Method for obtaining optimal low-frequency anisotropic five-mode metamaterial structure based on finite element method

Abstract

The invention discloses a method for obtaining an optimal low-frequency anisotropic five-mode metamaterial structure based on a finite element method. The method comprises the following steps: 1) obtaining structure parameters and material parameters of an original isotropic five-mode metamaterial; 2) introducing anisotropy to obtain four types of anisotropic five-mode metamaterials; 3) running in a simulation environment, updating structural information data, and calculating an energy band frequency value; (4) acoustic characteristic parameters such as quality factors, single modes and first band gaps of the four types of anisotropic five-mode metamaterials are calculated through a finite element algorithm; and 5) comparing the obtained acoustic characteristic parameters to obtain the optimal low-frequency anisotropic five-mode metamaterial structure. The finite element algorithm is applied to research the structure of the low-frequency anisotropic five-mode metamaterial, and compared with an original structure, the quality factor of the anisotropic five-mode metamaterial can be improved by 79.7% at most, the single-mode bandwidth can be improved by 98%, and the relative bandwidth of the first band gap can be improved by 500%.

Description

Technical Field

[0001] The present invention belongs to the technical field of topological properties of acoustic metamaterials, and in particular relates to a method for obtaining an optimal low-frequency anisotropic five-mode metamaterial structure based on a finite element method. Background Art

[0002] Acoustic invisibility has always been a typical problem in transformation acoustics. According to the different forms of characteristic parameters, it can be divided into two types: inertial acoustic cloak and five-mode acoustic cloak. Since inertial acoustic cloak will produce singular values ​​when using the transformation method, it requires a sudden change in body density, so it is not easy to achieve in engineering. Compared with the stringent requirements of inertial acoustic cloak on body density, five-mode acoustic cloak only requires the anisotropy of its modulus. Therefore, due to the compatibility of body density and fluid properties, as well as the perfect combination with the transformation method, the research on five-mode metamaterial acoustic wave control devices has become an important direction for future underwater acoustic wave control.

[0003] In the specific design of the five-mode metamaterial acoustic wave control device, it is necessary to design the corresponding cellular microstructure according to the macroscopic equivalent properties of the five-mode metamaterial. This process is the inverse problem of the homogenization method and often requires the use of optimization methods. In addition, due to the limitations of the requirements of the transformation acoustics theory, the equivalent parameters of the five-mode metamaterial cloak need to satisfy continuous changes. The design of the five-mode metamaterial underwater acoustic cloak is generally structurally gradual and non-ideal, which not only reduces the wave transmission efficiency, but also reduces the stability of the control device. Therefore, it is of great significance and research value to explore the design of five-mode metamaterial underwater acoustic wave control devices with high transmission efficiency and good robustness based on new mechanisms and new methods.

[0004] In recent years, the research on five-mode metamaterials is mainly based on the microstructure design based on the transformation acoustic principle and the generalized Snell's law. In the design process, the deformation and anisotropy of the cellular structure will be caused, thereby destroying the spatial symmetry of the five-mode metamaterial. This destruction of spatial symmetry will bring some novel properties to the five-mode metamaterial, such as topologically protected topological transport properties. However, this topological transport property in the five-mode metamaterial has not yet attracted the attention of researchers, and there is a lack of feasible solutions to realize topological transport properties in the five-mode metamaterial.

[0005] Topological transport refers to the phenomenon that topological edge states are transmitted along the edge of a crystal, and its most important feature is that it is immune to defects and disorder. The topological state in a phononic crystal can be achieved not only through methods such as modulation of time and space, acoustic ring coupling, and design of lattice symmetry, but also by applying a background flow velocity field. Then, for a five-mode metamaterial with phononic crystal characteristics, the study of designing a three-dimensional five-mode metamaterial underwater acoustic cloak based on the principle of acoustic transformation not only needs to consider the influence of its anisotropy, but also needs to reduce its operating frequency. Therefore, the present invention breaks the structural symmetry of the three-dimensional five-mode metamaterial primitive, designs a three-dimensional isotropic five-mode metamaterial structural unit based on an asymmetric bipyramidal primitive, proposes a method for suppressing internal sound waves, and uses the principle of local resonance to reduce its corresponding operating frequency, thereby designing an acoustic device for efficient transmission and regulation of underwater sound waves. Summary of the invention

[0006] The present invention aims to provide a method for obtaining an optimal low-frequency anisotropic five-mode metamaterial structure based on a finite element method.

