Dual-mass resonator structure, design method and shape and function fused metamaterial structure

Abstract

The invention belongs to the technical field of vibration reduction metamaterial structure design, and aims to solve the problem of poor vibration reduction effect in metamaterial structure design. The invention provides a dual-mass resonator structure, a design method and a shape and function fused metamaterial structure, the dual-mass resonator structure comprises a plurality of connected cell structures, and two adjacent cell structures are connected through a cell outer frame; the double-bridge-arm structure comprises two bridge arms which are led out from the inner frame of the cell element outer frame to the inner side; the dual-mass structure comprises two groups of local resonant columns, and one group of local resonant columns is arranged at one end, far away from the cell outer frame, of any bridge arm; and meanwhile, a shape and function fused metamaterial with a customizable vibration isolation belt is designed and prototype, and various metamaterial shapes are integrated into different functional frames by the structure, so that the coherent design of forms and functions is realized. By utilizing the characteristics of the metamaterial, the vibration and noise reduction performance of the structure is effectively improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of vibration reduction metamaterial structure design, and in particular relates to a dual-mass resonator structure, a design method and a shape-function fusion metamaterial structure. Background Art

[0002] Mechanical metamaterials are a type of material that exhibits unconventional mechanical properties and structural characteristics through carefully designed geometric structures. They have attracted widespread attention in the field of mechanical research. By carefully designing their microstructures and geometric shapes, metamaterials exhibit unique properties such as negative refractive index, negative Poisson's ratio, negative mass density and negative elastic modulus. The design and preparation of metamaterials have shown great potential in the fields of electromagnetic wave regulation, acoustic wave control, photonics, etc.

[0003] With the development of science and technology, vibration and noise reduction technology has become increasingly important in engineering applications. Traditional methods such as sound-absorbing materials and sound-insulating structures are inefficient or unsuitable in some scenarios. Therefore, metamaterial structure design as an emerging vibration and noise reduction technology has received widespread attention in recent years.

[0004] The existing technical solutions have the defect of poor vibration reduction effect in the metamaterial structure design. Summary of the invention

[0005] In order to solve at least one of the above technical problems existing in the prior art, the present invention provides a dual-mass resonator structure, a design method and a shape-function fusion metamaterial structure.

[0006] The present invention is implemented by the following technical scheme: a dual-mass resonant substructure, comprising a plurality of connected cell structures, wherein the cell structure comprises a cell outer frame, a double bridge arm structure and a dual-mass structure; two adjacent cell structures are connected via the cell outer frame; the double bridge arm structure comprises two bridge arms extending inward from the inner frame of the cell outer frame; the dual-mass structure comprises two groups of local resonance columns, one end of any bridge arm away from the cell outer frame is provided with a group of local resonance columns, the number of resonance columns in any group of local resonance columns is an even number, and the resonance columns are symmetrically arranged at the upper and lower end surfaces of the bridge arm.

[0007] Preferably, the end of the bridge arm connected to the outer frame of the cell is the tail, the end with the local resonance column is the head, there is a separation gap between the heads of the two bridge arms, and there is a separation gap between the head of the bridge arm and the outer frame of the cell.

[0008] Preferably, the structural parameters of the dual-mass resonant substructure include the size of the matrix and the size of the local resonance unit, wherein p' in the matrix size represents the initial width of the bridge arm, q' represents the reference position of the bridge arm, r2 and r1 represent the outer chamfer radius and the inner chamfer radius of the bridge arm respectively, and j' represents the centerline length of the bridge arm; a represents the length of the outer frame of the cell, b represents the width of the outer frame of the cell, c represents the height of the outer frame of the cell, and d represents the thickness of the outer frame of the cell;

[0009] In the local resonance unit size, S' represents the area of ​​the local resonance column, and h represents the height from the bottom surface of the local resonance column to the bottom surface of the cell outer frame.

