A locally elastically buckling vibration damping metamaterial structure and a method of manufacturing the same

Abstract

The application provides a locally elastically buckled damping metamaterial structure and a preparation method thereof, and solves the problem that the existing compression-torsion structure cannot simultaneously meet the excellent compression-torsion effect and structural stability requirement. The damping metamaterial structure is a cylindrical structure formed by sequentially stacking M compression-torsion structure units along an axial direction, adjacent compression-torsion structure units are connected through annular connecting panels, and annular connecting panels are coaxially arranged at both ends of the entire damping metamaterial structure. The compression-torsion structure unit is a cylindrical structure formed by sequentially connecting N curved surface structure unit cells in a head-to-tail manner. The angle of each curved surface structure unit cell bending in the circumferential direction of the cylinder is 360° / N. The curved surface structure unit cell comprises a circular ring main body and a circular arc ligament assembly arranged on the outer periphery of the circular ring main body. Under the action of an axial load, the circular arc ligament preferentially undergoes local elastic buckling deformation, and drives the circular ring main body to rotate, so that the structure forms a compression-torsion response, thereby realizing recoverable energy absorption and damping.

Description

Technical Field

[0001] This invention belongs to the field of vibration reduction and absorption metamaterials technology, specifically relating to a local elastic buckling vibration reduction metamaterial thin-walled tube structure and its preparation method. Background Technology

[0002] Thin-walled tubing, with its advantages of light weight, high specific strength, and mature processing technology, has become a key core component in high-end equipment such as aviation, aerospace, marine, and transportation, and is widely used in wing main spars, fuselage frames, underwater weapon bodies, and pipeline supports. However, in these high-end applications, thin-walled tubing operates under harsh conditions, facing complex load environments such as aircraft turbulent vibration and complex sea conditions. Traditional thin-walled tubing thus reveals the following significant problems:

[0003] First, traditional thin-walled pipe fittings have a large length-to-diameter ratio and thin walls, making them highly susceptible to global buckling instability when subjected to axial compression, bending, and impact loads. This sudden and uncontrollable overall instability can directly lead to a sharp drop in the structure's load-bearing capacity, causing irreversible equipment failure or even catastrophic accidents.

[0004] Secondly, traditional thin-walled tubular components suffer from insufficient axial stiffness and weak vibration reduction performance. Under dynamic excitations such as periodic vibration and turbulence, their inherent damping is low, making them prone to resonance and fatigue failure. Their energy absorption mainly relies on structural plastic deformation, which not only has limited energy absorption efficiency but also cannot recover after deformation, resulting in low material utilization and failing to meet the needs of long-term repeated use.

[0005] Third, traditional thin-walled pipe fittings have a single form and cannot simultaneously meet the requirements of lightweight, high load-bearing capacity, buckling resistance and vibration reduction, which limits their further application in high-end equipment.

[0006] Energy absorption performance is a core indicator for evaluating material properties. In traditional materials, strength and density are interrelated and difficult to balance simultaneously. While traditional energy-absorbing materials such as foamed metals and metal honeycomb can absorb energy through plastic deformation, they cannot recover after deformation, which not only reduces material utilization but also leaves room for improvement in energy absorption efficiency. Although existing mechanical metamaterials attempt to achieve performance decoupling, performance contradictions still exist in compression-torsional coupled structures: chiral structures have limited compression-torsional effects, while diagonal bar structures, due to their structural characteristics, are prone to damage, instability, eccentricity, and fracture under load, making it difficult to simultaneously meet the requirements of excellent compression-torsional effects and structural stability.

[0007] Therefore, how to break through the performance bottleneck of traditional thin-walled pipes and provide a new type of structure that can simultaneously possess high load-bearing stability and efficient reversible energy absorption and vibration reduction characteristics is a core technical problem that urgently needs to be solved in current engineering applications. Summary of the Invention

[0008] This invention provides a locally elastic buckling damping metamaterial thin-walled tube structure and its preparation method, aiming to solve the shortcomings of existing compression-torsion structures that cannot simultaneously meet the requirements of excellent compression-torsion effect and structural stability. The locally elastic buckling damping metamaterial thin-walled tube structure designed in this invention has the characteristics of significant compression-torsion effect, simple structure and obvious local elastic buckling.

