An X-shaped negative Poisson's ratio local resonance module and its supporting metamaterial disk structure

Abstract

The present invention discloses an X-shaped negative Poisson's ratio local resonance module and its supporting metamaterial disc structure. The X-shaped negative Poisson's ratio local resonance module includes an X-shaped structural wall, an X-shaped negative Poisson's ratio structural unit and a local oscillator, wherein the local oscillator includes a soft coating layer and a cylindrical core, and the local oscillator is fixed on the X-shaped negative Poisson's ratio structural unit in an embedded form; the supporting metamaterial disc structure is composed of a plurality of X-shaped negative Poisson's ratio local resonance modules. The X-shaped negative Poisson's ratio structural units are circumferentially distributed around the outer wall of the inner circular ring column in the X-shaped structural wall to the inner wall of the outer circular ring column, and the outer wall of the inner circular ring column and the inner wall of the outer circular ring column are connected by the X-shaped structural unit wall. The X-shaped negative Poisson's ratio local resonance module is installed on a beam-type or tube-type base structure through the inner circular ring column. The present invention can achieve multi-scale and multi-level vibration suppression through the X-shaped negative Poisson's ratio local resonance module, improve the stability of the disc-shaped parts, and is easy to install and convenient to process.

Description

Technical Field

[0001] The present invention belongs to the technical field of new materials and new structures for vibration reduction and impact resistance, and specifically relates to an X-shaped negative Poisson's ratio local resonance module and its supporting metamaterial disc structure, which can be applied to modern transportation vehicles (ships, aircraft, high-speed railways, new energy vehicles), functional buildings (bridges, subway waiting rooms, tunnels), etc. Background Art

[0002] Negative Poisson's ratio metamaterial is a material with special mechanical properties, including lateral expansion, high compressibility, good impact resistance and energy absorption characteristics, and the ability to adjust bending stiffness. These excellent properties give it broad application prospects in aerospace, electronic devices, building structures, automotive industry, shipbuilding, and biomedical engineering.

[0003] Locally resonant phononic crystals, or LOs for short, are the origin of acoustic metamaterial research. Locally resonant phononic crystals are artificial periodic structures formed by periodically arranging local resonant units in an elastic medium. They exploit the local resonance effect of elastic waves in the subwavelength band to create a low-frequency elastic band gap, thereby achieving low-frequency, small-scale vibration and noise reduction. By periodically attaching local resonant units to traditional engineering structures (such as rods, beams, and plates), a type of local resonant acoustic metamaterial structure can be constructed. This new type of structure can produce low-frequency band gap characteristics, which can be utilized to effectively control structural vibration and noise.

[0004] In mechanical transmission systems, disc-shaped parts often play an important role in supporting and connecting. However, due to the lack of effective vibration reduction measures in traditional disc-shaped parts, the vibration of the power source is easily transmitted to other components, reducing system performance and even causing structural damage in severe cases. In addition, the noise generated by the vibration can also cause harm to people. The problem with existing negative Poisson's ratio structures is that they are usually arranged in a flat or out-of-plane array, and there are very few in-plane circular arrays. This makes it impossible for the negative Poisson's ratio structure to fully exert its excellent performance. The general negative Poisson's ratio structure or local resonance structure is single, and due to the lack of a reinforcement structure, its impact resistance and overall stability are also poor. Summary of the Invention

[0005] Based on the concept of metamaterial structure and the insufficient impact resistance of negative Poisson's ratio structures, the present invention provides an X-shaped negative Poisson's ratio local resonance module and its supporting metamaterial disc structure. The local oscillator can be fixed to the X-shaped negative Poisson's ratio structural unit by mechanical fixing, chemical bonding, hot melt welding, or thermosetting plastic connection. The X-shaped negative Poisson's ratio structural unit is circumferentially distributed around the outer wall of the inner circular ring column in the X-shaped structural wall to the inner wall of the outer circular ring column, and the outer wall of the inner circular ring column is connected to the inner wall of the outer circular ring column through the X-structure unit wall, thereby achieving a vibration reduction effect in both radial and axial directions. The parameters of the X-shaped negative Poisson's ratio structural unit and the local oscillator are designed according to actual conditions to achieve multi-scale vibration reduction. Moreover, the combination and arrangement of the X-shaped negative Poisson's ratio local resonance modules can achieve multi-level and multi-application vibration suppression, ensuring that the disc-shaped parts remain stable during the support and connection process.