[0010] Preferably, the outer frame of the cell is a square frame structure, and the two bridge arms and the two groups of local resonance columns are arranged in a central symmetry with respect to the center position of the square frame structure; the bridge arm is a special-shaped part, the tail of the bridge arm is connected to a point on one side of the outer frame of the cell, the diameter of the extension part of the tail of the bridge arm toward its head gradually increases, and the head of the bridge arm is a semicircular structure; the local resonance column is a cylinder, and the center line of the local resonance column passes through the center of the head of the bridge arm.

[0011] A second aspect of the present invention provides a dual-mass resonator structure design method, comprising the following steps:

[0012] S1: Based on the structural analysis of the double-mass resonator, a mechanical model of the double-mass-double-spring unit structure of the cell structure is established;

[0013] S2: Arrange n continuous cell structures in a one-dimensional array and establish a mechanical model of the entire array;

[0014] S3: Select two adjacent cell structures as research objects to form equivalent repeated cells;

[0015] S4: Remodel the equivalent cell and study the low-frequency characteristics of the dual-mass local resonance metamaterial cell structure.

[0016] Preferably, the steps of studying the low-frequency characteristics of the dual-mass localized resonance metamaterial cell structure include:

[0017] S41: Establish the motion equation of the equivalent repeated cell and obtain the equivalent mass m of the equivalent repeated cell eff ;

[0018] S42: Ignore the difference between boundary and internal cells, combine n equivalent repeated cells, establish a linear homogeneous equation system, and substitute it into the motion equation of a single equivalent repeated unit cell to obtain the dispersion relation expression of the dual-mass resonator;

[0019] S43: Based on the dispersion relation expression of the double-mass resonator, the motion equation of the n-periodic system is simplified, and the theoretical transmission loss formula Tr' of the mechanical model is derived.

[0020] The third aspect of the present invention provides a shape-function fusion metamaterial structure, including a matrix structure and a plurality of embedded structures, wherein the embedded structure is embedded in the hole structure of the matrix structure, and the embedded structure is composed of a one-dimensional array arrangement of n consecutive dual-mass resonant sub-cell structures.

[0021] Preferably, the embedded structure comprises n dual-mass resonant sub-cell structures of different types or of the same type with different structural parameters, for adjusting the resonance frequency of the superstructure.

[0022] Preferably, the matrix structure is a hexagonal tubular honeycomb structure, slots are provided in the internal hole structure, and plug connectors matching the slots are provided on both sides of the cell structure of the dual-mass resonator.

[0023] Compared with the prior art, the present invention has the following beneficial effects:

[0024] The present invention designs and studies a type of dual-mass resonant substructure, establishes a mechanical theoretical model, and compares it with the traditional structure. Through theoretical model comparison and analysis, the "dual-unit" metamaterial structure has three theoretical negative mass band gaps. Finite element simulation and experiments on the model show that this structure performs well in low-frequency vibration and has a wide bandgap in the low-frequency range.

[0025] It has a low-frequency band designable shape-function fusion metamaterial structure. Through finite element simulation and experimental verification, the maximum vibration reduction amplitude is reduced from 10μm to 3μm. In addition, embedding a dual-mass resonant substructure in the hole structure of the matrix structure can not only reduce the amplitude, but also reduce the high-frequency components, making the entire structure more stable, and can be used for customized shock absorption and noise reduction and structural lightweight design.

[0026] In the research of mechanical fusion metamaterials, a superstructure with customized band gap is realized through intelligent layout. This technological innovation will be applied to the field of vibration reduction and noise reduction of precision instruments and rotating machinery. By utilizing the characteristics of metamaterials, structures with specific frequency band gaps can be designed, which effectively improves vibration resistance and reduces noise levels. The results of this research are expected to bring significant applications in the field of precision instruments and rotating machinery and promote the development of the industry. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. 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 these drawings without paying creative work.