[0009] To achieve the above objectives, the technical solution provided by this invention is:

[0010] A vibration-damping metamaterial structure with local elastic buckling is characterized in that the vibration-damping metamaterial structure is a cylindrical structure formed by sequentially stacking M compression-torsion structural units along the axial direction, where M takes the value 1-10.

[0011] The two adjacent compression-torsion structural units are connected by annular connecting panels, and the entire vibration-damping metamaterial structure has annular connecting panels coaxially arranged at both ends; the annular connecting panels are used to realize the axial connection and support between the compression-torsion structural units.

[0012] The compression-torsion structural unit is a cylindrical structure formed by connecting N curved structural unit cells end to end in sequence, where N is 4-8; the angle at which each curved structural unit cell bends upward around the cylinder is 360° / N; for example, when N is 4, the angle at which a single curved structural unit cell bends upward around the cylinder is 90°; when N is 8, the angle at which a single curved structural unit cell bends upward around the cylinder is 45°.

[0013] The curved structure unit cell includes a circular ring body and an arcuate ligament assembly disposed on the outer periphery of the circular ring body.

[0014] The main body of the ring is bent along the circumference of the cylinder.

[0015] The circular arc ligament assembly extends along the outer circumference of the ring body and includes an upper circular arc ligament group, a lower circular arc ligament group, a right circular arc ligament, and a left circular arc ligament; wherein, the upper and lower circular arc ligament groups each include two circular arc ligaments; the connection points of all circular arc ligaments to the ring body are evenly distributed circumferentially along the outer circumferential surface of the ring body, and each circular arc ligament is arranged in the same direction of rotation; the right and left circular arc ligaments are both located between the upper and lower circular arc ligament groups and are rotationally symmetrical about the geometric center of the ring body; the upper and lower circular arc ligament groups are rotationally symmetrical about the geometric center of the ring body.

[0016] Each of the upper and lower circular arc ligament groups comprises an arc segment and a straight connecting segment. The arc segment extends and curves along the outer circumference of the circular ring body, and the straight connecting segment is tangentially connected to the end of the arc segment. The straight connecting segment in the upper circular arc ligament group extends upward and connects to the annular connecting panel above it; the straight connecting segment in the lower circular arc ligament group extends downward and connects to the annular connecting panel below it.

[0017] The right circular arc ligament includes an arc segment (bending and extending along the outer circumference of the ring body) connected to the outer circumference of the ring body, and a right straight connecting segment at the end of the arc segment. The right straight connecting segment is used to connect with the adjacent curved surface structure unit cell on the right. The left circular arc ligament includes an arc segment (bending and extending along the outer circumference of the ring body) connected to the outer circumference of the ring body, and a left straight connecting segment at the end of the arc segment. The left straight connecting segment is used to connect with the adjacent curved surface structure unit cell on the left. The straight connecting segment is used to connect with the adjacent curved surface structure unit cell, so that multiple curved surface structure unit cells can be continuously connected along the circumferential direction to form a complete cylindrical compression-torsion structural unit.

[0018] Furthermore, the inner diameter of the pressure-torsion structural unit is 30-45 mm, the radial thickness is 2-8 mm, and the height is 20 mm;

[0019] The inner and outer diameters of the annular connecting panel match the inner and outer diameters of the compression-torsion structure unit, i.e., the inner diameter is 30-45 mm and the radial thickness is 2-8 mm; the height of the annular connecting panel is 1-3 mm.

[0020] The outer diameter of the main body of the ring is 6-12 mm, the inner diameter is 4-10 mm, and the ring width is 1-3 mm;

[0021] The unit cell of the curved structure in its unbent state has a cell length of 21 mm and a cell height of 20 mm.

