Self-similar structure mechanics metamaterial with support and vibration isolation functions

Abstract

The application provides a mechanical metamaterial with supporting and vibration isolation functions, and the internal structure is a self-similar structure arranged in order. Each basic structural unit of the metamaterial is composed of a trapezoidal unit and a rectangular unit. The upper bottom end of the trapezoidal unit is connected with one end of the rectangular unit, and two same rectangles are connected with the original rectangle along the vertical direction of the other end of the rectangular unit, and on this basis, the trapezoidal structure is connected with the rectangular structure, and through continuous extension, the self-similar structure is formed. The structure greatly widens the band gap, forms super-wide band gap and super-low frequency band gap, so that the application can block the propagation of elastic waves in a certain frequency range, thereby having good sound insulation and noise reduction performance, and the structure itself has a certain deformation resistance. These advantages make the application have good development prospect in the mechanical field which needs vibration isolation, buffering and supporting.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary field of vibration isolation and noise reduction technology and advanced structural functional materials, and in particular relates to a self-similar structural mechanical metamaterial with support and vibration isolation functions. Background Technology

[0002] Metamaterials are composite materials or structural arrays that precisely control physical fields at subwavelength scales through artificial microstructures. As artificially synthesized products, metamaterials possess many advantages not found in natural materials. Generally, artificial composite materials with the following two characteristics are metamaterials: structurally, they consist of artificially designed subwavelength microstructures arranged in a specific manner; functionally, they possess powerful physical field manipulation capabilities. Metamaterials not only exhibit extraordinary properties surpassing traditional natural materials on a macroscopic scale, but also achieve structural-functional integration. Furthermore, due to their unique wave propagation bandgap, they hold immense application potential in engineering fields such as vibration isolation, sound absorption and noise reduction, stealth, optical information, and electromagnetic waves. The development of metamaterials and related technologies has shown a clear trend of generalization, with the "metamaterial family" giving rise to an increasing number of new concepts, structures, methods, functions, and applications.

[0003] In terms of mechanical load-bearing capacity and multifunctional design and application, scholars at home and abroad have paid extensive attention to a class of self-similar metamaterials. Typical representatives of these metamaterials are structures with a specific form of periodic distribution, similar unit cell shapes, and simple structures. Metamaterials that have undergone artificial design and structural optimization can exhibit superior performance. Multi-scale structures can help widen the bandwidth to a certain extent, and the material structure has good anisotropy. Compared with ordinary materials, these materials have better resistance to deformation.

[0004] During the production and processing of various industrial machines, a significant amount of noise pollution is generated, directly impacting people's lives and work. Simultaneously, the deformation of surrounding structures caused by workpieces subjected to various stresses during processing is also a problem worth considering. Therefore, designing a metamaterial that can absorb noise and mechanical vibrations while exhibiting resistance to deformation is an urgent issue to address. Summary of the Invention

[0005] To address the challenges of effective noise control and insufficient pressure resistance in industrial machinery production, this invention aims to provide a self-similar structural mechanical metamaterial with both support and vibration isolation functions. Due to its unique self-similar structure, this metamaterial can significantly widen the bandgap, forming an ultra-wide and ultra-low frequency bandgap. This greatly expands the frequency range for sound absorption and vibration reduction, and also provides significant advantages for low-frequency sound insulation.

[0006] To achieve the objectives of this invention, the following technical solutions are provided:

[0007] A self-similar structural metamaterial with support and vibration isolation functions, the internal structure of which is a neatly arranged self-similar structure;

[0008] The smallest unit of the self-similar structure is the first unit cell, which is formed by connecting a trapezoidal unit and a rectangular unit. The second unit cell is mirrored with the bottom edge of the trapezoidal unit as the axis of symmetry and consists of two trapezoidal units and two rectangular units. After the upper base of the upper trapezoidal unit in the second unit cell A is connected to the rectangular unit, the midpoint of the rectangular side that is not connected to the trapezoid is used as the upper right and upper left corners of the rectangular sides of the other two second unit cells B and C, that is, rotated ±90°. The above three second unit cells together form the third unit cell.