[0028] Figure 1is a diagram of the construction process of the equivalent repeating cell of the present invention;

[0029] Figure 2 It is a schematic diagram of the negative mass region of the "Tai Chi dual-unit" metamaterial structure of the present invention;

[0030] Figure 3 It is the dispersion relation diagram of the "Tai Chi dual unit" metamaterial structure of the present invention;

[0031] Figure 4 It is the theoretical transmission loss diagram of the "Tai Chi dual-unit" metamaterial structure of the present invention;

[0032] Figure 5 It is a formation diagram of a dual-mass resonant substructure in the COMSOL software of the present invention in a process from wave vector Γ to X with a frequency of 128.53 Hz;

[0033] Figure 6 It is a formation diagram of a dual-mass resonant substructure in the COMSOL software of the present invention in a process from wave vector M to Γ with a frequency of 24.075 Hz;

[0034] Figure 7 The structural energy band diagram drawn by calculating 20 sets of characteristic frequencies in the software of the present invention;

[0035] Figure 8 yes Figure 7 Schematic diagram of data enlargement from 3500Hz to 6500Hz;

[0036] Fig. 9 It is the simulation result diagram of the dual mass resonance substructure under different parameters;

[0037] Fig.10 This is a schematic diagram of the structure of the "Tai Chi dual unit" metamaterial structure of the present invention. Figure 1 ;

[0038] Fig.11 This is a schematic diagram of the structure of the "Tai Chi dual unit" metamaterial structure of the present invention. Figure 2 ;

[0039] Fig.12 This is a schematic diagram of the structure of the "Tai Chi dual unit" metamaterial structure of the present invention. Figure 3 ;

[0040] Fig.13 is a schematic diagram of a shape-function fusion metamaterial structure of the present invention;

[0041] Fig.14 yes Fig.13 The enlarged schematic diagram of point A in the middle;

[0042] Fig.15 This is a diagram showing the vibration reduction effect of the shape-function fusion metamaterial structure of the present invention;

[0043] Fig.16 It is a simulation comparison diagram of the shape-function fusion metamaterial structure of the present invention.

[0044] In the figure: 1-cell outer frame; 2-bridge arm; 3-local resonance column; 4-vibration reduction base; 5-metamaterial structure. DETAILED DESCRIPTION

[0045] In conjunction with the drawings in the embodiments of the present invention, the technical solutions in the embodiments of the present invention are clearly and completely described. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other implementation methods obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0046] It should be noted that the structures, proportions, sizes, etc. illustrated in the drawings of this specification are only used to match the contents disclosed in the specification so that people familiar with this technology can understand and read them. They are not used to limit the conditions under which the present invention can be implemented, and therefore have no substantive technical significance. Any structural modification, change in proportional relationship or adjustment of size should fall within the scope of the technical contents disclosed in the present invention without affecting the effects and purposes that can be achieved by the present invention. It should be noted that in this specification, relational terms such as first and second are only used to distinguish one entity from several other entities, and do not necessarily require or imply any actual relationship or order between these entities.

[0047] The present invention provides an embodiment:

[0048] like Figures 1 to 9 As shown, a dual-mass resonant substructure includes a plurality of connected cell structures, wherein the cell structure includes a cell outer frame 1, a dual bridge arm structure and a dual-mass structure; two adjacent cell structures are connected via the cell outer frame 1; the dual bridge arm structure includes two bridge arms 2 extending inward from the inner frame of the cell outer frame 1; the dual-mass structure includes two groups of local resonance columns 3, and a group of local resonance columns 3 are arranged at one end of any bridge arm 2 away from the cell outer frame 1, and the number of resonance columns in any group of local resonance columns 3 is an even number, and they are symmetrically arranged at the upper and lower end surfaces of the bridge arm 2.

[0049] In this embodiment, the end of the bridge arm 2 connected to the cell outer frame 1 is the tail, and the end with the local resonance column 3 is the head. There is a separation gap between the heads of the two bridge arms 2, and there is a separation gap between the head of the bridge arm 2 and the cell outer frame 1.

