Design method of disordered multifunctional metamaterial structure with low-frequency vibration isolation and negative Poisson's ratio effects

Abstract

The invention discloses a design method of a disordered multifunctional metamaterial structure with low-frequency vibration isolation and negative Poisson's ratio effects, and the method comprises the steps: generating a cell element center dot matrix with disordered super-uniform characteristics in a two-dimensional plane, and selecting a working domain from the cell element center dot matrix; taking a dot matrix in a working area as a positioning dot matrix of chiral unit cell distribution, and performing chiral unit construction and network connection by utilizing the positioning dot matrix to generate a disordered super-uniform chiral negative Poisson's ratio network; a plurality of oscillators with cruciate ligament elastic units are assembled into the disordered super-uniform chiral negative Poisson's ratio network to form a disordered super-uniform chiral negative Poisson's ratio metamaterial structure; and performing three-dimensional modeling on the disordered super-uniform chiral negative Poisson's ratio metamaterial structure, and importing finite element analysis software to perform finite element analysis. The method can meet the urgent requirements of a complex engineering structure for vibration control and function reliability.

Description

Technical Field

[0001] This invention belongs to the field of metamaterial design, specifically relating to a design method for a disordered multifunctional metamaterial structure that combines low-frequency vibration isolation and negative Poisson's ratio effect. Background Technology

[0002] To meet the urgent demand for multifunctional integrated materials in aerospace, precision manufacturing, and special transportation fields, materials that combine low-frequency vibration isolation and negative Poisson's ratio effect have attracted much attention due to their ability to achieve wave-mechanical synergistic design. These materials demonstrate great potential in achieving integrated high-efficiency energy absorption, shock resistance, and flexible protection.

[0003] Chiral negative Poisson's ratio structures, based on a "rotation-expansion" unit deformation mechanism, can enhance equivalent shear stiffness and energy absorption, making them an effective way to achieve integrated vibration isolation and stable load-bearing. Existing designs of chiral negative Poisson's ratio metamaterials are mainly based on strict periodic arrangements, i.e., constructing metamaterial structures through the infinite replication of a single unit cell in space. However, such periodic-based structures have significant limitations: in terms of wave modulation, their bandgap characteristics are highly dependent on the regular arrangement of the lattice, leading to significant directional sensitivity in vibration isolation behavior; in terms of load-bearing, their mechanical properties exhibit strong anisotropy, limiting their applicability under multi-directional loads. Although introducing disorder is considered a potential path to break periodic dependence, completely disordered arrangements would disrupt long-range correlations in the structure, making it difficult to form an effective bandgap for elastic wave modulation and potentially causing stress concentration and mechanical instability. Faced with the urgent need for vibration control and functional reliability in complex engineering structures, there is a pressing need to develop a design method for disordered multifunctional metamaterial structures that combines low-frequency vibration isolation and negative Poisson's ratio effects. Summary of the Invention

[0004] Purpose of the invention: The purpose of this invention is to provide a design method for disordered multifunctional metamaterial structures that combine low-frequency vibration isolation and negative Poisson's ratio effect, which can meet the urgent needs of complex engineering structures for vibration control and functional reliability.

[0005] Technical solution: The present invention provides a design method for a disordered multifunctional metamaterial structure that combines low-frequency vibration isolation and negative Poisson's ratio effect, comprising:

[0006] In a two-dimensional plane, a lattice of cell center points exhibiting disordered and ultra-uniform characteristics is generated, and a working domain is selected from the lattice of cell center points.

[0007] The lattice in the working domain is used as the positioning lattice for chiral unit cell seeding. The positioning lattice is used to construct chiral units and connect networks to generate disordered ultra-uniform chiral negative Poisson's ratio networks.

[0008] Several oscillators with cruciate ligament elastic units are assembled into a disordered ultrauniform chiral negative Poisson's ratio network to form a disordered ultrauniform chiral negative Poisson's ratio metamaterial structure.

[0009] A three-dimensional model of a disordered, ultra-uniform chiral, negative Poisson's ratio metamaterial structure was created and imported into finite element analysis software for finite element analysis.

[0010] Furthermore, the step of generating a disordered ultrauniform lattice in a two-dimensional plane and selecting a working domain from the disordered ultrauniform lattice includes:

[0011] In a two-dimensional plane, the disordered super-uniformity order parameter and the number of cells are set as required. By excluding wavelet number scattering and combining simulated annealing and molecular dynamics algorithms, a set of cell center points exhibiting disordered super-uniform characteristics is obtained, and the working domain is selected from the cell center point lattice.