[0007] Based on the above purpose, the present invention adopts the following technical solutions:

[0008] The method for obtaining an optimal low-frequency anisotropic five-mode metamaterial structure based on the finite element method comprises the following steps:

[0009] 1) Obtaining the structural parameters and material parameters of the original isotropic five-mode metamaterial;

[0010] 2) introducing anisotropy into the isotropic five-mode metamaterial of step 1) to obtain four types of anisotropic five-mode metamaterials;

[0011] 3) running the four anisotropic five-mode metamaterials in step 2) in a simulation environment, updating the structural information data, and calculating the band frequency values;

[0012] 4) The band frequency values ​​obtained in step 3) are calculated by the finite element method to obtain acoustic characteristic parameters such as quality factor, single mode and first band gap of four types of anisotropic five-mode metamaterials;

[0013] 5) Compare the acoustic characteristic parameters obtained in step 4) to obtain the optimal low-frequency anisotropic five-mode metamaterial structure.

[0014] As a further preferred embodiment of the present invention, the unit cell of the anisotropic five-mode metamaterial in step 2) is a face-centered cubic lattice formed by the intersection of sixteen asymmetric bipyramids, and the lattice constant of the unit cell is a.

[0015] As a further preferred embodiment of the present invention, each asymmetric bicone is composed of two truncated cone-shaped primitives, the bottom wide diameter ends of the two primitives are connected and the diameter of the wide diameter end is D, and the top narrow diameter ends of the two primitives are d 1 and d 2 ; The total height of the two primitives is H.

[0016] As a further preferred embodiment of the present invention, each unit cell is composed of 32 units connected at the narrow diameter end to form a face-centered cubic structure; 16 units connected inside the unit cell are made of soft material, and the rest are made of hard material, wherein the narrow diameter of the soft material unit is d 2 , the narrow diameter of the hard material element is d 1 .

[0017] As a further preferred embodiment of the present invention, the hard material is a resin polymer, and the soft material is silicone rubber.

[0018] As a further preferred embodiment of the present invention, in step 2), anisotropy is introduced by moving the intersection point P of the isotropic five-mode metamaterial along the four directions of X-axis, Y-axis, Z-axis and diagonal respectively, breaking the spatial symmetry, and constructing four types of anisotropic five-mode metamaterials; the degree of anisotropy can make the originally identical four primitives in the primitive cell different according to the moving distance (deviation) of the narrow diameter intersection of the primitive cell, and active regulation is realized at the same time.

[0019] As a further preferred embodiment of the present invention, the specific method of introducing anisotropy in step 2) is to set the acoustic coordinates P (m) of the intersection point where the narrow diameter ends of each asymmetric double cone are connected. 1 a,m 2 a,m 3 a), m i (i=1,2,3) is in the range of 0.05~0.475, the isotropic five-mode metamaterial takes the coordinates of point P (0.25a,0.25a,0.25a) as the standard, and the narrow diameter d of the hard material is 1 and soft material narrow diameter d 2 The ratio of is defined as the asymmetry N is 0.6, 0.8, 1.0, 1.2, and 1.4. In subsequent research, the anisotropy is introduced into the five-mode metamaterial by moving the coordinates of point P and changing the value of N.

[0020] As a further preferred embodiment of the present invention, the finite element algorithm in step 4) comprises the following steps:

[0021] a) Data preprocessing;

[0022] b) Iterative training: Through the dynamic update strategy and Adam optimizer, in each training iteration, the loss function is calculated and then the model parameters are updated through back propagation;

[0023] c) Model evaluation: Use validation sets or cross-validation methods to evaluate the trained model to check the performance and generalization ability of the model;

[0024] d) Model application: Use the trained and validated model to predict insulator structural parameter data.

[0025] As a further preferred embodiment of the present invention, step a) data preprocessing: the parameter data of the insulator structure is cleaned and normalized, and then divided into a training set and a test set.

[0026] The low-frequency anisotropic five-mode metamaterial obtained above will be used in future underwater sound wave regulation.