[0050] The structural parameters of the dual-mass resonant substructure include the base size and the local resonance unit size. In the base size, p' represents the initial width of the bridge arm, q' represents the reference position of the bridge arm, r2 and r1 represent the outer chamfer radius and the inner chamfer radius of the bridge arm, respectively, and j' represents the centerline length of the bridge arm; a represents the length of the outer frame of the cell, b represents the width of the outer frame of the cell, c represents the height of the outer frame of the cell, and d represents the thickness of the outer frame of the cell; in the local resonance unit size, S' represents the area of ​​the local resonance column, and h represents the height of the bottom surface of the local resonance column from the bottom surface of the outer frame of the cell, such as Figures 10 to 12 shown.

[0051] The cell outer frame 1 is a square frame structure, and the two bridge arms 2 and the two groups of local resonance columns 3 are arranged in a central symmetry relative to the center position of the square frame structure; the bridge arm 2 is a special-shaped part, the tail of the bridge arm 2 is connected to a point on one side of the cell outer frame 1, the diameter of the extension part from the tail of the bridge arm 2 to its head gradually increases, and the head of the bridge arm 2 is a semicircular structure; the local resonance column 3 is a cylinder, and the center line of the local resonance column 3 passes through the center of the head of the bridge arm 2.

[0052] A second aspect of the present invention provides a dual-mass resonator structure design method, comprising the following steps:

[0053] S1: Based on the structural analysis of the double-mass resonator, a mechanical model of the double-mass-double-spring unit structure of the cell structure is established;

[0054] The outer frame of the cell in the mechanical model of the i-th double-mass-double-spring unit structure is equivalent to the mass body M i.1 , the first group of bridge arms and local resonant columns are equivalent to mass body m i.2 The second group of bridge arms and local resonant columns are equivalent to mass body m i.3 The connection between the first group of bridge arms and the local resonant column and the outer frame of the cell is equivalent to a spring body k i.2 The connection between the second group of bridge arms and the local resonant column and the outer frame of the cell is equivalent to a spring body k i.3 , the connection between adjacent cell structures is equivalent to a spring body K i.1 .

[0055] S2: Arrange n continuous cell structures in a one-dimensional array and establish a mechanical model of the entire array;

[0056] The structure has a double oscillator characteristic, which is designed to transfer energy to the two internal mass bodies m of the i-th unit cell through the carrier during the vibration wave transmission process. i.2 and m i.3 The two equivalent springs on the left and right are k i.2 and k i.3 , the resonance units are not directly connected. In the specific vibration transmission, the external force F nActing on the outermost cell structure, the cell structures are connected by an equivalent spring K i.1 connected, the i-th structural cell structure will generate f i.1 and f i.2 The reaction forces act on the overall structure M i.1 .

[0057] S3: To simplify the calculation, assume that the parameters of each unit cell are the same, arrange the unit cells in an array, and select two adjacent unit cell structures as the research objects to form equivalent repeated units;

[0058] The equivalent repeated cell is composed of the second half of the i-1th cell structure and the first half of the i-th cell structure. In an equivalent repeated cell, the M of the i-1th cell structure and the i-th cell structure are combined. (i-1).1 / 2, K (i-1).1 、M i.1 / 2, m (i-1).3 , k (i-1).3 、m i.2 and k i.2 Relabel them as M1, K1, M3, m2, k2, m4 and k4, and convert the entire equivalent repeated cell into a mass body m eff , the connection between adjacent equivalent repeated cells is equivalent to a spring body k.

[0059] In Figure (a), a1 is the lattice constant, in Figure (b), b2 is the selected equivalent repeating unit cell, b1 is the cross section 1-1 of b2, the area of ​​a single cross section is S, b3 is the force diagram of a single cross section, where fn is the stress, and Figure (c) is a one-dimensional array structure model for establishing a dual-mass local resonance metamaterial. The cross-sectional area of ​​the equivalent repeating unit cell is S, and the stress received by the cross section is f n .

[0060] S4: Treat equivalent repeating cells as m eff , and are connected to each other through an equivalent spring k to study the low-frequency characteristics of the dual-mass localized resonance metamaterial cell structure.