[0009] Furthermore, the rectangular units connected by the lower bases of the lower trapezoidal units of the B units of the two third units are connected by a second unit, and the rectangular units connected by the lower bases of the lower trapezoidal units of the C units of the two third units are connected by a second unit. The third unit and the two second units together form the fourth unit.

[0010] Furthermore, the metamaterial has several center points, which are formed by four rectangular units connected by the lower base of the lower trapezoidal unit of the second unit cell A.

[0011] Furthermore, the first unit cell and / or the second unit cell and / or the third unit cell and / or the fourth unit cell are arranged in a periodic manner.

[0012] Furthermore, the mechanical metamaterial is made of aluminum, with key parameters including a Young's modulus of 76 GPa, a Poisson's ratio of 0.33, and a density of 2700 kg / m³. 3 .

[0013] Furthermore, the upper base of the trapezoidal unit of the mechanical metamaterial has a length of d = 2 mm, and the lower base has a length of D = 10 mm; the width of the rectangle has a width of d = 2 mm, and the longitudinal dimension after the trapezoidal unit and the rectangular unit are connected is ha = 100 / 3 mm.

[0014] Furthermore, the rectangular units in the metamaterial unit cell are all identical in shape and size;

[0015] The trapezoidal units in the metamaterial unit cell are similar in shape but not exactly the same in size.

[0016] Furthermore, in the aforementioned mechanical metamaterial, the longitudinal length of the structure composed of rectangular and trapezoidal units is reduced to 4 / 5 of its original length after each fractal.

[0017] Compared with the prior art, the present invention has the following advantages:

[0018] 1. The present invention provides a self-similar structural mechanical metamaterial with support and vibration isolation functions. Compared with previous metamaterials, this invention has a self-similar structure, which improves the low-frequency and broadband acoustic characteristics of the structure while having a certain ability to resist deformation.

[0019] 2. The present invention provides a self-similar structural mechanical metamaterial with support and vibration isolation functions, which has an ultra-wide bandwidth and an ultra-low frequency bandwidth.

[0020] 3. The present invention provides a self-similar structural mechanical metamaterial with support and vibration isolation functions. Its ultra-wide bandwidth can absorb elastic waves in a wide frequency range, thereby achieving better sound absorption and vibration reduction.

[0021] 4. The self-similar structural mechanical metamaterial with support and vibration isolation functions provided by this invention provides a research idea for the field of low-frequency sound insulation due to its ultra-low frequency band gap.

[0022] 5. The present invention provides a self-similar structural mechanical metamaterial with support and vibration isolation functions. The bandgap properties can be further improved by changing the size of the periodic unit, making it easier to control the frequency range.

[0023] Based on the above reasons, the present invention, due to its excellent performance, has broad application prospects in the fields of resistance to deformation and noise reduction and vibration damping. Attached Figure Description

[0024] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0025] Figure 1 This is a schematic diagram illustrating the formation process of periodic self-similar structures in the mechanical metamaterial with self-similar structures described in this invention.

[0026] Figure 2 This is a schematic diagram of the smallest unit with a periodic self-similar structure as described in this invention.

[0027] Figure 3 This is a band structure diagram of the smallest unit with a periodic self-similar structure as described in this invention.

[0028] Figure 4 This is a general schematic diagram of a mechanical metamaterial with a periodic self-similar structure as described in this invention.

[0029] Figure 5This is a stress-strain diagram of the self-similar structural mechanical metamaterial described in this invention under pressure.

[0030] Figure 6 This is a partial stress-strain diagram of the self-similar mechanical metamaterial described in this invention under pressure. Detailed Implementation

[0031] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0032] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the present invention or its application or use. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0033] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0034] Unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps described in these embodiments do not limit the scope of the invention. It should also be understood that, for ease of description, the dimensions of the various parts shown in the drawings are not drawn to actual scale. Techniques, methods, and devices known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters in the following figures denote similar items; therefore, once an item is defined in one figure, it need not be further discussed in subsequent figures.