[0027] The present invention selects a narrow diameter intersection point P of a primitive cell as a reference point, and moves the intersection point P along four different directions to construct a three-dimensional anisotropic five-mode metamaterial. The corresponding anisotropic unit cell structure is as follows: Figure 1 (a)- Figure 1 (d) are shown, respectively named as Model 1 (X-axis), Model 2 (Y-axis), Model 3 (Z-axis), and Model 4 (body diagonal). The present invention achieves the purpose of the invention by adopting an isotropic five-mode metamaterial with a symmetrical double-cone structure. First, four anisotropic five-mode metamaterials are constructed by changing the position of the narrow diameter intersection, which are used to simulate the influence of the anisotropy generated by the body diagonal and the four situations of the X-axis, Y-axis, and Z-axis in the spatial geometry on the acoustic properties of the five-mode metamaterial, and then the boundary topology conditions are set based on the finite element method, and the five-mode metamaterial structure is meshed and parameterized. Scan. Finally, the obtained parameters are processed by matlab, and the acoustic characteristics are deeply studied through finite element numerical simulation, and the influence of the generation of anisotropy on the low-frequency characteristics of the five-mode metamaterial is analyzed and compared, so as to obtain the optimal low-frequency anisotropic five-mode metamaterial structure.

[0028] Compared with the prior art, the present invention has the following beneficial effects:

[0029] 1) The present invention selects the finite element method as a numerical method. The finite element method is a numerical method used to solve complex engineering and mathematical physics problems. The finite element method can conveniently consider various material properties. For linear materials, the deformation relationship can be accurately calculated based on basic theories such as Hooke's law. At the same time, boundary conditions are also one of the important conditions for the numerical calculation of five-mode metamaterials. The finite element method can flexibly apply various boundary conditions, such as displacement boundary conditions, force boundary conditions, thermal boundary conditions, etc. When simulating the introduction of anisotropy through deformation of five-mode metamaterials, appropriate displacement and force boundary conditions are applied to analyze stress distribution and deformation.

[0030] 2) In the study of low-frequency acoustic properties, the present invention constructs four different types of anisotropic five-mode metamaterials for comparative analysis. In three-dimensional geometric space, anisotropy is introduced from four different directions: body diagonal, X-axis, Y-axis, and Z-axis. Through comparative analysis, the differences in acoustic properties of different types of anisotropic five-mode metamaterials at low frequencies can be deeply explored. Each type of metamaterial may also have a unique microstructure and physical mechanism, and these differences will be reflected in the low-frequency acoustic properties. In addition, through experimental measurement and comparative analysis of four different types of metamaterials, the theoretical model can be verified and corrected to make it more accurately reflect the physical behavior of actual materials and improve the reliability and predictive ability of the theoretical model.

[0031] 3) When constructing the anisotropic five-mode metamaterial, the present invention uses a composite material for its double cone structure, namely a soft material (rubber material) and a hard material. Soft materials (rubber materials) and hard materials have completely different physical properties. Rubber materials usually have a low elastic modulus and can produce large deformations when subjected to sound waves. This large deformation characteristic makes it possible for rubber materials to exhibit unique vibration modes and energy dissipation mechanisms at low frequencies. Hard materials have a higher elastic modulus and a smaller deformation capacity. It may be more inclined to reflect and scatter sound waves in low-frequency acoustic characteristics. Combining the two can cover a wider range of acoustic characteristics, including absorption, reflection, scattering of sound waves, and wave propagation modes. In addition, during the propagation of low-frequency sound waves, hard materials can serve as a structural skeleton to provide a stable support and reflection interface, while soft materials can be attached to the surface of hard materials or filled in their internal gaps, using their own viscoelasticity to absorb the energy of low-frequency sound waves.

[0032] 4) The present invention sets the acoustic coordinates P of the intersection point where the narrow diameter ends of each asymmetric double cone are connected and the narrow diameter d of the hard material. 1 and soft material narrow diameter d 2 The ratio asymmetry N of the five-mode metamaterial is used to realize the active adjustable function of the anisotropic five-mode metamaterial. In previous studies, the five-mode metamaterials are often designed with a single structure, and when designed for low-frequency bands, they do not have a good structural size, which will make it difficult to apply them in real life in the future. By setting the structural parameters, the performance of the five-mode metamaterial can be obtained according to the specific low-frequency acoustic requirements, and by continuously adjusting the parameters, the sound absorption coefficient of the material can be increased, the reflectivity can be reduced, or the wave propagation mode can be improved. These parameters enable the five-mode metamaterial to meet these diverse needs. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1(a) Anisotropic five-mode metamaterial model structure in the diagonal direction (model 1); (b) Anisotropic five-mode metamaterial model structure in the X-axis direction (model 2); (c) Anisotropic five-mode metamaterial model structure in the Y-axis direction (model 3); (d) Anisotropic five-mode metamaterial model structure in the Z-axis direction (model 4); (e) Isotropic five-mode metamaterial model structure; where a = 37.3 mm, D = 3 mm, d 1 =0.55mm,d 2 =N×d 1 mm, H = h 1 +h 2 ;