[0012] Furthermore, the step of using the lattice in the working domain as a positioning lattice for chiral unit cell seeding, and utilizing the positioning lattice for chiral unit construction and network connection to generate a disordered ultra-uniform chiral negative Poisson's ratio network includes:

[0013] The points in the working domain are used as the location points of the chiral unit cell. All the location points in the location points are delaunay triangulated. The points directly connected to any location point are defined as the direct neighbors of that location point. This determines the direct neighbor connection topology of each location point.

[0014] Generate several circular boundaries with radius r, centered at each location point;

[0015] By selecting every two neighboring circular boundaries in the triangulation, a straight line segment tangent to the two circular boundaries is generated as a connecting ligament, thereby generating a disordered ultra-uniform chiral negative Poisson's ratio network.

[0016] Furthermore, the disordered ultrauniform chiral negative Poisson's ratio network is made of resin material.

[0017] Furthermore, the assembly of several oscillators with cruciate ligament elastic units into a disordered ultrauniform chiral negative Poisson's ratio network to form a disordered ultrauniform chiral negative Poisson's ratio metamaterial structure includes:

[0018] Inside each circular boundary of a disordered, ultrauniform chiral negative Poisson's ratio network, an oscillator with a cruciate ligament elastic unit is assembled, thus forming a disordered, ultrauniform chiral negative Poisson's ratio metamaterial structure.

[0019] Furthermore, the oscillator with the cruciate ligament elastic unit includes a mass block, a mass block outer cover, and four elastic ligaments symmetrically distributed in a cruciate shape on the mass block outer cover; the oscillator is arranged at a positioning point in the positioning point array.

[0020] Furthermore, one end of the elastic ligament is connected to the outer cladding of the mass block, and the other end is connected to the inner wall of the circular boundary.

[0021] Furthermore, the mass block is a cylindrical copper mass block, and the elastic ligament and the outer covering layer of the mass block are made of rubber material.

[0022] Furthermore, in the finite element analysis process, the material properties of the oscillator with cruciate elastic elements and the disordered ultra-uniform chiral negative Poisson's ratio network are first assigned; then, a quasi-static uniaxial compressive displacement load is applied to the three-dimensional model of the disordered ultra-uniform chiral negative Poisson's ratio metamaterial structure, and the equivalent Poisson's ratio of the model is solved.

[0023] Furthermore, during the finite element analysis process, periodic boundary conditions are applied to the three-dimensional model of the disordered ultrauniform chiral negative Poisson's ratio metamaterial structure in the finite element analysis software, and characteristic frequency analysis is performed on the disordered ultrauniform chiral negative Poisson's ratio metamaterial structure. By solving the distribution of characteristic frequencies on the boundary of the first irreducible Brillouin zone, the band structure diagram of the metamaterial structure is drawn.

[0024] Beneficial effects: Compared with the prior art, the significant technical effects of the present invention are as follows: The present invention introduces a disordered ultra-uniform lattice design chiral network, which breaks the anisotropy of the band gap of the traditional periodic structure and realizes a quasi-isotropic low-frequency vibration isolation band gap in the disordered structure, significantly broadening the effective vibration isolation range. (2) The disordered chiral network constructed by the present invention has its "rotation-expansion" deformation mechanism being uniformly excited in multiple directions, realizing a more stable negative Poisson's ratio effect, successfully integrating unique dynamic wave performance with excellent mechanical properties, and broadening its application prospects in vibration reduction, noise reduction and protection. Attached Figure Description

[0025] Figure 1 This is a schematic diagram of the process of the present invention;

[0026] Figure 2 This is a schematic diagram of the cell center lattice exhibiting disordered and ultra-uniform characteristics in this invention.

[0027] Figure 3 This is a schematic diagram of the disordered ultrauniform chiral negative Poisson's ratio network in this invention;

[0028] Figure 4 This is a schematic diagram of the disordered, ultra-uniform chiral negative Poisson's ratio metamaterial structure in this invention. Detailed Implementation

[0029] The technical solution of the present invention will now be described in detail with reference to specific embodiments and accompanying drawings.

