阅读说明：本技术 一种基于多层圆柱型三维五模超构材料 (Multilayer cylindrical three-dimensional five-mode super-structural material ) 是由 蔡成欣 王雪 秦瑶 李明星 贺广臣 王其富 葛宏义 廉飞宇 于 2021-09-15 设计创作，主要内容包括：本发明属于噪声控制技术领域,具体为基于多层圆柱型三维五模超构材料,超构材料的周期点阵结构形式为面心立方晶格结构,面心立方晶格结构是由16个基元在窄直径处相连构成；面心立方晶格结构的单元长度为a,基元的长度每个基元结构均由6个圆柱体组成。鉴于传统五模超构材料对应双锥单元为点接触,本发明采用圆柱体替代不仅有效改善了结构的稳定性,而且结构的可调参数更加丰富(d-(1)、D-(2)D-(1)、D-(3)、d-(2)、h-(1)、h-(2)、h-(3)),通过精细调节结构参数,可以设计出具有更优异的五模特性、频率更低的完全声子禁带的五模超材料。在水下声波低频宽带调控、声隐身、减振降噪、地震防护等领域具有潜在的应用价值。(The invention belongs to the technical field of noise control, and particularly relates to a multi-layer cylindrical three-dimensional five-mode metamaterial-based periodic lattice structure, wherein the periodic lattice structure of the metamaterial is a face-centered cubic lattice structure which is formed by connecting 16 elements at a narrow diameter; the unit length of the face-centered cubic lattice structure is a, and the length of the element Each cell structure consists of 6 cylinders. In view of the fact that the traditional five-mode metamaterial is in point contact with the double-cone unit, the invention adopts the cylinder to replace the traditional five-mode metamaterial, thereby effectively improving the stability of the structure and enabling the adjustable parameters of the structure to be richer (d) 1 、D 2 D 1 、D 3 、d 2 、h 1 、h 2 、h 3 ) By finely adjusting the structural parameters, the five-mode metamaterial with more excellent five-mode characteristics and lower frequency and complete phonon forbidden band can be designed. The method has potential application value in the fields of underwater sound wave low-frequency broadband regulation, sound stealth, vibration and noise reduction, earthquake protection and the like.)

1. A three-dimensional five-mode super-structure material based on multilayer cylindrical type is characterized in that: the periodic lattice structure of the metamaterial is a face-centered cubic lattice structure, and the face-centered cubic lattice structure is formed by connecting 16 elements at a narrow diameter; face centered cubic latticeUnit length of structure is a, length of elementEach cell structure consists of 6 cylinders.

2. The multilayer cylindrical three-dimensional five-mode metamaterial according to claim 1, wherein the 6 cylinders constituting the cellular structure have corresponding diameters d from top to bottom₁、D₁、D₃、D₃、D₂、d₂The height of the corresponding cylinder is h₁、h₂、h₃、h₃、h₂、h₁And satisfy d₁≤D₁≤D₃≤a，d₂≤D₂≤D₃≤a，h₁+h₂+h₃1/2H.

3. The multilayer cylindrical three-dimensional five-mode metamaterial according to claim 2, wherein the metamaterial is a hard material or consists of a hard material and a soft material.

4. The multilayer cylindrical three-dimensional five-mode metamaterial according to claim 3, wherein the hard material is one of a high polymer, metallic aluminum and lead; the soft material is silicon rubber.

5. The multilayer cylindrical three-dimensional five-mode metamaterial according to claim 4, wherein the high polymer is one or a mixture of more than two of polystyrene resin, graphene and photosensitive resin.

6. The multilayer cylindrical three-dimensional five-mode metamaterial according to claim 5, wherein the high polymer comprises the following composition material parameters: young modulus E is 3Gpa, Poisson ratio upsilon is 0.4, and mass density rho is 1190kg/m³(ii) a The above-mentionedThe composition material parameters of the silicon rubber are as follows: young's modulus E of 0.1175X 10^-3Gpa, Poisson's ratio upsilon of 0.47, and mass density ρ of 1300kg/m³。