[0061] The steps to study the low-frequency characteristics of the dual-mass local resonance metamaterial cell structure include:

[0062] S41: Establish the motion equation of the equivalent repeated cell and obtain the equivalent mass m of the equivalent repeated cell eff ;

[0063] Construct the equations of motion for the equivalent repeating cell:

[0064]

[0065] The displacement x of the i-th moving block i =Xi e jwt ,i=1,2,3,4,X i is the amplitude of the i-th motion block, j is the imaginary unit, and w is the angular frequency; the force is 2*S*f n =F n e jwt , F n is the force acting on the dual-mass resonant substructure; Formula 1 is further simplified into Formula 2.

[0066]

[0067] Solving the above formula, the solution X1 X1 expression is:

[0068]

[0069] in The equation of motion for a single unit cell is:

[0070]

[0071] Combining formulas 3 and 4, we can solve for the equivalent mass m of a single unit cell: eff The expression is:

[0072]

[0073] Substituting the solution of X1 into Formula 5, the specific equivalent mass m eff It can be expressed as formula 6:

[0074]

[0075] S42: Ignore the difference between boundary and internal cells, combine n equivalent repeated cells, establish a linear homogeneous equation system, and substitute it into the motion equation of a single equivalent repeated unit cell to obtain the dispersion relation expression of the dual-mass resonator;

[0076] When considering the motion of each equivalent repeated unit cell, the motion equation of the nth equivalent repeated unit cell is:

[0077]

[0078] Ignoring the difference between boundary and internal cells, the motion equation of each equivalent repeated unit cell is the same. Combining n equivalent repeated unit cells, a solution similar to elastic waves is:

[0079]

[0080] Where q is the wave vector, w is the angular frequency, A q is the amplitude, a1 is the distance between each equivalent repeating unit cell, that is, the lattice constant.

[0081] Substitute 8 into the equation of motion and solve:

[0082]

[0083] The dispersion relation is expressed as:

[0084]

[0085] To further illustrate the convenience of drawing, 10 is organized as follows:

[0086]

[0087] From formula 9, the motion equation of the n-periodic system is simplified as follows, where the first formula represents the internal cells and the second formula represents the boundary conditions:

[0088]

[0089] S43: Based on the dispersion relation expression of the double-mass resonator, the motion equation of the n-periodic system is simplified, and the theoretical transmission loss formula Tr' of the mechanical model is derived.

[0090] In order to study the propagation characteristics of the structure, the frequency transmission loss function Tr is defined as shown in Formula 13, where Pout is the displacement of the output measurement point and Pin is the displacement of the excitation measurement point.

[0091]

[0092] Based on formulas 12 and 13, the theoretical transmission loss formula Tr' of the mechanical model is derived as follows:

[0093]

[0094] The present invention takes the "Tai Chi dual-unit" metamaterial structure as an example:

[0095] In order to more intuitively represent the change in the equivalent mass of the “Tai Chi dual-unit” metamaterial structure, Formula 6 is visualized and analyzed, and the parameters are set as follows:

[0096] k=k1=2N / m, k2=k4=1N / m, m1=m3=1Kg, m2=m4=4Kg, such as Figure 2 When the equivalent mass is infinite, the positive real number w is A = 0.40 rad / s, C = 0.50 rad / s and E = 1.75 rad / s. When the equivalent mass is 0, the positive real number w is

[0097] B = 0.44rad / s, D = 1.12rad / s and F = 2.25rad / s. The three gray areas in the figure show the three negative equivalent mass areas of the "double-unit" metamaterial structure, which are: 0.40-0.44rad / s, 0.50-1.12rad / s and 1.75-2.25rad / s. When the equivalent mass approaches infinity, the local mass block moves in the opposite direction to the matrix material, and it is difficult for the structural wave to be transmitted through the matrix, which effectively suppresses the vibration and energy of the matrix.