[0035] In the description of this invention, it should be understood that the orientation or positional relationship indicated by directional terms such as "front, back, up, down, left, right", "horizontal, vertical, horizontal" and "top, bottom" is generally based on the orientation or positional relationship shown in the accompanying drawings, and is only for the convenience of describing this invention and simplifying the description. Unless otherwise stated, these directional terms do not indicate or imply that the device or element referred to must have a specific orientation or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on the scope of protection of this invention. The directional terms "inner" and "outer" refer to the inner and outer contours relative to the outline of each component itself.

[0036] For ease of description, spatial relative terms such as "above," "over," "on the upper surface of," "above," etc., are used herein to describe the spatial positional relationship of a device or feature as shown in the figures to other devices or features. It should be understood that spatial relative terms are intended to encompass different orientations in use or operation besides the orientation of the device as described in the figures. For example, if the device in the figures is inverted, a device described as "above" or "above" other devices or structures would subsequently be positioned as "below" or "under" other devices or structures. Thus, the exemplary term "above" can include both "above" and "below." The device may also be positioned in other different ways (rotated 90 degrees or in other orientations), and the spatial relative descriptions used herein will be interpreted accordingly.

[0037] Furthermore, it should be noted that the use of terms such as "first" and "second" to define components is merely for the purpose of distinguishing the corresponding components. Unless otherwise stated, the above terms have no special meaning and therefore should not be construed as limiting the scope of protection of this invention.

[0038] This embodiment discloses a mechanical metamaterial with support and vibration isolation functions, wherein the metamaterial is a "rectangular microstructure" composed of one or more unit cells of the same size;

[0039] The metamaterial unit cell is formed by connecting trapezoidal and rectangular units;

[0040] After the upper base of the trapezoidal unit in the metamaterial unit cell is connected to the rectangular unit, the above structure is rotated by ±90° with the midpoint of the rectangular side that is not connected to the trapezoid as the center to form a "T-shaped" combined unit.

[0041] The microstructure formed by the combined unit through fractal transformation is the smallest periodic unit of this self-similar structure.

[0042] The rectangular units in the metamaterial unit cell are all identical in shape and size.

[0043] The trapezoidal units in the metamaterial unit cell are similar in shape but not exactly the same in size.

[0044] The smallest unit configuration in the two-dimensional unit cell of the metamaterial is as follows: Figure 1 As shown in (a), the upper base of the trapezoid is d and the lower base is D.

[0045] The smallest unit configuration in the two-dimensional unit cell of the metamaterial is as follows: Figure 1 As shown in (a), the width of the rectangle is d.

[0046] The smallest unit configuration in the two-dimensional unit cell of the metamaterial is as follows: Figure 1 As shown in (a), the longitudinal dimension of the trapezoidal unit and the rectangular unit after connection is ha.

[0047] The smallest unit configuration in the two-dimensional unit cell of the metamaterial is as follows: Figure 1 As shown in (a), the total length of the structure formed by the two sets of the above connections through the trapezoidal lower base is l.

[0048] The metamaterial replaces the arms with a self-similar structure composed of rectangular and trapezoidal units, forming a first-order fractal. Figure 1 The structure shown in (a) is shown;

[0049] The metamaterial replaces the arms with a self-similar structure composed of rectangular and trapezoidal units, forming a second-order fractal structure. Figure 1 The structure shown in (b);

[0050] The metamaterial replaces the arms with a self-similar structure composed of rectangular and trapezoidal units, and is formed through third-order fractals. Figure 1 The structure shown in (d) is shown;

[0051] The metamaterial forms a third-order permutation ultra-low frequency bandgap by replacing the arms with a self-similar structure composed of rectangular and trapezoidal units.