[0022] The radius of curvature of the arc segment is 12-18 mm, and the width is 1-2 mm.

[0023] Furthermore, M is set to 4-6; N is set to 6; and the central angle between the connection points of two adjacent arcuate ligaments and the main body of the ring is 60°. The connection points of each arcuate ligament and the main body of the ring are evenly distributed along the circumferential direction of the outer circumference of the main body of the ring, the central angle between two adjacent connection points is 60°, and each arcuate ligament is arranged to bend along the same direction of rotation.

[0024] Furthermore, the material is nylon (PA12).

[0025] This invention also provides a method for preparing the aforementioned locally elastic buckling damping metamaterial structure, characterized by the following steps:

[0026] 1) Draw the unit cell model of the curved surface structure.

[0027] Using 3D modeling software, sketches of curved surface structure unit cells are drawn, and curved surface structure unit cell models are generated.

[0028] The curved structure unit cell is the curved structure unit cell in the aforementioned locally elastically buckling vibration-damping metamaterial structure;

[0029] 2) Draw the compression-torsion structural unit model

[0030] Using 3D modeling software, with the central axis of the outer curved surface of the curved structure unit cell model as the reference axis, N curved structure unit cell models are arranged in a circular array around the reference axis, and adjacent curved structure unit cells are connected end to end to form a cylindrical compression-torsion structure unit model.

[0031] The compression-torsion structural unit is the compression-torsion structural unit in the aforementioned locally elastic buckling vibration-damping metamaterial structure;

[0032] 3) Draw a vibration-damping metamaterial structure model with local elastic buckling.

[0033] Using 3D modeling software, first, draw an intermediate annular connecting panel model on the upper end of the compression-torsion structural unit model obtained in step 2), which is coaxial with the compression-torsion structural unit model and has a matching inner and outer diameter; then, according to the layer requirements of the compression-torsion structural unit in the target structure, continue to copy and add the compression-torsion structural unit model and the intermediate annular connecting panel model along the axial direction on the upper end, so that adjacent compression-torsion structural unit models are connected by a shared intermediate annular connecting panel model; finally, draw end annular connecting panel models on both ends of the overall structure, which are coaxial with the compression-torsion structural unit model and have a matching inner and outer diameter, to obtain a vibration-damping metamaterial structure model with local elastic buckling.

[0034] 4) Printing vibration-damping metamaterial structures with localized elastic buckling

[0035] Using the locally elastic buckling damping metamaterial structure model obtained in step 3) as input, the structure is directly printed using 3D printing technology to obtain the locally elastic buckling damping metamaterial structure.

[0036] Furthermore, step 1) specifically involves:

[0037] Use 3D modeling software to draw a rectangular sketch with length a and width b. Generate a cuboid with a target thickness t by using the extrude boss function. Draw a curved surface structure unit cell sketch with the front face of the cuboid as the reference face. Draw two concentric circles with the center of the front face as the center to form an annulus with a width of d. Then draw six circular arc ligaments with the same width d on the outer circumference of the annulus.

[0038] The flat curved structure unit cell model is obtained by stretching and cutting; then the flat curved structure unit cell model is bent 360° / N by solid bending to obtain the curved structure unit cell model.

[0039] Furthermore, step 3) specifically involves:

[0040] 3.1) Using 3D modeling software, on the plane where the upper end face of the compression-torsion structural unit model is located, with the intersection of the reference axis and the plane as the center, draw a ring with the same inner and outer diameters as the compression-torsion structural unit model. Through the extrusion boss function, generate the intermediate annular connecting panel model of the target thickness.

[0041] 3.2) Based on the layer requirement of the compression-torsion structural unit in the target structure, continue to copy and alternately add the compression-torsion structural unit model and the new intermediate annular connecting panel model along the axial direction at the upper end of the intermediate annular connecting panel model, so that adjacent compression-torsion structural unit models are fixedly connected by the shared intermediate annular connecting panel model until the required number of layers is reached.

