A five-mode material structure with an asymmetric single cone

Abstract

The present invention relates to a five-mode material structure with an asymmetric single cone. The five-mode material structure is composed of a periodic arrangement of multiple identical two-dimensional unit cell structures. Each unit cell structure is composed of seven node structures and six single cone structures. The node structure located inside the unit cell structure is a circular solid, with the center of the circle located at the intersection point of the single cone structures. The outer node structure is a sector, with the center of the circle located at the end point of the bottom edge of the single cone. The circular node structure inside the unit cell structure is composed of three sector node structures. A local connection structure is formed between the sector node and the central circular node through two single cone structures and the node circle at their intersection point. The present invention has good five-mode characteristics. It not only has a single-mode transmission region with shear wave suppression and compression wave propagation, but also has a phonon bandgap, which can prevent the propagation of all sound waves within the bandgap frequency range. On the basis of inheriting the width of the single-mode transmission region of the traditional double-cone unit cell configuration, it has a bandgap with a lower frequency and a larger bandwidth.

Description

Technical Field

[0001] The present invention relates to the field of acoustic wave regulation of five-mode materials, and more specifically, to a five-mode material structure with an asymmetric single cone. Background Art

[0002] Milton and Cherkaev first proposed the concept of five-mode metamaterials in 1995. For the artificial periodic structure of solids, through the design of structural units, the overall equivalent elastic characteristics can be made such that in the six-dimensional stress space, only the eigenvalue of the volume compression mode is non-zero, while the other five eigenvalues corresponding to shear are zero. Such a solid structure as a whole exhibits the mechanical characteristics of traditional fluids, has an artificially adjustable bulk modulus, can achieve arbitrary regulation of acoustic waves, and the acoustic metamaterial formed by the periodic arrangement of its structural units can achieve perfect matching with water. The five-mode characteristics of the designed five-mode material can be characterized by the five-mode figure of merit (FOM = B / G). The larger the figure of merit, the more difficult it is to couple the compression wave and the shear wave. When the five-mode figure of merit is greater than 1000, the designed five-mode material structure has better five-mode characteristics.

[0003] Currently, the unit cell configuration of the five-mode material structure is mostly a symmetric double-cone configuration. The phonon bandgap of the five-mode material is located at a relatively high frequency, with poor bandwidth performance, and the conical structures are in point contact, resulting in poor structural stability. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a five-mode material structure with an asymmetric single cone, which can achieve better acoustic wave regulation ability and structural stability.

[0005] The technical solution adopted by the present invention to solve its technical problems is: to construct a five-mode material structure with an asymmetric single cone, the five-mode material structure is composed of a plurality of identical two-dimensional unit cell structures arranged periodically; each unit cell structure is composed of seven node structures and six single cone structures; the node structure located inside the unit cell structure is a circular solid, the center of the circle is located at the intersection point of the single cone structures, and the outer node structure is a sector, the center of the circle is located at the end point of the base of the single cone; the circular node structure inside the unit cell structure is composed of three sector node structures; each two single cone structures and the node circle at their intersection point and the sector node structure on the outside form a local structure that is rotationally symmetric about the center of the circle of the inner central node, and the rotation angle between the local structures is 120°; the sector node and the central circular node are connected by a local connection structure formed by two single cone structures and the node circle at their intersection point; in the local connection structure, each two single cones with different axial lengths form an asymmetric single cone.

[0006] According to the above solution, the asymmetric single cone is each two single cones connected by a node circle, and the single cone structure is asymmetric.

[0007] According to the above solution, the asymmetric single cone is composed of two single cones with unequal axial lengths, and the base angle of the single cone is less than 60°.

[0008] According to the above solution, the single cone structure and the node circle connecting two asymmetric single cones are filled with TC4 titanium alloy, and other node structures are filled with vulcanized rubber.

[0009] Thus, the present invention provides a five-mode material structure with asymmetric single cones, which is composed of periodic arrangements of unit cell structures. Each unit cell structure is composed of seven node structures and six single cone structures; the single cone structure forms a closed figure by three straight edges. Every two single cone structures connected by a node circle are asymmetric. The single cone is composed of two single cones with unequal axial lengths, and the base angle of the single cone is less than 60°. For the asymmetric single cone, one can take the end point of the base angle of a single cone as the base point, rotate it 120° around the base point to obtain another single cone, and change the axial length of one of the single cones to obtain the asymmetric single cone structure in the unit cell; the unit cell structure is replicated horizontally and staggered vertically to obtain the five-mode material structure.