7. The multilayer cylindrical three-dimensional five-mode metamaterial according to claim 3, wherein when the metamaterial is made of hard materials, the primitive cell structure parameters are as follows: 37.3mm for a, 16.15mm for H, D₃＝3mm,D₁＝D₂＝1.5mm,d₁＝0.55mm,h₁＝h₂＝h₃＝1/6H。

8. The multilayer cylindrical three-dimensional five-mode metamaterial according to claim 4, wherein when the metamaterial is composed of hard materials and soft materials, primitive cell structure parameters of the metamaterial are as follows: 37.3mm for a, 16.15mm for H, D₃＝3mm,D₁＝D₂＝1.5mm,d₁＝0.55mm,h₁＝0.1H、h₂＝0.3H、h₃＝0.1H。

9. The multilayer cylindrical three-dimensional five-mode metamaterial according to any one of claims 1 to 8, wherein for convenience of analysis, the unit structure is narrow at two ends and has a diameter d₁And d₂Is defined as N, i.e. d₂/d₁N, wherein N ranges from 0.1 to 3.0.

10. The multilayer cylindrical three-dimensional five-mode metamaterial according to claim 9, wherein the multilayer cylindrical three-dimensional five-mode metamaterial is prepared by a 3D printing technology.

Technical Field

The invention relates to the technical field of noise control, in particular to a multilayer cylindrical three-dimensional five-mode metamaterial.

Background

The metamaterial is a novel artificial synthetic material, is generally formed by arranging periodic structures or non-periodic artificial microstructures, and has peculiar physical properties which are not possessed by natural materials. The five-mode metamaterial has the advantages of low frequency, wide band and omnidirection as a metamaterial with good fluid properties. The five-mode metamaterial with the complete phonon forbidden band not only has good fluid properties in a single-mode working frequency range, but also has a complete phonon forbidden band frequency range. An important parameter for measuring the five-mode characteristics is the figure of merit (FOM), which is defined as the ratio of the bulk modulus B to the shear modulus G, and the larger the figure of merit, the larger the bulk modulus is larger than the shear modulus, the better the fluid characteristics of the five-mode metamaterial.

The concept of five-mode metamaterials was originally proposed by Milton in 1995, but the proposed ideal five-mode metamaterials have point contact between the double-cone unit structures, and the point contact collapses under stress due to the instability of the structures, so that the five-mode metamaterials have no practicability. In 2012, Kadic proposed and produced five-mode metamaterials with certain structural stability for the first time, but because the biconical unit has good symmetry, the phonon band gap can be opened only when the narrow diameter is small. Cai et al propose asymmetric biconical five-mode metamaterials, and obtain broadband phonon band gaps by reducing lattice symmetry. However, the overlapping area formed by adjacent connected double cones causes certain errors between the actual effective narrow-end contact diameter and the defined contact cone diameter, and in addition, the geometric adjustable parameters of the structure are limited (only adjustable D, D), so that when a 3D printing technology is used for preparing a macroscale three-dimensional five-mode metamaterial, the structural unit cannot be recycled, and therefore, a novel five-mode metamaterial is expected to be constructed and designed.

The five-mode metamaterial composed of simple substance materials generally belongs to Bragg scattering type five-mode metamaterial, and the size of the crystal lattice of the five-mode metamaterial is generally in the same order of magnitude as the wavelength of the acoustic wave corresponding to the working frequency. If the Bragg scattering type five-mode metamaterial is used for regulating and controlling the low-frequency sound wave below 500Hz underwater, the structural size of a sound wave regulating and controlling device needs at least tens of meters, which brings great difficulty to the engineering application. Therefore, a method and a mechanism for regulating underwater low-frequency sound waves by using small-size five-mode metamaterial are researched, and a regulation and control method of working frequency bands in three dimensions is an urgent core problem to be solved.