[0042] 3.3) At both ends of the overall structure, draw rings in the same way as in step 3.1), and generate the end ring connection panel model of the target thickness through the extrude boss function to obtain the vibration reduction metamaterial structure model with local elastic buckling.

[0043] Furthermore, the 3D modeling software is SolidWorks 2024.

[0044] Furthermore, in step 4), the 3D printing technology is multi-flow melt fusion 3D printing technology, and the printing substrate material is nylon (PA12).

[0045] Invention concept:

[0046] Thin-walled tubular components are widely used in aerospace, marine, and high-end equipment industries due to their light weight and good load-bearing capacity. However, traditional thin-walled tubular components are prone to overall buckling instability when subjected to axial vibration, impact, or cyclic compressive loads. Once overall buckling occurs, the structure usually experiences large, irreversible deformation, resulting in limited vibration reduction and energy absorption effects, and potentially leading to structural failure. Therefore, traditional thin-walled tubular components often struggle to simultaneously meet the requirements of lightweight design, load-bearing capacity, buckling resistance, and vibration reduction performance.

[0047] To address the aforementioned problems, this invention introduces the structural design concept of mechanical metamaterials into the thin-walled cylindrical structure, combining a local elastic buckling mechanism with curved compression-torsion structural units to propose a vibration-damping metamaterial structure with recoverable deformation capability. This structure utilizes circular arc ligaments with specific rotational directions (clockwise or counterclockwise) arranged on the cylindrical structure. Under axial compression or vibration loads, the structure no longer directly experiences overall instability, but instead preferentially generates local elastic bending and buckling deformation at the circular arc ligaments, further inducing a certain torsional response in the structure.

[0048] Principle of this invention:

[0049] This invention relies on two core mechanisms—compression-torsion coupling and local elastic buckling stability—to construct a novel energy transfer and dissipation path not found in traditional structures:

[0050] 1. Pressure-torsion coupling mechanism

[0051] Traditional thin-walled tubular components primarily rely on axial compression for load bearing, resulting in a relatively simple deformation mode and limited energy absorption efficiency. This invention features a circular ring body on a curved tubular wall, with circular arc ligaments of the same rotational direction arranged around the outer circumference of the ring body, forming a curved structural unit cell. Under axial load, the connection area between the ring body and the circular arc ligaments undergoes directional rotation, while the circular arc ligaments simultaneously undergo controllable bending deformation. This transforms axial compression deformation into torsional deformation at the unit cell level, which is then transmitted to the overall structure through a circumferential array of multiple curved structural unit cells, forming a stable compression-torsional coupling effect. Specifically, under axial load, the circular arc ligaments preferentially undergo local elastic buckling deformation, driving the ring body to rotate, resulting in a compression-torsional response and achieving recoverable energy absorption and vibration reduction. This mechanism expands the structure's energy absorption mode from single axial compression to torsional-bending coupled deformation, enriching energy dissipation pathways and improving the structure's vibration reduction and energy absorption capacity.

[0052] 2. Local elastic buckling stabilization mechanism

[0053] Unlike traditional structures that suffer from global instability, this invention precisely constrains buckling deformation within specific regions such as ligaments and nodes. This small-scale, recoverable elastic buckling can safely and efficiently dissipate vibration and impact energy, ensuring that the structure does not suffer irreversible damage. Simultaneously, the annular arrangement of unit cells and rigid interlayer connections constrain radial deformation at the overall structural level, improving the overall stiffness and stability of the structure and providing a global boundary guarantee for the stable occurrence of local buckling.

[0054] Advantages of this invention:

[0055] 1. Benefiting from the curved structure unit cell configuration composed of a central circular ring and six circular arc ligaments (belonging to the chiral ligament class of units, achieving a compression-torsion effect through ligament bending and node rotation), this invention can actively induce and constrain deformation in the ligament and node regions, replacing the catastrophic global instability of traditional thin-walled tubular components with controllable and recoverable local elastic buckling. This fundamentally solves the inherent defect of weak buckling resistance in traditional thin-walled tubular components, while significantly improving load dispersion and vibration / impact energy absorption capabilities, achieving efficient axial energy absorption and target frequency band vibration reduction, ultimately achieving integrated functions of load bearing, buckling resistance, and vibration reduction.