[0006] To achieve the above-mentioned object, the present invention provides an X-shaped negative Poisson's ratio local resonance module, comprising an X-shaped structural wall, an X-shaped negative Poisson's ratio structural unit and a local oscillator.

[0007] The X-shaped structural wall comprises an outer wall of an inner circular ring column, an inner wall of an outer circular ring column and a plurality of X-shaped structural units.

[0008] The outer wall of the inner circular ring column is connected to the inner wall of the outer circular ring column through a plurality of X-shaped structural units.

[0009] There are several X-shaped negative Poisson's ratio structural units, each of which has a through hole at its center. The X-shaped negative Poisson's ratio structural unit and the X-shaped structural unit share an X-shaped structural wall. The two are connected in pairs on the X-shaped structural wall, and are arranged in a periodic array from small to large along the radial direction in the space between the outer wall of the inner circular ring column and the inner wall of the outer circular ring column and are distributed circumferentially.

[0010] The local oscillator comprises a soft coating layer and a cylindrical core body, and the local oscillator is fixed in a through hole of an X-shaped negative Poisson's ratio structural unit in an embedded manner.

[0011] In one embodiment, the X-shaped structural unit is composed of a pair of X-shaped structural unit walls, and the two X-shaped structural unit walls are cross-connected in opposite directions. The X-shaped structural unit wall is an arc-shaped connecting rib connected to the space between the outer wall of the inner circular ring column and the inner wall of the outer circular ring column. The X-shaped structural unit and the X-shaped negative Poisson's ratio structural unit share the X-shaped structural unit wall, and the two are connected and alternately arranged in pairs on the X-shaped structural unit wall, and are radially periodically arrayed and circumferentially distributed in the space between the outer wall of the inner circular ring column and the inner wall of the outer circular ring column. On the circumferential connection layer in the space between the outer wall of the inner circular ring column and the inner wall of the outer circular ring column, adjacent X-shaped structural units are connected by annular reinforcement ribs, and adjacent X-shaped negative Poisson's ratio structural units are connected by annular reinforcement ribs.

[0012] In one embodiment, the structure of the local oscillator is a cylinder, and the local oscillator is distributed in a periodic lattice in the space between the outer wall of the inner circular cylinder and the inner wall of the outer circular cylinder.

[0013] In one embodiment, the cylindrical core is a cylindrical body, the soft coating is a circular cylinder, and the soft coating covers the cylindrical core. The radial thickness of the soft coating increases locally from the outer wall of the inner circular cylinder to the inner wall of the outer circular cylinder.

[0014] In one embodiment, the number of connecting layers consisting of annular reinforcement ribs is adjustable.

[0015] In one embodiment, the X-shaped negative Poisson's ratio structural unit is a ring structure nested on the wall of the X-shaped structural unit.

[0016] In one embodiment, there are multiple local vibrators, each of which is spatially spaced along the arc direction of the X-shaped structural unit wall, from the outer wall of the inner circular column to the inner wall of the outer circular column. Each local vibrator is distributed in an annular pattern on the X-shaped structural wall. The soft coating layer is connected to the structure of the cylindrical core in a one-to-one pairing, and the soft coating layer can be nested in the through hole by mechanical fixing, chemical bonding, hot melt welding, or thermosetting plastic connection. After the size of the local vibrators of the first connection layer on the outer wall of the inner circular column is determined, the size of the local vibrators on the remaining layers increases proportionally with the number of layers.

[0017] In one embodiment, the soft covering layer and the cylindrical core can be fixedly connected by mechanical fixing, chemical bonding, hot melt welding or thermosetting plastic connection.

[0018] To achieve the above objectives, the present invention also provides a supporting metamaterial disk structure, comprising two or more X-shaped negative Poisson's ratio local resonance modules, each of which is arranged in a predetermined manner. Different arrangements will produce different band gap effects, and through design, a multi-scale vibration reduction effect can be achieved in the X-shaped structural unit wall.