[0034] Figure 2 Effect of anisotropy on the band structure of five-mode metamaterials; (a) Band structure diagram of model 1 under acoustic coordinates (0.3a, 0.3a, 0.3a); (b) Band structure diagram of model 2 under acoustic coordinates (0.3a, 0.25a, ​​0.25a); (c) Band structure diagram of model 3 under acoustic coordinates (0.4a, 0.25a, ​​0.25a); (d) Band structure diagram of model 4 under acoustic coordinates (0.4a, 0.25a, ​​0.25a); The gray area represents the single-mode region of the five-mode metamaterial, and the black area represents the first band gap region of the five-mode metamaterial;

[0035] Figure 3 Effect of anisotropy on the quality factor of five-mode metamaterials; (a) Quality factor comparison of model 1; (b) Quality factor comparison of model 2; (c) Quality factor comparison of model 3; (d) Quality factor comparison of model 4;

[0036] Figure 4 Effect of anisotropy on the single-mode upper bound frequency of five-mode metamaterials; (a) Single-mode upper bound frequency comparison of model 1; (b) Single-mode upper bound frequency comparison of model 2; (c) Single-mode upper bound frequency comparison of model 3; (d) Single-mode upper bound frequency comparison of model 4;

[0037] Figure 5 Effect of anisotropy on the single-mode lower bound frequency of five-mode metamaterials; (a) Single-mode lower bound frequency comparison of model 1; (b) Single-mode lower bound frequency comparison of model 2; (c) Single-mode lower bound frequency comparison of model 3; (d) Single-mode lower bound frequency comparison of model 4;

[0038] Figure 6 Effect of anisotropy on the single-mode relative bandwidth of five-mode metamaterials; (a) Single-mode relative bandwidth comparison of model 1; (b) Single-mode relative bandwidth comparison of model 2; (c) Single-mode relative bandwidth comparison of model 3; (d) Single-mode relative bandwidth comparison of model 4;

[0039] Figure 7 Effect of anisotropy on the upper frequency of the first band gap of five-mode metamaterials; (a) Comparison of the upper frequency of the first band gap of model 1; (b) Comparison of the upper frequency of the first band gap of model 2; (c) Comparison of the upper frequency of the first band gap of model 3; (d) Comparison of the upper frequency of the first band gap of model 4;

[0040] Figure 8 Effect of anisotropy on the upper frequency of the first band gap of five-mode metamaterials; (a) Comparison of the upper frequency of the first band gap of model 1; (b) Comparison of the upper frequency of the first band gap of model 2; (c) Comparison of the upper frequency of the first band gap of model 3; (d) Comparison of the upper frequency of the first band gap of model 4;

[0041] Fig. 9 Effect of anisotropy on the relative bandwidth of the first band gap of five-mode metamaterials; (a) Comparison of the relative bandwidth of the first band gap of model 1; (b) Comparison of the relative bandwidth of the first band gap of model 2; (c) Comparison of the relative bandwidth of the first band gap of model 3; (d) Comparison of the relative bandwidth of the first band gap of model 4; DETAILED DESCRIPTION

[0042] The present invention will be further described below in conjunction with specific implementations and accompanying drawings.

[0043] Example 1

[0044] The method for obtaining an optimal low-frequency anisotropic five-mode metamaterial structure based on the finite element method of this embodiment includes the following steps:

[0045] 1) Obtaining the structural parameters and material parameters of the original isotropic five-mode metamaterial;

[0046] 2) introducing anisotropy into the isotropic five-mode metamaterial of step 1) to obtain four types of anisotropic five-mode metamaterials;

[0047] 3) running the four anisotropic five-mode metamaterials in step 2) in a simulation environment, updating the structural information data, and calculating the band frequency values;

[0048] 4) The band frequency values ​​obtained in step 3) are calculated by the finite element method to obtain acoustic characteristic parameters such as quality factor, single mode and first band gap of four types of anisotropic five-mode metamaterials;

[0049] 5) Compare the acoustic characteristic parameters obtained in step 4) to obtain the optimal low-frequency anisotropic five-mode metamaterial structure.