[0098] By using formula 11, we can draw the dispersion relationship diagram of the metamaterial structure: Figure 3 is the dispersion relation of the “double-unit” metamaterial structure. It is found that the “double-unit” metamaterial structure has three band gaps (indicated by the gray area).

[0099] In order to further study the theoretical transmission loss and simplify the calculation, n=6 in formula 16, and draw a theoretical transmission loss diagram, as shown in Figure 4 This is the transmission loss diagram of the “Tai Chi dual-unit” metamaterial structure, such as Figure 4 The three parts where the transmission loss is less than 0 are represented by gray areas, and there are obvious negative transmission loss areas.

[0100] Through theoretical modeling research, it is found that the "double-unit" metamaterial structure has a wider band gap and a larger number, and has a more restraining and controlling effect on the transmission of structural waves. Through theoretical design, a theoretical design method is provided for subsequent engineering applications. Through theoretical back calculation, the specific negative mass area, dispersion relation and transmission loss required can be designed to more accurately control the structural waves.

[0101] Calculated equivalent mass of the mechanical model. Figure 2 The equivalent mass of the designed “Tai Chi dual-unit” metamaterial structure, where the three gray areas are three negative mass areas. A, B, C, D and E, F are the coordinates of w corresponding to negative infinity and zero of the three negative mass areas, respectively. Figure 3 This is the dispersion relationship diagram of the "Tai Chi dual-unit" metamaterial structure. Figure 4 This is the theoretical transmission loss diagram of the "Tai Chi dual-unit" metamaterial structure.

[0102] There are many parameters in the forward design of the dual-unit metamaterial model. Structural parameters and material parameters are important factors that determine its band gap width and performance. Structural parameters include metamaterial matrix structural size parameters and local resonance unit size parameters, and material parameters include material density, Poisson's ratio and Young's modulus. By establishing a finite element model and calculating the structural band diagram, the metamaterial structure is optimized and the performance is predicted.

[0103] By analyzing the dual-mass resonant substructure, the Brillouin zone of the metamaterial structure is established. Through COMSOL software, periodic boundary conditions are set. By introducing the Bloch wave vector k, the value is taken along the Brillouin zone boundary, the reciprocal lattice is calculated, and the Wigner-Seitz primitive cell is selected. It is converted into an eigenvalue problem to describe the natural frequency characteristics of the structural monomer. In the software, the matrix material of the dual-unit structure is set to nylon, and the local unit is a lead block. Through the COMSOL solid mechanics module, the characteristic frequency search base value is set to 0Hz, the required characteristic frequency is 20, and the structural energy band diagram is drawn to intuitively view the bandgap range of the structural monomer. Study the transmission characteristics of its transmission wave, such as Figure 8 In the gray area, it is found that in the range of 4912.2 Hz to 5114.3 Hz, the structure exhibits a complete band gap range of 202.1 Hz.

[0104] Figure 5 The array diagram of the double-mass resonator structure in the COMSOL software with a frequency of 128.53 Hz in the process of wave vector Γ to X is shown in mm. The arrows in the figure represent the displacement field on the surface. Figure 6 The array diagram of the double-mass resonator structure in the COMSOL software with a frequency of 23.997 Hz in the process of wave vector M to Γ is shown in mm. The arrows in the figure represent the displacement field on the surface. Figure 7 It shows the structural band diagram drawn by 20 sets of characteristic frequencies calculated in the software. From the band diagram, it can be seen that the phonon complete band gap width appears near the frequency of 5000Hz. Figure 8 In order to more clearly show the complete band gap width, the data from 3500Hz to 6500Hz in Figure c is enlarged, and the specific band gap width is represented by the gray area.

[0105] By calculating each group of eigenvalues ​​along the Brillouin zone for the wave vector k, when more than 15 groups of eigenvalue frequencies are calculated, the frequency has reached more than 1 kHz. In order to simplify the calculation of different parameters in the initial neural network data training database, we set the number of eigenfrequency solutions to 20 to ensure that most results exceed 500 Hz.