Disclosure of Invention

Aiming at the defects or improvement technologies in the prior art, the invention provides a multilayer cylindrical three-dimensional five-mode metamaterial, which can effectively solve the technical problems that the traditional biconical three-dimensional five-mode metamaterial has high sample processing precision difficulty, the overlapping area formed by adjacent connected bipyramids causes certain error between the actual effective narrow-end contact diameter and the defined contact cone diameter, the adjustable parameters of a unit structure are limited (only adjustable D, D) and the like, and a novel three-dimensional five-mode metamaterial is designed, and has the characteristics of more excellent five-mode characteristics, lower complete phonon band gap frequency, rich adjustable parameters and the like; aiming at the defects of the Bragg scattering type five-mode metamaterial in the aspect of low-frequency sound wave regulation, the local resonance type five-mode metamaterial can be designed to be made of a composite material, compared with the traditional bipyramid type three-dimensional local resonance type five-mode metamaterial, the local resonance type five-mode metamaterial designed by the invention can reduce the band gap frequency to be lower than 100Hz, the band gap width is increased, and theoretical basis and reference are provided for promoting the application of the three-dimensional five-mode metamaterial in the aspect of underwater low-frequency sound wave regulation and control.

In order to realize the purpose, the invention adopts the following technical scheme:

a is based on the cylindrical three-dimensional five-mode metamaterial of multilayer, the periodic lattice structural form of the said metamaterial is face-centered cubic lattice structure, face-centered cubic lattice structure is formed by 16 pieces of basic unit links up in the narrow diameter place; the unit length of the face-centered cubic lattice structure is a, and the length of the elementEach cell structure consists of 6 cylinders.

Preferably, the 6 cylinders constituting the cell structure have respective diameters d from top to bottom₁、D₁、 D₃、D₃、D₂、d₂The height of the corresponding cylinder is h₁、h₂、h₃、h₃、h₂、h₁And satisfy d₁≤D₁≤D₃≤a，d₂≤D₂≤D₃≤a，h₁+h₂+h₃1/2H.

Preferably, the metamaterial is a hard material or consists of a hard material and a soft material.

Further preferably, the hard material is one of a high molecular polymer, metallic aluminum and lead; the soft material is silicon rubber.

Further preferably, the high molecular polymer is one or a mixture of two or more of polystyrene resin, graphene and photosensitive resin.

Further preferably, the composition material parameters of the high molecular polymer are as follows: young modulus E is 3Gpa, Poisson ratio upsilon is 0.4, and mass density rho is 1190kg/m³(ii) a The silicon rubber comprises the following components in parts by weight: young's modulus E of 0.1175X 10^-3Gpa, Poisson's ratio upsilon of 0.47, and mass density ρ of 1300kg/m³。

Preferably, when the metamaterial is made of hard materials, the primitive cell structure parameters are as follows: 37.3mm for a, 16.15mm for H, D₃＝3mm,D₁＝D₂＝1.5mm,d₁＝0.55mm,h₁＝h₂＝h₃＝1/6H。

Preferably, when the metamaterial is composed of hard materials and soft materials, the primitive cell structure parameters are as follows: 37.3mm for a, 16.15mm for H, D₃＝3mm,D₁＝D₂＝1.5mm,d₁＝0.55mm,h₁＝0.1H、 h₂＝0.3H、h₃＝0.1H。

For convenient analysis, the unit structure is narrowed at two ends by a diameter d₁And d₂Is defined as N, i.e. d₂/d₁N, wherein N ranges from 0.1 to 3.0.

The multilayer cylindrical three-dimensional five-mode metamaterial is prepared by a 3D printing technology.

The metamaterial is prepared by adopting a 3D printing technology, and the geometric structure parameter D of the metamaterial is adjusted₁、D₂D₁、D₃、d₂、h₁、h₂、h₃And the like, a new configuration with more excellent five-mode characteristics and lower phonon forbidden band frequency can be designed.

Compared with the prior art, the invention has the following advantages and beneficial effects:

1) with more adjustable parameters (d) made up of 6 cylinders by designing the cell₁、D₂D₁、D₃、d₂、 h₁、h₂、h₃) The five-mode super-structure material can be used for carrying out fine adjustment on the structure in a targeted manner to realize better low-frequency sound insulation performance.

2) The thin end connecting point of the traditional biconical five-mode metamaterial is small, and errors are easy to generate in the actual manufacturing process.

3) By designing the local resonance type five-mode metamaterial composed of the composite material, the problem that the Bragg scattering type three-dimensional five-mode metamaterial requires a lattice size of tens of meters when used for underwater low-frequency sound wave regulation is effectively solved, and compared with the traditional bipyramid local resonance type five-mode metamaterial, the Bragg scattering type three-dimensional five-mode metamaterial can reduce the band gap frequency to be lower than 100Hz and increase the band gap width.