[0030] like Figure 1 As shown, the present invention discloses a design method for a disordered multifunctional metamaterial structure that combines low-frequency vibration isolation and negative Poisson's ratio effect, comprising the following steps:

[0031] S1. In a two-dimensional plane, generate a lattice of cell center points exhibiting disordered and ultra-uniform characteristics, and select a working domain from the lattice of cell center points.

[0032] Disordered hyperhomogeneous states are a new type of matter that lies between crystalline order and complete disorder. They exhibit anomalously suppressed density fluctuations on large scales, and their degree of order is defined by the order index χ.

[0033] ;

[0034] in, In the wavenumber interval The number of independent wave vectors that are internally constrained; The dimension of the space; The number of points.

[0035] In step S1, within a two-dimensional plane, the disordered super-uniformity order parameters and the number of cells are set as required. By excluding wavelet number scattering and combining simulated annealing and molecular dynamics algorithms, a set of cell center points exhibiting disordered super-uniform characteristics can be obtained, and the working domain is selected from the cell center point lattice.

[0036] The reason for selecting the working domain from the cell center lattice is as follows: the disordered hyperuniform state is defined under the limit of infinite systems, but practical applications need to deal with finite samples, which inevitably introduces boundaries and dimensions.

[0037] Effects. To mitigate these limitations, a central square region with side length L needs to be extracted from the large-scale point set as the working domain. As a specific implementation, the side length of the working domain is set... Setting the degree of order to control the ultra-uniform distribution The value is 0.45, and the points within this region are the final chiral unit cell seeding points, such as... Figure 2 As shown.

[0038] S2. Use the lattice in the working domain obtained in step S1 as the positioning lattice for chiral unit cell planting, and use the positioning lattice to construct chiral units and connect networks to generate a disordered ultra-uniform chiral negative Poisson's ratio network.

[0039] Step S2 involves performing network assembly based on the positioning lattice generated in step 1 to construct a disordered, ultra-uniform chiral negative Poisson's ratio network.

[0040] like Figure 3 As shown, Figure 3Figure (a) in the diagram is a schematic diagram of the Delaunay triangulation of the positioning lattice. Figure 3 Figure (b) in the diagram is a schematic diagram of generating a circular boundary. Figure 3 Figure (c) is a schematic diagram of network assembly. The specific implementation process of step S2 is as follows:

[0041] S2.1. Using the lattice in the working domain as the location lattice for chiral unit cell distribution, perform Delaunay triangulation on all location points in the location lattice, defining points directly connected to any location point as its direct neighbors, thereby determining the direct neighbor connection topology for each location point, such as... Figure 3 As shown in Figure (a);

[0042] S2.2. Using each positioning point as the center, generate several circular boundaries with a radius of r, such as... Figure 3 As shown in Figure (b);

[0043] S2.3. Select every two neighboring circular boundaries in the triangulation and generate a straight line segment tangent to the two circular boundaries as a connecting ligament, thereby generating a disordered, ultra-uniform chiral negative Poisson's ratio network, such as... Figure 3 As shown in Figure (c).

[0044] In this embodiment, the radius of the circular boundary The disordered, ultra-uniform chiral negative Poisson's ratio network is made of resin material. ,density Poisson's ratio .

[0045] S3. Assemble several oscillators with cruciate ligament elastic units into a disordered ultrauniform chiral negative Poisson's ratio network to form a disordered ultrauniform chiral negative Poisson's ratio metamaterial structure.

[0046] In step S3, an oscillator with a cruciate ligament elastic unit is assembled inside each circular boundary of the disordered ultrauniform chiral negative Poisson's ratio network obtained in step S2, thereby forming a disordered ultrauniform chiral negative Poisson's ratio metamaterial structure.

[0047] In this embodiment, the oscillator with cruciate ligament elastic units includes a mass block, a mass block outer cladding, and four elastic ligaments symmetrically distributed in a cruciate shape on the mass block outer cladding. The oscillator is positioned at the location point generated in step S1. One end of each of the four elastic ligaments is connected to the mass block outer cladding, and the other end is connected to the inner wall of the circular boundary, ultimately forming a disordered, ultra-uniform chiral negative Poisson's ratio metamaterial structure.

[0048] In this embodiment, the mass block is a cylindrical copper mass block with a radius of 9mm. The material parameters of copper are: Young's modulus. ,density Poisson's ratio The mass block is covered by a mass block outer layer, which is connected to a disordered, ultra-uniform chiral negative Poisson's ratio network by four elastic ligaments symmetrically distributed in a cross shape.