[0106] The present invention designs and studies a type of dual-mass resonator structure, and systematically studies the different size parameters and material parameters of the "dual-unit" metamaterial structure. A mechanical theoretical model is established, and compared with the traditional structure. Through theoretical model comparison and analysis, the "dual-unit" metamaterial structure has three theoretical negative mass band gaps. Finite element simulation and experiments on the model show that this structure performs well in low-frequency vibration and has a wide bandgap in the low-frequency range.

[0107] The third aspect of the present invention provides a shape-function fusion metamaterial structure, including a matrix structure and a plurality of embedded structures, wherein the embedded structure is embedded in the hole structure of the matrix structure, and the embedded structure is composed of a one-dimensional array arrangement of n consecutive dual-mass resonant sub-cell structures. The matrix has a specific geometric configuration, and contains various types or the same type of dual-mass resonant sub-cell structures with different structural parameters, thereby realizing customizable functions.

[0108] This application uses various metamaterial shapes to embed metamaterials with different functions, realizing the integrated design of shape and function. A prototype of shape-function integrated metamaterial with customizable vibration attenuation band is proposed. The matrix structure is designed as a hexagonal tubular honeycomb structure with slots in its pores. In these slots, metamaterial units of dual-mass local resonators with different structural parameters can be embedded to adjust the vibration absorption frequency, thereby designing a specific vibration attenuation band, such as Fig.13 As shown. By selecting a dual-mass resonant subcell structure with different parameters, an adjustable frequency band can be achieved within the shape-function integrated metamaterial. This functionally integrated metamaterial not only retains the function of the traditional vibration-damping base, but also integrates the characteristics of the metamaterial, showing excellent performance in vibration control and damping. The metamaterial designed using the method described in this article has reduced vibration amplitude, minimized high-frequency components, and significantly enhanced overall structural stability.

[0109] Fig.16 A prototype metamaterial with integrated shape and function is designed, featuring circular and hexagonal honeycomb matrices in which dual-mass local resonator metamaterials (dual-mass resonant sub-cell structures) with different parameters are embedded. Fig.16 As shown, three simulation sets were performed. The first metamaterial had no embedded empty structure, while the second metamaterial and the third contained dual-mass resonators with different parameters. The frequency response of the overall structure was analyzed and it was shown that these structures exhibited different amplitude responses at the same frequency, indicating that different or variable parameterized functional metamaterials can achieve customizable functions.

[0110] The shape-function fusion metamaterial structure in this application has been verified through finite element simulation and experiments, and it was found that the maximum vibration reduction amplitude was reduced from 10μm to 3μm. In addition, embedding a dual-mass resonant subcell structure in the matrix can not only reduce the amplitude, but also reduce the high-frequency components, making the entire matrix structure more stable, indicating that this structure has great potential in mechanical equipment, industrial equipment, construction engineering, aerospace and automotive fields, and can be used for customized shock absorption and noise reduction and structural lightweight design.

[0111] In the research of mechanical fusion metamaterials, the function and shape of the customized band gap fusion metastructure is realized through intelligent layout. This technological innovation will be applied to the field of vibration reduction and noise reduction of precision instruments and rotating machinery. By utilizing the characteristics of metamaterials, a base structure with a specific frequency band gap can be designed, thereby effectively improving the vibration resistance and reducing the noise level. The results of this research are expected to bring significant applications in the field of precision instruments and rotating machinery and promote the development of the industry.

[0112] The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be based on the protection scope of the claims.

Claims

1. A dual-mass resonator structure, characterized in that: It comprises a plurality of connected cell structures, wherein the cell structure comprises a cell outer frame (1), a double bridge arm structure and a double mass structure; Two adjacent cell structures are connected via a cell outer frame (1); the double bridge arm structure comprises two bridge arms (2) extending inward from the inner frame of the cell outer frame (1); the double mass structure comprises two groups of local resonance columns (3), one end of each bridge arm (2) away from the cell outer frame (1) is provided with a group of local resonance columns (3), the number of resonance columns in each group of local resonance columns (3) is even, and the resonance columns are symmetrically arranged at the upper and lower end surfaces of the bridge arm (2).