[0056] 2. Benefiting from the segmented elastic response design of the curved structure unit cell, this invention absorbs energy through macroscopic deformation of ligament bending in the early stage of load bearing, and achieves synergistic load bearing through unit cell contact in the later stage, resulting in a stable, plateau-like rise in the force-displacement curve during compression. This ensures efficient energy absorption in the fully recoverable elastic stage, overcoming the limitations of traditional energy-absorbing structures that have low energy absorption and large, unrecoverable deformation in the low elastic stage.

[0057] 3. Thanks to the modular interlayer assembly architecture based on compression-torsion structural units and annular connecting panels, this invention can flexibly adjust the load-bearing capacity, buckling resistance, and vibration reduction bandwidth of the structure by simply adjusting parameters such as wall thickness and the number of compression-torsion structural unit layers, without changing the overall external dimensions, thus adapting to various engineering conditions. This design innovation is the key guarantee for ultimately achieving the integrated functions of efficient compression-torsion coupling, local buckling vibration reduction, and global structural stability.

[0058] 4. Structurally, this invention integrates local elastic buckling with compression-torsion metamaterials, proposing a curved compression-torsion elastic unit spatial topology design to overcome the bottleneck of traditional thin-walled pipe fittings being prone to global buckling. In terms of mechanism, it achieves the integrated transmission of axial load, local elastic buckling, torsional deformation, and energy dissipation. In terms of performance, it possesses recoverable elastic buckling characteristics, which can efficiently absorb energy and reduce vibration while maintaining overall stability, solving the core problem that traditional thin-walled components cannot simultaneously achieve load-bearing and vibration reduction. Attached Figure Description

[0059] Figure 1 This is a schematic diagram of the vibration-damping metamaterial structure with local elastic buckling in Example 1;

[0060] Figure 2 This is a schematic diagram of a single compression-torsion structural unit in Example 1;

[0061] Figure 3 This is a schematic diagram of a unit cell model of a curved surface structure in its unbent state.

[0062] Figure 4 A schematic diagram of the reference axis;

[0063] Figure 5 A schematic diagram showing the specific parameters of a unit cell for a curved surface structure;

[0064] Figure 6 The diagram shows four metamaterial structures with different wall thicknesses or numbers of compression-torsion structural unit layers; where a is a 4-layer compression-torsion structural unit with a wall thickness of 2mm; b is a 4-layer compression-torsion structural unit with a wall thickness of 4mm; c is a 4-layer compression-torsion structural unit with a wall thickness of 6mm; and d is an 8-layer compression-torsion structural unit with a wall thickness of 2mm.

[0065] Figure 7 The diagrams show four metamaterial structures with different wall thicknesses and numbers of layers; (a) is a 4-layer compression-torsion structural unit with a wall thickness of 2 mm, i.e., model a; (b) is a 4-layer compression-torsion structural unit with a wall thickness of 4 mm, i.e., model b; (c) is a 4-layer compression-torsion structural unit with a wall thickness of 6 mm, i.e., model c; and (d) is an 8-layer compression-torsion structural unit with a wall thickness of 2 mm, i.e., model d.

[0066] Figure 8 Schematic diagrams of the simulation and experimental force-displacement curves for four models;

[0067] Figure 9 A schematic diagram of the vibration reduction experimental apparatus used in Example 1 (existing apparatus);

[0068] Figure 10 The diagram shows the time-acceleration curves of vibration reduction effect at different frequencies in Example 1; where (a) is 100Hz excitation; (b) is 200Hz excitation; and (c) is 300Hz excitation.