[0010] Implementing the five-mode material structure with asymmetric single cones of the present invention has the following beneficial effects:

[0011] The present invention has good five-mode characteristics, and its five-mode figure of merit FOM > 10 3 , and can regulate sound waves like an ideal five-mode material; replacing the traditional double cone structure with a single cone structure reduces the overall structure mass; introducing asymmetric single cones and the node circle structure between single cones increases the number of adjustable parameters; replacing the point contact between conical structures with node structures improves the structural stability; in addition, this five-mode material structure has a wider phonon band gap and can block the propagation of all sound waves within the band gap frequency range. Brief Description of the Drawings

[0012] The present invention will be further described below in conjunction with the drawings and embodiments. In the drawings:

[0013] Figure 1 is a schematic diagram of the unit cell structure of the five-mode material structure with asymmetric single cones of the present invention;

[0014] Figure 2 is a partial view of the asymmetric single cone of the present invention and the node circle at its intersection, used for the establishment of the overall unit cell model;

[0015] Figure 3 is a partially enlarged schematic diagram of the circular node structure of the unit cell of the present invention;

[0016] Figure 4 is a schematic diagram of the five-mode material structure of the present invention;

[0017] Figure 5Schematic diagram of the simplified Brillouin of the present invention;

[0018] Figure 6 Phonon band diagram of the unit cell of the present invention. Detailed implementation manners

[0019] For a clearer understanding of the technical features, objectives, and effects of the present invention, the detailed implementation manners of the present invention will now be described in detail with reference to the accompanying drawings.

[0020] As Figure 1 shown is an embodiment of the unit cell of the five-mode material structure introducing an asymmetric single cone. The embodiment is a planar structure. Those skilled in the art can also change the base angle of the conical structure according to actual needs, which all fall within the protection scope of the present invention.

[0021] From Figure 1 it can be seen that for an asymmetric single cone, three straight lines can be taken to enclose a closed triangle to form a single cone, and it is ensured that the base angle of the single cone is less than 60°, then a single cone structure of the unit cell can be obtained. Then, taking the endpoint on the base of the single cone as the rotation center and the rotation angle as 120°, another single cone is obtained by rotational replication. By changing the axial length of this single cone, every two asymmetric single cone structures are connected by a node circle. Then, taking the endpoint of a single cone except the node circle as the rotation center and rotating 120° twice for rotational replication, the unit cell structure of the five-mode material structure is obtained. The unit cell structure of the five-mode material in the embodiment is replicated along the horizontal direction and staggered along the vertical direction, and the periodic multi-cell structure under the embodiment is obtained. Thus, the five-mode material structure with an asymmetric single cone includes multiple unit cell structures, and each unit cell structure is composed of seven node structures and six single cone structures; the node structure inside the unit cell is a circular solid, and the center of the circle is at the intersection of the single cone structures. The outer node structure is a sector, and the center of the circle is at the endpoint of the base of the single cone; the circular node structure inside the unit cell can be regarded as composed of three sector node structures; the local part formed by every two single cone structures, the node circle at their intersection, and the outer sector node structure is rotationally symmetric about the center of the inner central node circle, and the rotation angle between the local structures is 120°; the sector node and the central circular node are connected by the local part formed by two single cone structures and the node circle at their intersection; every two single cones with different axial lengths in the local structure form an asymmetric single cone; each unit cell structure is replicated in an array along the horizontal direction and staggered along the vertical direction to obtain the five-mode material structure.

[0022] Taking the five-mode material structure introducing an asymmetric axial length single cone as an example for specific illustration, as Figure 1 、 2 、3, and 4 show the five-mode material structure introducing an asymmetric axial length single cone of the present invention, including multiple unit cell structures (such as Figure 1) Each unit cell structure is composed of seven node structures 2, 5 and six single-cone structures 1. Each single-cone structure is composed of three straight edges 4, and the bottom angle of the single cone is less than 60°, thus forming a single-cone structure 1; the circular node 3 can be regarded as composed of three sector nodes 5; the local structure formed by every two single-cone structures 1, the node circle 2 at their intersection and the outer sector node 5 is rotationally symmetric about the center of the circular node 3, and the rotation angle between local structures is 120°; the sector node 5 and the central circular node 3 are connected locally by the node circle 2 formed by two single-cone structures 1 at their intersection; in the local structure, every two single-cones 1 with different axial lengths form an asymmetric single-cone;

[0023] Multiple unit cell structures are connected to each other horizontally through the sector nodes 5, so as to extend horizontally to form a continuous unit layer. Multiple unit layers are also connected to each other vertically in the same way that three sector nodes 5 form a circular node 3 through the sector nodes 5, and so on, thus forming a multi-layer periodically arranged five-mode material structure.

[0024] Select TC4 titanium alloy as the filling material for the single-cone structure 1 and the node circle 2, and vulcanized rubber as the filling material for the circular node 3 and the sector node 5.