[0050] In step 2), the anisotropic five-mode metamaterial unit cell is a face-centered cubic lattice formed by the intersection of sixteen asymmetric bipyramids, and the lattice constant of the unit cell is a, such as Figure 1As shown, each asymmetric bicone is composed of two truncated cone-shaped primitives, the bottom wide diameter ends of the two primitives are connected and the diameter of the wide diameter end is D, and the top narrow diameter ends of the two primitives are d 1 and d 2 ; The total height of the two primitives is H. Each unit cell is composed of 32 primitives connected at the narrow diameter end to form a face-centered cubic structure; the 16 primitives connected inside the unit cell are soft materials, and the rest are hard materials, where the narrow diameter of the soft material primitive is d 2 , the narrow diameter of the hard material element is d 1 The hard material is a resin polymer, and the soft material is silicone rubber.

[0051] In step 2), anisotropy is introduced by moving the intersection point P of the isotropic five-mode metamaterial along the four directions of X-axis, Y-axis, Z-axis and diagonal respectively, breaking the spatial symmetry and constructing four types of anisotropic five-mode metamaterials; the degree of anisotropy can make the four originally identical primitives in the primitive cell different according to the moving distance (deviation) of the narrow diameter intersection of the primitive cell, and realize active regulation at the same time.

[0052] The specific method of introducing anisotropy described in step 2) is to set the acoustic coordinates P (m 1 a,m 2 a,m 3 a), m i (i=1,2,3) is in the range of 0.05~0.475, the isotropic five-mode metamaterial is based on the coordinates of point P (0.25a,0.25a,0.25a), and the hard material narrow diameter d 1 and soft material narrow diameter d 2 The ratio of is defined as the asymmetry N is 0.6, 0.8, 1.0, 1.2, and 1.4. In subsequent research, the anisotropy is introduced into the five-mode metamaterial by moving the coordinates of point P and changing the value of N.

[0053] The finite element algorithm described in step 4) comprises the following steps:

[0054] a) Data preprocessing: cleaning the parameter data of the insulator structure, normalizing it, and dividing it into a training set and a test set;

[0055] b) Iterative training: Through the dynamic update strategy and Adam optimizer, in each training iteration, the loss function is calculated and then the model parameters are updated through back propagation;

[0056] c) Model evaluation: Use validation sets or cross-validation methods to evaluate the trained model to check the performance and generalization ability of the model;

[0057] d) Model application: Use the trained and validated model to predict insulator structural parameter data.

[0058] Experimental Example 1

[0059] Based on the traditional symmetrical isotropic five-mode metamaterial model, the present invention proposes four anisotropic five-mode metamaterials, such as Figure 1 The anisotropic three-dimensional five-mode metamaterial unit cell structure proposed in the present invention is as follows Figure 1 As shown in (a)-(d), the face-centered cubic lattice is formed by the intersection of sixteen symmetrical bipyramids. It is composed of 32 primitives connected at the narrow end to form a face-centered cubic structure. The wide diameter of the asymmetric bipyramid is D, and the narrow diameters of the hard and soft materials are d 1 and d 2 The height of the double cone is H, and the heights of the hard and soft materials are h 1 and h 2 , satisfying the equivalence relation h 1 +h 2 =H, the lattice constant is a, and the 16 connected primitives inside each unit cell are soft materials, and the rest are hard materials. There are many ways to construct three-dimensional anisotropic five-mode metamaterials. The most direct method is to select a narrow diameter intersection point P of a unit cell as a reference point, and move the intersection point P along the diagonal, X-axis, Y-axis, and Z-axis to construct a three-dimensional anisotropic five-mode metamaterial. The corresponding anisotropic unit cell structure is as follows: Figure 1 (a)-(d) are shown, respectively named as Model 1 (body diagonal), Model 2 (X axis), Model 3 (Y axis), Model 4 (Z axis). In the present invention, we set the acoustic coordinates of point P as (m 1 a,m 2 a,m 3 a), and an isotropic five-mode metamaterial ( Figure 1 (e)) is used as a reference, and the distance that point P moves is defined as the deviation In the present invention, the magnitude of the deviation can also represent the degree of anisotropy.

[0060] In order to study the energy band structure and transmission characteristics of the designed structure, the present invention uses the finite element analysis software COMSOL Multiphysics to perform numerical calculations to study the energy band structure and transmission characteristics of the phononic crystal. Among them, the fixed lattice constant a = 10mm, the air density ρ = 1.12Kg / m 3, the speed of sound c = 343m / s. When using COMSOL Multiphysics numerical simulation, boundary conditions should be applied to the anisotropic five-mode metamaterial, and 21 energy bands should be set for calculation. After obtaining the current energy band parameters, the energy band parameters are processed by finite element method using Matlab, and then various acoustic properties of the five-mode metamaterial are obtained, such as band structure, quality factor, single-mode characteristics, first band gap characteristics, etc.