[0069] Figure 11 The diagram shows a comparison of the 6th modal simulation results of the structure with a wall thickness of 2mm in Example 1 and a cylinder with the same wall thickness and height; where (a) is the comparison of the first modal; (b) is the comparison of the second modal; (c) is the comparison of the third modal; (d) is the comparison of the fourth modal; (e) is the comparison of the fifth modal; and (f) is the comparison of the sixth modal.

[0070] Figure 12 These are the harmonic response curves of four models in the frequency range of 0-300 Hz.

[0071] The attached figures are labeled as follows:

[0072] 1. Compression-torsion structural unit; 2. Annular connecting panel; 11. Circular ring body; 12. Circular arc ligament; 13. Upper circular arc ligament group; 14. Lower circular arc ligament group; 15. Right circular arc ligament; 16. Left circular arc ligament. Detailed Implementation

[0073] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0074] Example 1

[0075] like Figure 1 As shown, this embodiment discloses a locally elastic buckling damping metamaterial structure (hereinafter referred to as "metamaterial structure"). The metamaterial structure is a cylindrical structure formed by stacking four compression-torsion structural units sequentially along the axial direction. Adjacent compression-torsion structural units are coaxially connected by annular connecting panels (which can be referred to as intermediate annular connecting panels). Both ends of the entire damping metamaterial structure are coaxially provided with annular connecting panels (which can be referred to as end annular connecting panels). In this embodiment, the height of the end annular connecting panels is half the height of the intermediate annular connecting panels. The distance between two adjacent intermediate annular connecting panels is the height of the compression-torsion structural unit.

[0076] like Figure 2 As shown, the compression-torsion structural unit is a cylindrical structure formed by connecting six curved structural unit cells end to end. Each curved structural unit cell includes a circular ring body and an arcuate ligament assembly disposed on the outer circumference of the circular ring body, which bends upward at an angle of 60° around the cylinder circumference. The arcuate ligament assembly includes an upper arcuate ligament group, a lower arcuate ligament group, a right arcuate ligament, and a left arcuate ligament. Both the upper and lower arcuate ligament groups include two arcuate ligaments. The six arcuate ligaments extend clockwise from the outer circumference of the circular ring body and are evenly spaced. The intersection of each arcuate ligament with the outer circumference of the circular ring body divides the outer circumference of the circular ring body into six equal parts. The central angle between the connection points of two adjacent arcuate ligaments and the circular ring body is 60°. The right and left circular arc ligaments are both located between the upper and lower circular arc ligament groups and are rotationally symmetric about the geometric center of the ring body. The upper and lower circular arc ligament groups are also rotationally symmetric about the geometric center of the ring body. Each circular arc ligament in the upper and lower circular arc ligament groups includes an arc segment and a straight connecting segment. The arc segment extends along the outer circumference of the ring body, and the straight connecting segment is tangentially connected to the end of the arc segment. The straight connecting segment in the upper arcuate ligament group extends upward and connects to the annular connecting panel above it; the straight connecting segment in the lower arcuate ligament group extends downward and connects to the annular connecting panel below it; the right arcuate ligament includes an arcuate segment connected to the outer circumferential surface of the main ring and a right straight connecting segment connected to the end of the arcuate segment, the right straight connecting segment being used to connect to the adjacent curved surface structure unit cell on the right; the left arcuate ligament includes an arcuate segment connected to the outer circumferential surface of the main ring and a left straight connecting segment connected to the end of the arcuate segment, the left straight connecting segment being used to connect to the adjacent curved surface structure unit cell on the left.

[0077] The preparation steps of the above metamaterial structure are as follows:

[0078] 1) Draw the unit cell model of the curved surface structure.

[0079] Using 3D modeling software, sketches of curved surface structure unit cells are drawn, and curved surface structure unit cell models are generated.