[0052] It is worth noting that, in order to avoid the fractal structure from interfering with the overall structure (such as preventing the original structure from presenting its integrity on the plane), the longitudinal length of the structure composed of rectangular and trapezoidal units after each fractal must be reduced to 4 / 5 of the original length to ensure the integrity of the overall structure.

[0053] The geometry of the arm has a significant impact on the bandgap characteristics.

[0054] The overall configuration of the metamaterial is as follows: Figure 2 As shown, a cell with a self-similar structure is composed of a periodic arrangement of several trapezoidal and rectangular cells.

[0055] The regular periodic arrangement within the metamaterial periodic cells gives the invention good spatial anisotropy.

[0056] The overall structure of the metamaterial is formed by replacing the original structural arms with similar structures to create complete self-similar periodic units.

[0057] In the periodic cells of the metamaterial, replacing the original structural arms with self-similar structures can greatly widen the bandwidth, forming ultra-wide bandwidth and ultra-low frequency bandwidth.

[0058] Example 1

[0059] To explore the ability of the metamaterial to obtain ultra-wide and ultra-low frequency band gaps.

[0060] In the absence of external load, the propagation of elastic dynamic waves follows...

[0061]

[0062] Where: S=C:ε,

[0063]

[0064] u is the displacement vector, and C is the stiffness matrix.

[0065] According to Bloch-Floquet wave theory, the wave function in a perfectly periodic medium can be defined as a periodic function corresponding to the harmonic modulation of a periodic vector. Under the current boundary conditions, the band structure of a unit cell can be calculated by analyzing the eigenfrequency of the unit cell with matrix stiffness. A common practice for calculations using matrix stiffness is to search for the boundary of the irreducible Brillouin zone. The Brillouin zone varies with the type and size of the unit cell and can be obtained from the unit vector of the unit cell.

[0066] To obtain low-frequency or broadband band structures, a self-similar method was used to manipulate the structure of the unit cell. Replacing one arm with a combination of multiple similarly shaped arms yields a new unit cell. The band structure of the new unit cell is shown below. Figure 1 As shown in (a), the smallest unit that forms a self-similar structure after two fractals is as follows: Figure 2 As shown.

[0067] The study was conducted using the finite element software COMSOL Multiphysics, with the addition of solid mechanics analysis, and a self-similar structural model was constructed (e.g. Figure 1 As shown), the additive is aluminum, with the following properties: Young's modulus of 76 GPa, Poisson's ratio of 0.33, and density of 2700 kg / m³. 3 After adding boundary conditions, simulation was performed.

[0068] The experiment yielded the band structure diagram of the smallest unit of the self-similar structure (e.g.) Figure 3The figure shows that the metamaterial has both an ultra-wide bandgap and an ultra-low frequency bandgap. The ultra-wide bandgap is particularly prominent; within a frequency range of approximately 12500–34000 Hz, sound waves passing through this band are completely absorbed by the metamaterial, and the absorbed sound waves are stored as energy within the metamaterial. This is beneficial for the absorption and energy storage of some ultrasound. While the ultra-low frequency bandgap is not as wide as the high-frequency bandgap, it still possesses a certain range of width. Since low-frequency bandgap materials are difficult to obtain and have wide applications, the low-frequency bandgap of the metamaterial described in this paper also has significant application value and reference value in the field of low-frequency sound insulation.

[0069] The cell contains two important parameters, d and D (e.g., ...). Figure 1 As shown, broadband and low-frequency characteristics can be explored by changing the values ​​of d and D. The bandgap value of the unit cell is truncated based on the parameter changes, and the cell size is determined according to the desired low-frequency characteristics. Some bandgap structures still have lower bandgaps, but narrower bandwidths. Others stand out due to their relatively wide bandwidths. This unit can be used for low-frequency or broadband applications, or both.

[0070] Example 2

[0071] To investigate the ability of the metamaterial to resist deformation.