4) The structure is simple to process and prepare, has wide application range, and can be suitable for various low-frequency noise control environments.

Drawings

Fig. 1 is a schematic diagram of a cell structure and a unit structure of a multilayer cylindrical three-dimensional five-mode metamaterial according to an embodiment of the present invention;

FIG. 2 is a graph of energy band dispersion of a multilayer cylindrical three-dimensional five-mode metamaterial based on a narrow diameter ratio N of 0.4;

FIG. 3 is a graph showing the effect of the narrow diameter ratio N of a multilayer cylindrical three-dimensional five-mode metamaterial on a first phonon band gap;

FIG. 4 is an illustration of the effect of the narrow diameter ratio N on FOM based on a multilayer cylindrical three-dimensional five-mode metamaterial;

FIG. 5 is a graph showing the band dispersion curves of a soft silicone rubber material added at two ends based on a cylindrical three-dimensional five-mode metamaterial made of a multi-layer composite material;

FIG. 6 is a graph showing the influence of the narrow diameter ratio N of a cylindrical three-dimensional five-mode metamaterial based on a multilayer composite material on a first phonon band gap.

FIG. 7 is a graph showing the effect of a cylindrical three-dimensional five-mode metamaterial based on a multilayer composite on FOM along with the change of the narrow diameter ratio N.

Detailed Description

The technical solutions of the present invention are described in detail below, and the embodiments described with reference to the drawings are exemplary and should not be construed as limiting the present invention, and all other embodiments obtained by those skilled in the art without inventive step are within the scope of the present invention.

The invention is described in further detail below with reference to two specific examples.

Example 1

Referring to fig. 1(a), the invention provides a multilayer cylindrical three-dimensional five-mode metamaterial, which is formed by connecting 16 elements at narrow diameter to form a face-centered cubic lattice structure with a periodic unit length of aReferring to fig. 1(b), each cell structure is composed of 6 cylinders of single medium, and the corresponding diameters of the metamaterial from top to bottom are d₁、D₁、D₃、D₃、D₂、d₂The height of the corresponding cylinder is h₁、h₂、h₃、h₃、h₂、h₁And satisfy d₁≤D₁≤D₃≤a， d₂≤D₂≤D₃≤a，h₁+h₂+h₃1/2H.

In this embodiment, a commercial software package COMSOL Multiphysics is used to perform numerical calculation, a tetrahedron is used to perform mesh division, the maximum cell size is 0.002, the minimum cell size is 0.4e-5, the maximum cell growth rate is 1.5, the curvature factor is 0.6, and the resolution of a narrow region is 0.5.

In this embodiment, the metamaterial structure is prepared by a 3D printing technique, the metamaterial is a bragg scattering type multilayer cylindrical three-dimensional five-mode metamaterial composed of a single medium, the single medium is a high molecular polymer, the material of this embodiment is polystyrene resin, and the parameters thereof are as follows: young's modulus of 3GPa, Poisson's ratio of 0.4, and mass density of 1190kg/m³(ii) a The silicon rubber comprises the following components in parts by weight: young's modulus E of 0.1175X 10^-3GPa, Poisson's ratio upsilon of 0.47 and mass density rho of 1300kg/m³。

In this example, the primitive cell structure parameters for fixing the multilayer cylindrical three-dimensional five-mode metamaterial are a ═ 37.3mm, H ═ 16.15mm, and D₃＝3mm,D₁＝D₂＝1.5mm,d₁＝0.55mm,,h₁＝h₂＝h₃1/6H, the energy band dispersion curve when the narrow diameter ratio N is 0.4 is shown in figure 2, two phonon band gaps are opened simultaneously except for a single mode area of the multilayer cylindrical three-dimensional five-mode metamaterial, wherein the lower bound and the upper bound of the frequency of the first phonon band gap are respectively 3.50KHz and 4.89KHz, and the relative bandwidth is wideIs 0.33. The lower bound and the upper bound of the second sound sub-bandgap frequency are respectively 4.93KHz and 5.40KHz, and the relative bandwidth is 0.09. The lower and upper bound frequencies of the single-mode region are respectively 0.201KHz and 0.305KHz, and the relative bandwidth is 0.4.