[0061] In the present invention, we select the asymmetry N as 0.6, 0.8, 1.2, and 1.4 to simulate the effect of anisotropy on the band structure of the five-mode metamaterial, and set the coordinates of the narrow diameter intersection points P of the primitive cell to be uniformly (0.25a, ​​0.25a, ​​0.25a). The calculated band structures of the four types of anisotropic five-mode metamaterials are as follows: Figure 2 As shown. The horizontal and vertical coordinates correspond to the entire simplified Brillouin zone boundary and frequency respectively. The black area is the first band gap area, and the gray area is the single mode area. Figure 2 In (a), the acoustic coordinates of the narrow diameter intersection point P of model 1 are set to (0.3a, 0.3a, 0.3a) during the diagonal movement of the body. Figure 2 In (b), the acoustic coordinates of the narrow diameter intersection point P of model 2 are set to (0.3a, 0.25a, ​​0.25a) during the X-axis movement. Figure 2 In (c), the acoustic coordinates of the narrow diameter intersection point P of model 3 are set to (0.4a, 0.25a, ​​0.25a) during the Y-axis movement. Figure 2 In (d), the acoustic coordinates of the narrow diameter intersection point P are set to (0.4a, 0.25a, ​​0.25a) during the Z-axis movement of model 4. As can be seen from the figure, models 1, 2, and 3 all open a phonon band gap, while model 4 does not have a phonon band gap due to the introduction of anisotropy.

[0062] The quality factor of the anisotropic five-mode metamaterial can be obtained by the two line segments (C B and C G ) is obtained by the slope ratio of the first band gap. The propagation of compression waves and shear waves in the first band gap range will be suppressed. In the frequency range of the single-mode region, compression waves and shear waves will be decoupled. In other words, only compression waves can propagate and shear waves will be suppressed. The size of the quality factor indicates the ability of the five-mode metamaterial to decouple compression waves and shear waves. The quality factor has the following proportional relationship with the ratio of the phase velocity of compression waves and shear waves:

[0063] G=C 44 (1)

[0064] B=(C 11 +2C 12 ) / 3 (2)

[0065]

[0066] Where C 11 , C 12 , C 44 are the three independent elastic coefficients of the three-dimensional five-mode metamaterial elastic matrix, C B is the relative velocity of the five-mode metamaterial compression wave, C G is the shear wave relative velocity.

[0067] The above formula also reflects that the quality factor is determined by the slopes of the compression wave and shear wave of the phonon band gap structure.

[0068] The present invention discusses the influence of the quality factor caused by the introduction of anisotropy into the five-mode metamaterial. Figure 3 As shown. Figure 3 In (a), the quality factor of model 1 changes similarly to a sine function, showing a trend of first increasing, then decreasing, and then increasing again as the narrow diameter intersection point P moves. For model 1, the maximum value of the quality factor can reach 504. Figure 3 In (b), the quality factor of model 2 shows a change trend similar to a quadratic function, which increases first and then decreases as the narrow diameter intersection point P moves. For model 2, the maximum value of the quality factor can reach 319. Figure 3 In (c), the variation trend of model 3 is similar to that of model 2. For model 3, the maximum value of the quality factor can reach 318. Figure 3 In (d), as the narrow diameter intersection point P moves, the quality factor value shows a slow downward trend. For model 4, the maximum value of the quality factor can reach 2297, which can be increased by 79.7%. In addition, when the N value increases, the quality factor of the same type of anisotropic five-mode metamaterial at the same position will gradually decrease.

[0069] The present invention discusses the influence of the single-mode characteristics caused by the introduction of anisotropy into the five-mode metamaterial. Figure 4 , Figure 5 , Figure 6 The effect of anisotropy on the upper frequency of a single mode of a five-mode metamaterial is shown in Figure 4 As shown, through Figure 4 It can be seen that for the four models, the single-mode upper frequency shows a quadratic variation trend, and with the movement of the narrow diameter intersection point P, it shows a trend of first increasing and then decreasing. Figure 4 In (a), the single-mode upper frequency of model 1 is between 8.61Hz and 28.75Hz. Figure 4 In (b), the single-mode upper frequency of model 2 is between 14.79 Hz and 28.75 Hz. Figure 4 In (c), the single-mode upper frequency of model 3 is between 7.13 Hz and 28.76 Hz. Figure 4 In (d), the single-mode upper frequency of model 4 is between 14.71 Hz and 28.75 Hz.