[0019] In one embodiment, the parameters of the X-shaped structural units, the X-shaped negative Poisson's ratio structural units, and the local oscillators in each X-shaped negative Poisson's ratio local resonance module are the same or different. By varying the dimensions and material parameters of the X-shaped negative Poisson's ratio structural units and the local oscillators according to actual conditions, the equivalent negative Poisson's ratio structures can have different degrees of local resonance, thereby producing different local resonance effects. By varying the matrix parameters, different vibration reduction effects can be achieved.

[0020] The present invention provides an X-shaped negative Poisson's ratio local resonance module and its supporting metamaterial disc-shaped structure. Through the parameter design of the X-shaped negative Poisson's ratio local resonance module and the combined design of the X-shaped negative Poisson's ratio local resonance module, a negative Poisson's ratio and local resonance effect are achieved. In the radial direction, the negative Poisson's ratio structure can reduce vibration to a certain extent; in the axial direction, the additional local oscillator can dissipate a certain degree of out-of-plane elastic waves, which can hinder the wave transmission to other components and effectively suppress the multi-scale and multi-level vibration of disc-like parts on different mechanical connectors. Annular reinforcement ribs are used to form a triangular stable structure, which uniformly regulates the elastic waves in the inner axis plane and out of the outer axis plane. Because the surface curvature of the structure is continuous, a printing support structure of the model is not required during 3D printing, making the overall structure simple and more stable, and easy to install. It can be used not only for supporting drive shafts, but also for shaft connections and slewing bearings, overcoming the problems of the traditional negative Poisson's ratio structure in which the vibration of the power source is easily transmitted to other components, the system performance is reduced, and the structure is easily damaged. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the structures shown in these drawings without paying any creative work.

[0022] Figure 1 1 is an axonometric diagram of the X-shaped negative Poisson's ratio local resonance module in Example 1;

[0023] Figure 2 1 is a top view of the X-shaped negative Poisson's ratio local resonance module in Example 1;

[0024] Figure 3 Schematic diagram of the structure of a pair of X-shaped structural unit walls in Example 1;

[0025] Figure 4 This is a schematic structural diagram of a plurality of X-shaped negative Poisson's ratio structural units connected to a plurality of X-shaped structural units in Example 1;

[0026] Figure 5 This is a front view of the combination of the local oscillator and the X-shaped negative Poisson's ratio structural unit in Example 1;

[0027] Figure 6 It is a front view of the local oscillator structure in Example 1;

[0028] Figure 7 is a top view of the local oscillator structure in Example 1;

[0029] Figure 8This is a structural distribution diagram of the local oscillator nested in the X-shaped negative Poisson's ratio structural unit in Example 1;

[0030] Figure 9 is a cross-sectional view of the annular reinforcement rib in Example 1;

[0031] Reference numerals: X-shaped structural wall 1, X-shaped negative Poisson's ratio structural unit 2, local oscillator 3, annular reinforcement rib 4, X-shaped structural unit wall 5;

[0032] Inner circular column 11, outer circular column 12, X-shaped structural unit 13;

[0033] Soft coating layer 31, cylindrical core 32

[0034] The purpose, features and advantages of the present invention will be further described with reference to the accompanying drawings and in conjunction with the embodiments. DETAILED DESCRIPTION

[0035] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0036] It should be noted that all directional indications in the embodiments of the present invention (such as up, down, left, right, front, back, etc.) are only used to explain the relative position relationship, movement status, etc. between the various components under a certain specific posture (as shown in the accompanying drawings). If the specific posture changes, the directional indication will also change accordingly.

[0037] In addition, the terms "first," "second," and so on, used in this disclosure are for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of the technical features being referenced. Thus, a feature specified as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of this disclosure, "plurality" means at least two, such as two or three, unless otherwise specifically defined.

