amplitude distribution along the y direction in the figure, it can be seen that the full width at half maximum (FWHM) of the elastic energy bound at the interface is about 1.9a s , indicating that the topological edge state can be well localized on the interface.

[0041] Example 4: Topological refraction and robust transmission experiments of valley edge states

[0042] To verify the existence of topologically protected edge states at the interface composed of different valley topological phases, in this embodiment, a topologically protected waveguide composed of two different valley Hall phases PM of S1 and S3 is constructed, denoted as structure PMW. Bend defects and cavity defects are respectively introduced, as Figure 5 shown. The dashed line represents the interface between the two phases. When the excitation frequency f = 80 kHz, the displacement field is as Figure 5 shown in (b). It can be found that the waves excited in the curved interface can all propagate along the path of the interface. Even after passing through two bends, there is no obvious reflection. Next, a cavity defect is introduced at the interface to further explore the anti-scattering ability of the edge state to different defects, as Figure 5 shown in (c). The transmission of the edge state at a frequency of 80 kHz is numerically simulated. It can be seen that there is no strong reflection at the defect position (the inset part), and the edge state is hardly affected by the cavity during the transmission process. The above exploration finds that the valley topological edge state can well suppress the scattering caused by bend defects and cavity defects, and no backscattering will occur even when encountering defects during the edge state transport. Therefore, this valley topological protected interface waveguide has a higher transmission efficiency than the traditional defect waveguide.

[0043] Example 5: Experiment on the fluid characteristics of a topological waveguide

[0044] When a topological waveguide is used underwater, in order to improve its concealment, its fluid characteristics are analyzed. Theoretical analysis shows that the width t of the unit cell mainly controls the equivalent speed of the five-mode structure, and the side length w mainly controls its equivalent density, and the equivalent density is approximately equal to the average bulk density in the long-wave limit. In the band diagrams of the S1 and S3 structures, the branches 1 and 2 emerging from G are the dispersion curves of the "acoustic" shear wave and the compression wave respectively, and the slopes in the long-wave limit are the corresponding phase velocities. The blue dashed line represents the dispersion curve of water. Note that the dispersion curves of the S1 and S3 structures deviate from the dispersion curve of water only when f > 25 kHz. In addition, their equivalent densities are 1010 kg / m 3 . Therefore, the acoustic waveguide composed of these two structures (such as the PMW structure in (a) Figure 5 ) is similar to water in a wide frequency range and has good concealment when used for underwater acoustic transmission.

[0045] Figure 6 shows the full-wave simulation of the PMW structure under the action of a 6 kHz plane wave. From Figure 6As can be clearly seen in (a), the presence of PMW has little effect on the propagation mode of sound waves in water, indicating that the acoustic scattering of PMW is quite small. In other words, PMW exhibits acoustic properties consistent with water. The total scattering cross-section (TSCS), defined as the ratio of the scattered power in all directions to the incident power of the plane wave, is used to quantify wave scattering, as Figure 6 shown in (b). Obviously, the TSCS of PMW is very small (almost zero) over the entire frequency range from 1 kHz to 25 kHz.

[0046] From the above analysis, it can be seen that when the PWM structure is used in an underwater acoustic waveguide, it can have water-like properties in the frequency range of 1 kHz to 25 kHz, with good concealment. It has acoustic topological transmission characteristics at 74.4 kHz - 84.4 kHz, with excellent properties such as immune to structural defects, backscattering suppression, and low-loss unidirectional transmission.

[0047] In summary, the present invention has developed a PM structure with water-like characteristics. First, by changing dh, the Dirac cone at the K-point can be opened, realizing the inversion of the energy band. Then, based on the S1 and S3 structures, a topological phononic crystal is constructed, and numerical simulations of the topologically protected edge acoustic transmission are carried out. It is found that its energy is mainly concentrated at the interface between the two structures and decays exponentially into the body. And it is found that this edge state has good robustness to defects such as bending and cavities. Finally, the constructed PMW waveguide is studied, which has water-like characteristics in a wide frequency range. Therefore, when PMW is used underwater, it can have good acoustic stealth performance in the frequency range of 1 kHz to 25 kHz and acoustic topological transmission characteristics at 74.4 kHz - 84.4 kHz. The present invention provides the possibility for designing an underwater acoustic stealth waveguide and provides more ideas for the regulation of sound waves / elastic waves.

[0048] The above embodiments are only used to illustrate the present invention and are not intended to limit the present invention. Those of ordinary skill in the relevant technical fields can still make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, all equivalent technical solutions also belong to the scope of the present invention. The patent protection scope of the present invention shall be defined by the claims.

Claims

1. A dual-functional five-mode metamaterial structure with water-like and topological transmission characteristics, characterized in that It includes lattice units, and each lattice unit includes six metal arms. An additional counterweight is respectively arranged on each of the six metal arms, and there are six additional counterweights in total. The six additional counterweights are all in the shape of equilateral triangles, and are respectively four first additional counterweights, one second additional counterweight and one third additional counterweight. The side length of the first additional counterweight is w, the side length of the second additional counterweight is w - dh, and the side length of the third additional counterweight is w + dh, where dh represents a set constant; A plurality of the lattice units are provided, and in the plurality of lattice units, the value of dh in at least one lattice unit is -0.5 mm and the value of dh in at least one lattice unit is 0.5 mm; The lattice unit is in the shape of a regular hexagonal honeycomb; The side length of the lattice unit is 6 mm and the width is 0.126 mm; The value of the side length w of the first additional counterweight is 2.17 mm.

2. The dual-functional five-mode metamaterial structure with water-like and topological transmission characteristics as claimed in claim 1, wherein The value of dh is -0.5 mm.

3. The dual-functional five-mode metamaterial structure with water-like and topological transmission characteristics as claimed in claim 1, wherein The value of dh is 0.5 mm.

4. The dual-functional five-mode metamaterial structure with water-like and topological transmission characteristics as described in claim 1, wherein A hollow is arranged inside the lattice unit, and the hollow is filled with air.

5. The dual-functional five-mode metamaterial structure with water-like and topological transmission characteristics according to claim 1, characterized in that, The metal arm is made of titanium metal.

Images