[0049] In this embodiment, the outer layer of the mass block is 1 mm thick, and the elastic ligament is 5.4 mm long and 1 mm wide; both the elastic ligament and the outer layer of the mass block are made of rubber material, and the Young's modulus of the rubber is... ,density Poisson's ratio .

[0050] S4. Perform 3D modeling of the disordered, ultrahomogeneous, chiral, negative Poisson's ratio metamaterial structure and import it into finite element analysis software (such as ABAQUS, COMSOL Multiphysics, etc.) for finite element analysis. Figure 4 As shown, Figure 4 Figure (a) shows a schematic diagram of the simulation results of compression deformation of a disordered, ultra-uniform chiral, negative Poisson's ratio metamaterial structure. Figure 4 Figure (b) shows the band structure of a disordered, ultrauniform chiral, negative Poisson's ratio metamaterial.

[0051] In the finite element analysis process, the material properties of the disordered, ultra-uniform chiral negative Poisson's ratio network and the oscillator with cruciate ligament elastic elements are first strictly assigned according to their respective material properties. Then, a quasi-static uniaxial compressive displacement load is applied to the three-dimensional model of the disordered, ultra-uniform chiral negative Poisson's ratio metamaterial structure, and the equivalent Poisson's ratio of the model is solved. In this embodiment, the material properties of the resin frame, rubber ligament, mass block outer layer, and copper mass block are strictly assigned according to the material parameters defined in steps S2 and S3. A quasi-static uniaxial compressive displacement load is applied to the three-dimensional model of the disordered, ultra-uniform chiral negative Poisson's ratio metamaterial structure, and its equivalent Poisson's ratio is solved. Figure 4 The simulation results in Figure (a) clearly show that the structure undergoes lateral contraction under axial compression, exhibiting a negative Poisson's ratio effect with a Poisson's ratio of -0.4.

[0052] During the finite element analysis, periodic boundary conditions are applied to the three-dimensional model of the disordered ultrauniform chiral negative Poisson's ratio metamaterial structure in the finite element analysis software, and characteristic frequency analysis is performed on the disordered ultrauniform chiral negative Poisson's ratio metamaterial structure. By solving the distribution of characteristic frequencies on the boundary of the first irreducible Brillouin zone, the band structure diagram of the metamaterial structure is plotted.

[0053] To evaluate the ability of a disordered, ultrahomogeneous, chiral, negative Poisson's ratio metamaterial structure to modulate elastic waves, the structure was treated as a representative supercell, and periodic boundary conditions (Bloch boundary conditions) were applied in finite element analysis software. The band structure diagram of the material was plotted by solving for the distribution of characteristic frequencies at the first irreducible Brillouin zone boundary. The results are as follows: Figure 4 As shown in Figure (b), a distinct low-frequency bandgap exists within a specific frequency range (the area highlighted in the figure). This demonstrates that elastic waves are prohibited from propagating in any direction within this frequency band, thus physically ensuring the omnidirectional consistency of vibration isolation performance, indicating that this metamaterial possesses excellent vibration control potential.

[0054] The finite element analysis results above demonstrate that the disordered, ultrauniform chiral, negative Poisson's ratio metamaterial structure designed in this invention successfully integrates unique dynamic wave properties with excellent mechanical properties. This achieves the multifunctionality of metamaterials and broadens their application prospects in vibration reduction, noise reduction, and protection.

Claims

1. A design method for a disordered multifunctional metamaterial structure that combines low-frequency vibration isolation and negative Poisson's ratio effect, characterized in that, include: In a two-dimensional plane, a lattice of cell center points exhibiting disordered and ultra-uniform characteristics is generated, and a working domain is selected from the lattice of cell center points. The lattice in the working domain is used as the positioning lattice for chiral unit cell seeding. The positioning lattice is used to construct chiral units and connect networks to generate disordered ultra-uniform chiral negative Poisson's ratio networks. Several oscillators with cruciate ligament elastic units are assembled into a disordered ultrauniform chiral negative Poisson's ratio network to form a disordered ultrauniform chiral negative Poisson's ratio metamaterial structure. A three-dimensional model of a disordered, ultra-uniform chiral, negative Poisson's ratio metamaterial structure was created and imported into finite element analysis software for finite element analysis.