[0038] In the present invention, unless otherwise specified or limited, the terms "connection" and "fixation" should be understood in a broad sense. For example, "fixation" can mean fixed connection, detachable connection, or integration; it can mean mechanical connection, electrical connection, physical connection, or wireless communication connection; it can mean direct connection or indirect connection through an intermediate medium; it can mean internal communication between two elements or interaction between two elements, unless otherwise specified. For those skilled in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0039] In addition, the technical solutions between the various embodiments of the present invention can be combined with each other, but it must be based on the fact that ordinary technicians in this field can implement it. When the combination of technical solutions is mutually contradictory or cannot be implemented, it should be deemed that such a combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0040] Example 1

[0041] like Figure 1-2 The figure shows an X-shaped negative Poisson's ratio local resonance module disclosed in this embodiment, comprising an X-shaped structural wall 1, an X-shaped negative Poisson's ratio structural unit 22 and a local oscillator 33, wherein:

[0042] The X-shaped structural wall 1 includes an outer wall of an inner circular column 11 , an inner wall of an outer circular column 12 and a plurality of X-shaped structural units 13 .

[0043] The outer wall of the inner circular column 11 is connected to the inner wall of the inner circular column 11 through a plurality of X-shaped structural units 13 .

[0044] There are several X-shaped negative Poisson's ratio structural units 2, each of which has a through hole at its center. The X-shaped negative Poisson's ratio structural units 22 share the X-shaped structural unit 13 wall 5 with the X-shaped structural unit 13, and are connected to each other and arranged alternately on the X-shaped structural wall 1. They are also distributed circumferentially in a periodic array from small to large along the radial direction in the space between the outer wall of the inner circular ring column 11 and the inner wall of the outer circular ring column 12.

[0045] The local oscillator 3 includes a soft coating layer 31 and a cylindrical core 32 . The local oscillator 3 is fixed in the through hole of the X-shaped negative Poisson's ratio structural unit 2 in an embedded manner.

[0046] In this embodiment, the X-shaped negative Poisson's ratio structural unit 2 is a hollow disk or annular cylindrical structure, with the inner and outer annular columns 11 and 12 being flat annular cylindrical structures. The inner hole has a thickness along both the outer radial direction and the inner radial direction of the outer circle. Multiple groups of X-shaped structural unit walls (5) are evenly distributed on the outer wall of the inner hole, consisting of two intersecting arc-shaped connecting ribs running in opposite directions. These five groups of X-shaped structural unit walls intersect to form the X-shaped negative Poisson's ratio structural unit 2 and the X-shaped structural unit 13, extending to the inner wall of the outer circle. The X-shaped negative Poisson's ratio structural units 2 and 13 are connected in pairs and share the X-shaped structural unit walls 5. They are arranged circumferentially and radially in the area between the outer wall of the inner hole and the inner wall of the outer circle, forming a periodic array from small to large and from the inside out. A through hole is located at the center of the X-shaped negative Poisson's ratio unit, forming a negative Poisson's ratio structure. Localized oscillators 3 are arranged in the through hole to form a periodic lattice. Each layer of X-shaped negative Poisson's ratio structural units 2 and X-shaped structural units 13 are connected by annular reinforcement ribs 4, thereby forming a triangular reinforcement structure.

[0047] refer to Figure 3 As shown, on the outer wall of the inner hole is an X-shaped structural unit wall 5 composed of two arc-shaped connecting ribs in opposite directions and crossing each other. There are 24 groups of X-shaped structural unit walls 5 that cross each other to form X-shaped negative Poisson's ratio structural units 2 and X-shaped structural units 13 and extend to the inner wall of the outer circle.

[0048] refer to Figure 4 As shown, the X-shaped negative Poisson's ratio structural units 2 and the X-shaped structural units 13 are connected in pairs and share the X-shaped structural unit wall 5. They are arranged circumferentially and radially in the area between the outer wall of the inner hole and the inner wall of the outer circle, forming a periodic array from small to large and from inside to outside. There is a through hole at the center of the X-shaped negative Poisson's ratio structural unit, thereby forming a negative Poisson's ratio structure. The number of layers of the X-shaped negative Poisson's ratio structural unit 2 and the X-shaped structural unit 13 are 6 and 5, respectively.