2. The dual-mass resonator structure according to claim 1, characterized in that: The end of the bridge arm (2) connected to the cell outer frame (1) is the tail, and the end provided with the local resonance column (3) is the head. There is a separation gap between the heads of the two bridge arms (2), and there is a separation gap between the heads of the bridge arms (2) and the cell outer frame (1).

3. The dual-mass resonator structure according to claim 2, characterized in that: The structural parameters of the dual-mass resonant substructure include the base size and the local resonance unit size. In the base size, p' represents the initial width of the bridge arm, q' represents the reference position of the bridge arm, r2 and r1 represent the outer chamfer radius and the inner chamfer radius of the bridge arm respectively, and j' represents the center line length of the bridge arm; a represents the length of the outer frame of the cell, b represents the width of the outer frame of the cell, c represents the height of the outer frame of the cell, and d represents the thickness of the outer frame of the cell; In the local resonance unit size, S' represents the area of ​​the local resonance column, and h represents the height from the bottom surface of the local resonance column to the bottom surface of the cell outer frame.

4. The dual-mass resonator structure according to claim 2, characterized in that: The cell outer frame (1) is a square frame structure, and the two bridge arms (2) and the two groups of local resonance columns (3) are arranged in a central symmetric manner relative to the center position of the square frame structure; the bridge arm (2) is a special-shaped part, the tail of the bridge arm (2) is connected to a certain point on one side of the cell outer frame (1), the diameter of the extension part of the tail of the bridge arm (2) toward its head gradually increases, and the head of the bridge arm (2) is a semicircular structure; the local resonance column (3) is a cylinder, and the center line of the local resonance column (3) passes through the center of the head of the bridge arm (2).

5. A dual-mass resonant substructure design method, based on the dual-mass resonant substructure according to any one of claims 1 to 4, characterized in that: The following steps are involved: S1: Based on the structural analysis of the double-mass resonator, a mechanical model of the double-mass-double-spring unit structure of the cell structure is established; S2: Arrange n continuous cell structures in a one-dimensional array and establish a mechanical model of the entire array; S3: Select two adjacent cell structures as research objects to form equivalent repeated cells; S4: Remodel the equivalent cell and study the low-frequency characteristics of the dual-mass local resonance metamaterial cell structure.

6. The dual-mass resonator structure design method according to claim 5, characterized in that: The steps to study the low-frequency characteristics of the dual-mass local resonance metamaterial cell structure include: S41: Establish the motion equation of the equivalent repeated cell and obtain the equivalent mass m of the equivalent repeated cell eff ; S42: Ignore the difference between boundary and internal cells, combine n equivalent repeated cells, establish a linear homogeneous equation system, and substitute it into the motion equation of a single equivalent repeated unit cell to obtain the dispersion relation expression of the dual-mass resonator; S43: Based on the dispersion relation expression of the double-mass resonator, the motion equation of the n-periodic system is simplified, and the theoretical transmission loss formula Tr' of the mechanical model is derived.

7. A shape-function fusion metamaterial structure, comprising the dual-mass resonator structure according to any one of claims 1 to 4, characterized in that: It includes a matrix structure and several embedded structures. The embedded structure is embedded in the hole structure of the matrix structure. The embedded structure is composed of a one-dimensional array arrangement of n consecutive double-mass resonance sub-cell structures.

8. The shape-function fusion metamaterial structure according to claim 7, characterized in that: The embedded structure includes n double-mass resonant sub-cell structures of different types or of the same type with different structural parameters, which are used to adjust the resonance frequency of the superstructure.

9. The shape-function fusion metamaterial structure according to claim 7, characterized in that: The matrix structure is a hexagonal tubular honeycomb structure, slots are arranged in the internal hole structure, and plug connectors matching the slots are arranged on both sides of the cell structure of the dual-mass resonator.

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