[0072] Vibration simulations were performed using the finite element method software COMSOL Multiphysics. The material consists of an array of multiple unit cells, confined in a plane by two boundaries. Harmonic stress is applied to the left boundary, while the right boundary is set as a fixed constraint. The top and bottom boundaries are set as periodic conditions. Vibration simulations of the periodic structural metamaterial under different boundary loads were obtained, and the simulation results are as follows: Figure 5 As shown. From Figure 5 It can be clearly seen that after the application of harmonic pressure, the left boundary produces a certain amount of strain due to the pressure. However, due to the excellent characteristics of the self-similar structure, the deformation caused by the pressure will quickly decay. After passing through two layers of unit structure, the deformation caused by the pressure has disappeared. Although some parts of the self-similar structure bear almost several times the force of the harmonic pressure during this process, it is worth mentioning that this self-similar structure can indeed effectively absorb the deformation caused by the harmonic pressure.

[0073] This invention designs a self-similar structural mechanical metamaterial with both support and vibration isolation functions. Due to its unique structure, this metamaterial can form ultra-low frequency and ultra-wide frequency band gaps, absorbing the energy of low-frequency and broadband mechanical waves to achieve sound insulation and noise reduction. Simultaneously, its excellent internal structure provides a certain degree of compressive strength, enabling the metamaterial to resist deformation caused by external forces to a certain extent. Thus, this invention combines sound insulation and noise reduction with physical support, giving it better application prospects in sound insulation, noise reduction, and vibration reduction.

[0074] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A mechanical metamaterial with supporting and vibration isolation functions, characterized in that, Its internal structure is a neatly arranged self-similar structure; The smallest unit of the self-similar structure is the first unit cell, which is formed by connecting a trapezoidal unit and a rectangular unit. The second unit cell is mirrored with the bottom edge of the trapezoidal unit as the axis of symmetry and consists of two trapezoidal units and two rectangular units. After the upper base of the upper trapezoidal unit in the second unit cell A is connected to the rectangular unit, the midpoint of the rectangular side that is not connected to the trapezoid is used as the upper right and upper left corners of the rectangular sides of the other two second unit cells B and C. That is, rotate ±90°. The above three second unit cells together form the third unit cell. The second and third unit cells are both components of self-similar structures.

2. The mechanical metamaterial with supporting and vibration isolation functions according to claim 1, characterized in that, The rectangular units connected by the lower bases of the lower trapezoidal units of the B units of the two third units are connected by a second unit. The rectangular units connected by the lower bases of the lower trapezoidal units of the C units of the two third units are connected by a second unit. The two third units and the two second units together form the fourth unit.

3. The mechanical metamaterial with supporting and vibration isolation functions according to claim 2, characterized in that, The metamaterial has several center points, which are formed by four rectangular units connected by the lower base of the lower trapezoidal unit of the second unit cell A.

4. The mechanical metamaterial with supporting and vibration isolation functions according to claim 1, characterized in that, The first and / or second and / or third and / or fourth cells are arranged in a periodic pattern.

5. A mechanical metamaterial with supporting and vibration isolation functions according to claim 1, characterized in that, The aforementioned mechanical metamaterial is made of aluminum, with a Young's modulus of 76 GPa, a Poisson's ratio of 0.33, and a density of 2700 kg / m³. 3 .

6. A mechanical metamaterial with supporting and vibration isolation functions according to claim 1, characterized in that, The upper base of the trapezoidal unit of the first unit cell is d=2mm and the lower base is D=10mm; the width of the rectangle of the first unit cell is d=2mm, and the longitudinal dimension after connecting the trapezoidal unit and the rectangular unit is ha=100 / 3mm.

7. A mechanical metamaterial with supporting and vibration isolation functions according to claim 6, characterized in that, The rectangular units in the first unit cell are all identical in shape and size; The trapezoidal units in the first unit cell are similar in shape but not exactly the same in size.

8. A mechanical metamaterial with supporting and vibration isolation functions according to claim 7, characterized in that, In the aforementioned mechanical metamaterial, after each fractal, the longitudinal length of the structure composed of rectangular and trapezoidal units is reduced to 4 / 5 of its original length.

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