2. The design method for a disordered multifunctional metamaterial structure with both low-frequency vibration isolation and negative Poisson's ratio effect according to claim 1, characterized in that, The process of generating a disordered ultra-uniform lattice in a two-dimensional plane and selecting a working domain from the disordered ultra-uniform lattice includes: In a two-dimensional plane, the disordered super-uniformity order parameter and the number of cells are set as required. By excluding wavelet number scattering and combining simulated annealing and molecular dynamics algorithms, a set of cell center points exhibiting disordered super-uniform characteristics is obtained, and the working domain is selected from the cell center point lattice.

3. The design method for a disordered multifunctional metamaterial structure with both low-frequency vibration isolation and negative Poisson's ratio effect as described in claim 1, characterized in that, The step of using the lattice in the working domain as a positioning lattice for chiral unit cell seeding, and utilizing the positioning lattice for chiral unit construction and network connection to generate a disordered ultra-uniform chiral negative Poisson's ratio network includes: The points in the working domain are used as the location points of the chiral unit cell. All the location points in the location points are delaunay triangulated. The points directly connected to any location point are defined as the direct neighbors of that location point. This determines the direct neighbor connection topology of each location point. Generate several circular boundaries with radius r, centered at each location point; By selecting every two neighboring circular boundaries in the triangulation, a straight line segment tangent to the two circular boundaries is generated as a connecting ligament, thereby generating a disordered ultra-uniform chiral negative Poisson's ratio network.

4. The design method for a disordered multifunctional metamaterial structure with both low-frequency vibration isolation and negative Poisson's ratio effect as described in claim 1, characterized in that: The disordered, ultra-uniform chiral negative Poisson's ratio network is made of resin material.

5. The design method for a disordered multifunctional metamaterial structure with both low-frequency vibration isolation and negative Poisson's ratio effect according to claim 1, characterized in that, The assembly of several oscillators with cruciate ligament elastic units into a disordered, ultra-uniform chiral negative Poisson's ratio network to form a disordered, ultra-uniform chiral negative Poisson's ratio metamaterial structure includes: Inside each circular boundary of a disordered, ultrauniform chiral negative Poisson's ratio network, an oscillator with a cruciate ligament elastic unit is assembled, thus forming a disordered, ultrauniform chiral negative Poisson's ratio metamaterial structure.

6. The design method for a disordered multifunctional metamaterial structure with both low-frequency vibration isolation and negative Poisson's ratio effect as described in claim 5, characterized in that: The oscillator with cruciate ligament elastic units includes a mass block, a mass block outer cover, and four elastic ligaments symmetrically distributed in a cruciform shape on the mass block outer cover; the oscillator is arranged at positioning points in a positioning point array.

7. The design method for a disordered multifunctional metamaterial structure with both low-frequency vibration isolation and negative Poisson's ratio effect as described in claim 6, characterized in that: One end of the elastic ligament is connected to the outer cladding of the mass block, and the other end is connected to the inner wall of the circular boundary.

8. The design method for a disordered multifunctional metamaterial structure with both low-frequency vibration isolation and negative Poisson's ratio effect as described in claim 6, characterized in that: The mass block is a cylindrical copper mass block, and the elastic ligament and the outer covering of the mass block are made of rubber material.

9. The design method for a disordered multifunctional metamaterial structure with both low-frequency vibration isolation and negative Poisson's ratio effect according to claim 1, characterized in that: In the finite element analysis process, the material properties of the disordered ultra-uniform chiral negative Poisson's ratio network and the oscillator with cruciate ligament elastic elements are first assigned. Then, a quasi-static uniaxial compressive displacement load is applied to the three-dimensional model of the disordered ultra-uniform chiral negative Poisson's ratio metamaterial structure, and the equivalent Poisson's ratio of the model is solved.

10. The design method for a disordered multifunctional metamaterial structure with both low-frequency vibration isolation and negative Poisson's ratio effect according to claim 1, characterized in that: In the finite element analysis process, periodic boundary conditions are applied to the three-dimensional model of the disordered ultrauniform chiral negative Poisson's ratio metamaterial structure in the finite element analysis software, and characteristic frequency analysis is performed on the disordered ultrauniform chiral negative Poisson's ratio metamaterial structure. By solving the distribution of characteristic frequencies on the first irreducible Brillouin zone boundary, the band structure diagram of the metamaterial structure is drawn.

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