Fig. 3 shows the influence of the narrow diameter ratio N on the first phonon band gap of the multilayer cylindrical three-dimensional five-mode metamaterial. It can be seen that as N increases, the upper boundary of the phonon band gap gradually increases, and the lower boundary frequency of the phonon band gap tends to increase first and then decrease slowly. When N is between 0.1 and 0.4 and between 2.0 and 3.0, the band gap upper-bound frequency of the multilayer cylindrical three-dimensional five-mode metamaterial is greater than the band gap lower-bound frequency, and the phonon band gap is opened. The first bandgap lower bound frequency rises from 1.30KHz to 7.95 KHz.

Fixing other structural parameters constant, d₁The effect of the narrow diameter ratio N on the quality factor FOM of asymmetric biconical and three-dimensional multilayer cylindrical five-mode metamaterial at 0.4mm is shown in fig. 4. The quality factors of the two five-mode metamaterial are increased firstly and then reduced with the increase of N. The asymmetric biconical five-mode metamaterial reaches the maximum value of 528.17 when N is 0.6. The three-dimensional multilayer cylindrical five-mode metamaterial reaches the maximum value of 989.22 when N is 0.8, and compared with the asymmetric biconical five-mode metamaterial, the three-dimensional multilayer cylindrical five-mode metamaterial can increase the figure of merit (FOM) by 87.3% to the maximum.

Example 2

In this embodiment, the multilayer cylindrical three-dimensional five-mode metamaterial is the same as that in embodiment 1, except that: the metamaterial is a local resonance type multilayer cylindrical three-dimensional five-mode metamaterial composed of composite media, and is composed of hard materials and soft materials, in the embodiment, the hard materials are polystyrene resin, the soft materials are silicon rubber, and the primitive cell structural parameters are as follows: 37.3mm for a, 16.15mm for H, D₃＝3mm,D₁＝D₂＝1.5mm,d₁＝0.55mm,h₁＝0.1H、h₂＝0.3H、h₃The energy band dispersion curve when the narrow diameter ratio N is 0.6 is 0.1H, as shown in fig. 5, it can be seen that the cylindrical three-dimensional five-mode metamaterial of the multilayer composite material opens two complete phonon band gaps except for the single mode region, wherein the first one isThe lower and upper boundary frequencies of the phonon band gap are 51.16Hz and 79.95Hz respectively, and the relative bandwidth of the first band gapIs 0.439. The lower and upper band gap frequencies of the second band gap are 81.9Hz and 83.97Hz, respectively, and the relative bandwidth of the second band gap is 0.025.

The phonon band gap start-stop frequency of the local resonance type five-mode metamaterial can be equivalent by using a spring-mass system principle, and the variation trend of the band gap is further analyzed by analyzing equivalent parameters in a simplified model. In FIG. 6, when N varies from 0.1 to 2.0, since d₁And d₂All parts are deformed, so that the equivalent rigidity is expressed by d₁And d₂And (4) jointly determining. As N increases, the equivalent stiffness also increases, while the equivalent mass remains substantially constant, so that the first bandgap lower bound frequency with N₂Is increased.

FIG. 7 shows the effect of narrow diameter ratio N on the quality factor FOM of asymmetric biconical local resonance-type and multilayer composite cylindrical three-dimensional five-mode metamaterial. It can be seen that both show a tendency to increase and then decrease as the asymmetry increases. The FOM of the asymmetric double-cone local resonance type three-dimensional five-mode metamaterial reaches the maximum value of 514.29 when N is 0.9, and the FOM of the multilayer composite material cylindrical three-dimensional five-mode metamaterial reaches the maximum value of 723.1 when N is 0.8. Compared with an asymmetric double-cone local resonance type three-dimensional five-mode metamaterial, the multilayer composite cylindrical three-dimensional five-mode metamaterial can improve the quality factor by 40.6% to the maximum.

The above-mentioned preferred embodiments are not intended to be taken as the full scope of the present invention, and any modifications and substitutions based on the multilayer cylindrical type five-mode metamaterial of the present invention are within the protection scope of the present invention.