[0049] In this embodiment, Figure 5-7 As shown, the local oscillator 3 is installed in the through-hole of the X-shaped negative Poisson's ratio unit. It consists of a cylindrical core 32 and a soft coating 31. The cylindrical core 32 is a cylindrical structure, and the soft coating 31 is a circular ring structure. The cylindrical core 32 is covered by the soft coating 31. The local oscillator 3 has a total of 6 layers, with 24 cells per layer, for a total of 144 cells, forming a periodic lattice. The diameter of each layer of cylindrical core 32 and soft coating 31 increases with the number of layers. The thickness of the soft coating of the local oscillator 3 also partially changes with the number of layers. The thickness of layers 1 to 3 remains unchanged, while the thickness of layers 4 to 6 increases slightly.

[0050] like Figure 8As shown, the annular reinforcement ribs 4 have a total of 11 layers, corresponding to the 6-layer X-shaped negative Poisson's ratio structural unit 2 and the 5-layer X-shaped structural unit 13. The thickness of the annular reinforcement ribs 4 in layers 1, 3, 5, 7, 9, and 11 is consistent, and the thickness of layers 2, 4, 6, 8, and 10 is consistent, which is slightly thicker than the thickness of the annular reinforcement ribs 4 in layers 1, 3, 5, 7, 9, and 11.

[0051] It should be noted that as the number of structural layers increases, the overall stiffness increases. Therefore, the structural load-bearing capacity is proportional to the number of layers. However, increased stiffness can reduce the vibration damping performance of the structure. Therefore, the number of structural layers should be comprehensively considered based on actual conditions during design. In this embodiment, to ensure that the structure has better load-bearing capacity and vibration damping performance, the annular stiffeners 4 are designed to have 11 layers.

[0052] Example 2. This example discloses a metamaterial-supporting disk-shaped structure comprising two or more of the X-shaped negative Poisson's ratio local resonance modules of Example 1, each arranged in a predetermined pattern. The parameters of the X-shaped structural unit 13, the X-shaped negative Poisson's ratio structural unit 2, and the local oscillator 3 in the X-shaped negative Poisson's ratio local resonance module may be the same or different. In this example, the substrates in each X-shaped negative Poisson's ratio local resonance module are sequentially connected or integrally formed.

[0053] In this embodiment, the X-shaped negative Poisson's ratio structural unit 2 and the local oscillator 3 of the X-shaped negative Poisson's ratio local resonance module are both formed by resin material 3D printing technology. The X-shaped structural unit wall 5 is a mesh ring structure. Two inner circular ring columns 11 and outer circular ring columns 12 with the same parameters are connected through the crossed X-shaped structural unit walls 5. The X-shaped structural units 13 and the X-shaped negative Poisson's ratio structural units 2 are alternately embedded at the intersection of the annular reinforcement ribs 4.

[0054] The results show that a supporting metamaterial disk structure in this embodiment achieves both a negative Poisson's ratio and the vibration reduction characteristics of the localized oscillator 3, has good vibration and noise reduction and impact resistance capabilities, and can effectively improve the stability of the mechanical system.

[0055] It should be noted that all features disclosed in the above embodiments 1-2, or all methods disclosed, except for mutually exclusive features, can be combined in any way. The embedding mentioned in this specification is only a description of the structural space position of the X-shaped negative Poisson's ratio structural unit 2 and the local oscillator 3 relative to the X-shaped structural unit wall 5, and a description of the structural space position of the local oscillator 3 relative to the X-shaped negative Poisson's ratio structural unit 2. The specific installation method can be selected according to the actual situation, such as inserting, welding, etc. The connection using the annular reinforcement rib 4 proposed in this embodiment is only one of the preferred installation methods. Any feature disclosed in this specification, unless otherwise stated, can be replaced by other equivalent or alternative features with similar purposes. Unless otherwise stated, each feature is only an example of a series of equivalent or similar features.

[0056] The above description is only a preferred embodiment of the present invention and does not limit the patent scope of the present invention. All equivalent structural transformations made by using the contents of the present invention description and drawings under the inventive concept of the present invention, or direct / indirect application in other related technical fields are included in the patent protection scope of the present invention.