[0025] As Figure 2 shown, two single-cones with single-cone axial lengths L of 1.8 mm and 1.4 mm are taken to form the asymmetric single-cone of the five-mode material unit cell of the present invention. The bottom side length of the single-cone structure is D = 5 mm, the radius of the node circle of the unit cell structure is R = 1 mm, the diameter of the circular node is d = 0.6 mm, and the point contact between the conical structures is replaced by a node structure, improving the stability of the structure. Figure 5 It is a schematic diagram of the reduced Brillouin zone of the five-mode material structure unit cell. By using simulation software to set the wave vector value range and going around the boundary of the irreducible Brillouin zone once, the phonon band diagram of this unit cell structure can be obtained, as Figure 6 shown. The band diagram includes 7 dispersion curves. The horizontal axis is the path direction of the wave vector around the irreducible Brillouin zone passing through 3 high-symmetry points in the reciprocal lattice vector space, and the vertical axis is the characteristic frequency. The gray area with frequencies in the range of 17.4 Hz to 299 Hz in the figure is the single-mode transmission area with compressive wave propagation and shear wave suppression; the black area with frequencies in the range of 363.7 Hz to 660 Hz is the phonon band gap, and elastic waves with frequencies in this frequency band will be prohibited from propagating.

[0026] The five-mode characteristics of the five-mode material can be characterized by the five-mode figure of merit FOM. The larger the figure of merit, the greater the ratio of the bulk modulus B to the shear modulus G, and the more difficult it is to couple between the compressive wave and the shear wave. When the five-mode figure of merit FOM > 10 3When the designed five-mode material structure has good five-mode characteristics, it can regulate sound waves like an ideal five-mode material. The empirical formula for the quality factor of the five-mode material can be expressed as:

[0027]

[0028] where h is the length of the double cone 2L, d is the diameter of the circular node, and D is the base length. The phase velocity c of the compressional wave B can be expressed as:

[0029]

[0030] In the formula, ρ B is the effective dynamic mass density. Similarly, the phase velocity c of the shear wave G is expressed as:

[0031]

[0032] Since the five-mode material is difficult to be compressed and the deformation occurring during wave transmission is much smaller than its own structural size, according to the law of conservation of mass in continuum mechanics, it can be considered that the density remains unchanged before and after under such small strains, that is, the equivalent mass densities ρ B and ρ G can be regarded as the static mass density ρ0 (ρ B = ρ G = ρ0). At this time, the relationship between the five-mode quality factor and the phase velocity is:

[0033]

[0034] The values of c B and c G can be obtained by calculating the slopes of the corresponding energy band curves of the compressional wave and the shear wave in the energy band diagram. From Figure 6 the slopes of the energy band curves of the compressional wave and the shear wave, the five-mode quality factor of this five-mode material structure is obtained Therefore, this five-mode material structure has good five-mode characteristics. It not only has a single-mode transmission region with shear wave suppression and compressional wave propagation, but also has a phonon band gap and has good sound wave regulation ability.

[0035] The present invention has good five-mode characteristics. It not only has a single-mode transmission region with shear wave suppression and compressional wave propagation, but also has a phonon band gap, and can prevent the propagation of all sound waves within the band gap frequency range. And on the basis of inheriting the width of the single-mode transmission region of the traditional double-cone unit cell configuration, it has a band gap with lower frequency and larger bandwidth.

[0036] The embodiments of the present invention have been described above in conjunction with the accompanying drawings. However, the present invention is not limited to the above specific embodiments. The above specific embodiments are merely illustrative rather than restrictive. Under the inspiration of the present invention, those of ordinary skill in the art can also make many forms without departing from the purpose of the present invention and the scope protected by the claims. All of these are within the protection scope of the present invention.

Claims

1. A five-mode material structure with an asymmetric single cone, characterized in that The five-mode material structure is composed of multiple identical two-dimensional unit cell structures arranged periodically; each unit cell structure consists of seven node structures and six single-cone structures; the node structure located inside the unit cell structure is a circular solid with its center at the intersection point of the single-cone structures, and the outer node structure is a sector with its center at the end point of the base of the single-cone; the circular node structure inside the unit cell structure is composed of three sector node structures; the local structure formed by every two single-cone structures, the node circle at their intersection point, and the outer node structure is rotationally symmetric about the center of the circular node structure inside the unit cell structure, and the rotation angle between the local structures is 120°; the local connection structure is formed between the outer node structure and the circular node structure inside the unit cell structure by two single-cone structures and the node circle at their intersection point; in the local connection structure, every two single-cones with different axial lengths form an asymmetric single-cone.

2. The five-mode material structure with an asymmetric single cone according to claim 1, characterized in that, The asymmetric single-cone is composed of every two single-cones connected by a node circle, and the single-cone structure is asymmetric.

3. The five-mode material structure with an asymmetric single cone according to claim 1, characterized in that, The asymmetric single-cone is composed of two single-cones with unequal axial lengths, and the base angle of the single-cone is less than 60°.

4. The five-mode material structure with an asymmetric single cone according to claim 1, characterized in that, The single-cone structure and the node circle connecting two asymmetric single-cones are filled with TC4 titanium alloy, and the other node structures are filled with vulcanized rubber.

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