[0070] The effect of anisotropy on the single-mode lower frequency of the five-mode metamaterial is as follows: Figure 5 As shown in Figure 2, the overall trend is slowly increasing. Figure 4 In (a), the single-mode upper frequency of model 1 is between 1.9 Hz and 7.4 Hz. Figure 4 In (b), the single-mode upper frequency of model 2 is between 3.3 Hz and 7.65 Hz. Figure 4 In (c), the single-mode upper frequency of model 3 is between 3.27Hz and 7.28Hz. Figure 4 In (d), the single-mode upper frequency of model 4 is between 3.28 Hz and 7.30 Hz.

[0071] The effect of anisotropy on the single-mode relative bandwidth of the five-mode metamaterial is as follows: Figure 6 As shown, when the five-mode metamaterial is a highly symmetric structure, the single-mode relative bandwidth reaches the maximum under the influence of the deviation S = 0. Among the four models, the maximum single-mode relative bandwidth can reach 1.42, which is 98% higher than that of the symmetric structure.

[0072] The frequency range of the first band gap determines the lower limit of the frequency of low-frequency sound waves that can be manipulated by the anisotropic five-mode metamaterial. Figure 7 , Figure 8 , Fig. 9 The effect of anisotropy on the upper and lower bound frequencies of the first band gap and the relative bandwidth is discussed. Figure 7 In , when N = 1, the five-mode metamaterial is a highly symmetrical structure, and the first band gap is opened only when the acoustic coordinates of the narrow diameter intersection point P take a certain value. Figure 7 In (a), the upper frequency of the first band gap of model 1 is between 36.57 Hz and 170.62 Hz. Figure 7 In (b), the upper frequency of the first band gap of model 2 is between 20.93 Hz and 133.52 Hz. Figure 7 In (c), the upper bound frequencies of the first band gap of model 3 are 83.28 Hz and 134.69 Hz respectively. Figure 7 In (d), when N = 1, the first band gap does not appear in model 4. In addition, we further discuss the effect of the asymmetry S on the upper frequency of the first band gap when N ≠ 1. Due to the asymmetry of the biconical structure, each value of the acoustic coordinates of the narrow diameter intersection point P can open the first band gap, and the increase in the deviation S will shift the upper frequencies of these bands to higher frequencies.

[0073] The effect of anisotropy on the lower frequency of the first band gap of the five-mode metamaterial is as follows: Figure 8 shown. Figure 8 The influence of the deviation degree S on the lower limit frequency of the first band gap is proposed. When N=1, the lower limit frequency of the first band gap cannot appear at a certain value of the acoustic coordinates of the narrow diameter intersection P. When N≠1, as the deviation degree S increases, the lower limit frequency of the first band gap will show an increasing trend relative to the symmetrical structure.

[0074] The effect of anisotropy on the relative bandwidth of the first band gap of the five-mode metamaterial is as follows: Fig. 9 As shown. Fig. 9 In the figure, when the five-mode metamaterial is a highly symmetrical structure (N=1) and the deviation S=0, they have little effect on the relative bandwidth of the first band gap. However, when the five-mode metamaterial is an asymmetric structure (N≠1), the relative bandwidth of the first band gap will gradually increase due to the anisotropy caused by the change of the biconical structure and the movement of the narrow diameter intersection point P. Fig. 9 In (a), the first band gap relative bandwidth of model 1 can reach up to 0.62, which is 500% higher than that of the symmetric structure. Fig. 9 In (b), the first band gap relative bandwidth of model 2 can reach up to 0.13, which is 30% higher than that of the symmetric structure. Fig. 9 In (c), the first band gap relative bandwidth of model 3 can reach a maximum of 0.21, which is 110% higher than that of the symmetric structure. Fig. 9 In (d), the relative bandwidth of the first band gap of model 4 is similar to that of model 2, and can reach a maximum of 0.13, which is a relative increase of 30%.

[0075] The four anisotropic three-dimensional five-mode metamaterials proposed in the present invention for studying low-frequency acoustic properties break the spatial structural symmetry of the local resonance five-mode metamaterial by changing the spatial position of the narrow diameter connection point P. Compared with the isotropic three-dimensional five-mode metamaterial, anisotropy will improve the acoustic properties of the five-mode metamaterial. The method of the present invention provides a basis for the further application of anisotropic three-dimensional five-mode metamaterials in future low-frequency sound wave control devices.