Claims

1. An X-shaped negative Poisson's ratio local resonance module, characterized in that: It includes an X-shaped structural wall, several X-shaped negative Poisson's ratio structural units and local oscillators; The X-shaped structural wall comprises an outer wall of an inner circular column, an inner wall of an outer circular column and a plurality of X-shaped structural units; The outer wall of the inner circular ring column is connected to the inner wall of the outer circular ring column through a plurality of X-shaped structural units; A through hole is provided at the center of the X-shaped negative Poisson's ratio structural unit, the X-shaped negative Poisson's ratio structural unit and the X-shaped structural unit share the X-shaped structural wall, and the X-shaped negative Poisson's ratio structural units are distributed in a circumferential array from small to large along the radial direction in the space between the outer wall of the inner circular ring column and the inner wall of the outer circular ring column; The local oscillator includes a soft coating layer and a cylindrical core, and the local oscillator is fixed in the through hole of the X-shaped negative Poisson's ratio structural unit in an embedded manner.

2. The X-shaped negative Poisson's ratio local resonance module according to claim 1, characterized in that: The X-shaped structural unit is composed of a pair of X-shaped structural unit walls, and the two X-shaped structural unit walls are cross-connected in opposite directions; The X-shaped structural unit wall is an arc-shaped connecting rib connected to the space between the outer wall of the inner circular ring column and the inner wall of the outer circular ring column; The X-shaped structural units and the X-shaped negative Poisson's ratio structural units are alternately arranged in pairs on the X-shaped structural wall; In the circumferential connection layer of the space between the outer wall of the inner circular ring column and the inner wall of the outer circular ring column, adjacent X-shaped structural units are connected by annular reinforcement ribs, and adjacent X-shaped negative Poisson's ratio structural units are connected by annular reinforcement ribs.

3. The X-shaped negative Poisson's ratio local resonance module according to claim 1, characterized in that: The structure of the local oscillator is a cylinder, and the local oscillator is distributed in a periodic lattice in the space between the outer wall of the inner circular ring column and the inner wall of the outer circular ring column.

4. The X-shaped negative Poisson's ratio local resonance module according to claim 1, characterized in that: The structure of the cylindrical core is a cylinder, the structure of the soft coating layer is a circular column, and the soft coating layer covers the cylindrical core; The radial thickness of the soft coating layer increases locally along the radial direction from the outer wall of the inner circular ring column to the inner wall of the outer circular ring column.

5. The X-shaped negative Poisson's ratio local resonance module according to claim 2, characterized in that: The number of connecting layers composed of the annular reinforcement ribs can be adjusted.

6. The X-shaped negative Poisson's ratio local resonance module according to claim 1, characterized in that: The X-shaped negative Poisson's ratio structural unit is a ring-shaped structure nested on the wall of the X-shaped structural unit.

7. The X-shaped negative Poisson's ratio local resonance module according to any one of claims 1 to 6, characterized in that: There are multiple local vibrators, each of which is spaced apart in the X-shaped structural unit wall from the outer wall of the inner circular ring column to the inner wall of the outer circular ring column along the arc direction of the X-shaped structural unit wall, and the local vibrators are distributed in a ring shape on the X-shaped structural wall; The soft coating layer is connected to the structure of the cylindrical core in a one-to-one pairing manner, and the soft coating layer can be nested in the through hole by a mechanical fixing method, a chemical bonding method, a hot melt welding method or a thermosetting plastic connection method; After the size of the local oscillators in the first connection layer on the outer wall of the inner circular column is determined, the sizes of the local oscillators in the remaining layers increase proportionally with the number of layers.

8. The X-shaped negative Poisson's ratio local resonance module according to any one of claims 1 to 6, characterized in that: The soft coating layer and the cylindrical core can be fixedly connected by mechanical fixing, chemical bonding, hot melt welding or thermosetting plastic connection.

9. A metamaterial supporting disk structure, characterized in that: The invention comprises two or more X-shaped negative Poisson's ratio local resonance modules according to any one of claims 1 to 8, wherein each of the X-shaped negative Poisson's ratio local resonance modules is arranged in a predetermined manner.

10. The supporting metamaterial disc structure according to claim 9, characterized in that: The parameters of the X-shaped structural unit, the X-shaped negative Poisson's ratio structural unit and the local oscillator in each of the X-shaped negative Poisson's ratio local resonance modules are the same or different.

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