Claims

1. A method for obtaining an optimal low-frequency anisotropic five-mode metamaterial structure based on the finite element method, characterized in that: The following steps are involved: 1) Obtaining the structural parameters and material parameters of the original isotropic five-mode metamaterial; 2) introducing anisotropy into the isotropic five-mode metamaterial of step 1) to obtain four types of anisotropic five-mode metamaterials; 3) running the four anisotropic five-mode metamaterials in step 2) in a simulation environment, updating the structural information data, and calculating the band frequency values; 4) Calculating the band frequency values ​​obtained in step 3) by finite element algorithm to obtain acoustic characteristic parameters such as quality factor, single mode and first band gap of four types of anisotropic five-mode metamaterials; 5) Compare the acoustic characteristic parameters obtained in step 4) to obtain the optimal low-frequency anisotropic five-mode metamaterial structure.

2. The method for obtaining an optimal low-frequency anisotropic five-mode metamaterial structure based on the finite element method according to claim 1, characterized in that: The unit cell of the anisotropic five-mode metamaterial in step 2) is a face-centered cubic lattice formed by the intersection of sixteen asymmetric bipyramids, and the lattice constant of the unit cell is a.

3. The method for obtaining an optimal low-frequency anisotropic five-mode metamaterial structure based on the finite element method according to claim 1, characterized in that: Each asymmetric bicone is composed of two primitives with a truncated cone structure. The wide diameter ends of the bottom surfaces of the two primitives are connected and the diameter of the wide diameter end is D. The diameters of the narrow diameter ends of the top surfaces of the two primitives are d1 and d2 respectively; the total height of the two primitives is H.

4. The method for obtaining an optimal low-frequency anisotropic five-mode metamaterial structure based on the finite element method according to claim 3, characterized in that: Each unit cell is composed of 32 units connected at the narrow diameter end to form a face-centered cubic structure; the 16 units connected inside the unit cell are made of soft materials, and the rest are made of hard materials, where the narrow diameter of the soft material unit is d2, and the narrow diameter of the hard material unit is d1.

5. The method for obtaining an optimal low-frequency anisotropic five-mode metamaterial structure based on the finite element method according to claim 4, characterized in that: The hard material is a resin polymer, and the soft material is silicone rubber.

6. The method for obtaining an optimal low-frequency anisotropic five-mode metamaterial structure based on the finite element method according to claim 5, characterized in that: In step 2), anisotropy is introduced by moving the intersection point P of the isotropic five-mode metamaterial along the four directions of X-axis, Y-axis, Z-axis and diagonal respectively to break the spatial symmetry to construct four types of anisotropic five-mode metamaterials. The degree of anisotropy can make the four originally identical primitives in the primitive cell different according to the moving distance (deviation) of the narrow diameter intersection of the primitive cell, and active regulation can be achieved at the same time.

7. The method for obtaining an optimal low-frequency anisotropic five-mode metamaterial structure based on the finite element method according to claim 6, characterized in that: The specific method of introducing anisotropy described in step 2) is to set the acoustic coordinates P (m1a, m2a, m3a) of the intersection point where the narrow diameter ends of each asymmetric double cone are connected, m i (i=1,2,3) is in the range of 0.05~0.

475. The isotropic five-mode metamaterial takes the coordinates of point P (0.25a,0.25a,0.25a) as the standard, and defines the ratio of the narrow diameter d1 of the hard material to the narrow diameter d2 of the soft material as the asymmetry N is 0.6, 0.8, 1.0, 1.2, or 1.

4.

8. The method for obtaining an optimal low-frequency anisotropic five-mode metamaterial structure based on the finite element method according to claim 1, characterized in that: The finite element algorithm described in step 4) comprises the following steps: a) Data preprocessing; b) Iterative training: Through the dynamic update strategy and Adam optimizer, in each training iteration, the loss function is calculated and then the model parameters are updated through back propagation; c) Model evaluation: Use validation sets or cross-validation methods to evaluate the trained model to check the performance and generalization ability of the model; d) Model application: Use the trained and validated model to predict the insulator structural parameter data.

9. The method for obtaining an optimal low-frequency anisotropic five-mode metamaterial structure based on the finite element method according to claim 7, characterized in that: Step a) Data preprocessing: The parameter data of the insulator structure is cleaned and normalized, and then divided into a training set and a test set.

10. Application of the low-frequency anisotropic five-mode metamaterial prepared by the method according to any one of claims 1 to 9 in future underwater sound wave control.

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