[0080] The curved structure unit cell is the curved structure unit cell in the aforementioned locally elastically buckling vibration-damping metamaterial structure;

[0081] Using 3D modeling software, draw a rectangular sketch of length *a* and width *b*. Then, use the extrude boss function to generate a cuboid with a target thickness of *t*. Using the front face of the cuboid as the reference plane, draw a unit cell sketch of the curved surface structure. Draw two concentric circles with the center of the front face as the center, forming an annulus of width *d*. Next, draw six circular arc ligaments, each with width *d*, on the outer circumference of the annulus. These six circular arc ligaments are divided into an upper circular arc ligament group, a lower circular arc ligament group, a left circular arc ligament, and a right circular arc ligament. The upper and lower circular arc ligament groups each contain two ligaments. To avoid the circular arc ligaments crossing each other, at the ends of the ligaments, a straight line is drawn tangent to the arc and extended to the edge of the cuboid. Figure 3 As shown. The end of the right arcuate ligament is an approximately triangular connection region; specifically, first, the intersection of the right arcuate ligament and the right boundary of the underlying rectangle is taken as the first point ①; then, this point is symmetrical about the horizontal axis to obtain the second point ②; then, a horizontal line is drawn through the first point ①, intersecting with the other boundary of the arcuate ligament to obtain the third point ③; connecting the second point ② and the third point ③ forms the oblique boundary of the end of the right arcuate ligament; this approximately triangular region is used to connect with adjacent structures; the left arcuate ligament is similar, as shown... Figure 3 As shown.

[0082] The flat curved structure unit cell model is obtained by stretching and cutting; then the flat curved structure unit cell model is bent by 60° by solid bending to obtain the curved structure unit cell model.

[0083] 2) Draw the compression-torsion structural unit model

[0084] Using 3D modeling software, the central axis of the outer curved surface of the unit cell model of the curved structure is used as the reference axis (see...). Figure 4 Six curved surface structure unit cell models are arranged in a circular array around the reference axis, and the ends of adjacent curved surface structure unit cells are connected one after another to form a cylindrical compression-torsion structure unit model.

[0085] The compression-torsion structural unit is the compression-torsion structural unit in the aforementioned locally elastic buckling vibration-damping metamaterial structure;

[0086] 3) Draw a vibration-damping metamaterial structure model with local elastic buckling.

[0087] 3.1) Using 3D modeling software, on the plane containing the upper end face of the compression-torsion structural unit model, with the intersection of the reference axis and this plane as the center, draw a ring with the same inner and outer diameters as the compression-torsion structural unit model. Then, using the extrude boss function, generate a ring with a target thickness of [missing information]. The model of the middle ring connecting panel;

[0088] 3.2) Based on the layer requirement of the compression-torsion structural unit in the target structure, continue to copy and alternately add the compression-torsion structural unit model and the new intermediate annular connecting panel model along the axial direction at the upper end of the intermediate annular connecting panel model, so that adjacent compression-torsion structural unit models are fixedly connected by the shared intermediate annular connecting panel model until the required number of layers is reached.

[0089] 3.3) At both ends of the overall structure, draw rings in the same manner as in step 3.1), and generate a target thickness using the extrude boss function. The end-connection layer model was used to obtain a vibration-damping metamaterial structure model with local elastic buckling.

[0090] 4) Printing vibration-damping metamaterial structures with localized elastic buckling

[0091] Using the locally elastic buckling damping metamaterial structure model obtained in step 3) as input, the structure is directly printed using 3D printing technology to obtain the locally elastic buckling damping metamaterial structure.

[0092] This embodiment is a preferred design obtained within the aforementioned structural parameter range. The locally elastic buckling damping metamaterial structure is cylindrical in shape and is formed by stacking four compression-torsion structural units sequentially along the axial direction. Adjacent compression-torsion structural units are connected by annular connecting panels. Each compression-torsion structural unit has a height of 20 mm, an inner diameter of 36.11 mm, an outer diameter of 40.11 mm, and a thickness of 2 mm. The height of the uppermost and lowermost annular connecting panels is 1.5 mm, and the height of the remaining annular connecting panels between adjacent compression-torsion structural units is 3 mm. Therefore, the total height of the metamaterial structure is 92 mm.

[0093] Each compression-torsion structural unit is a cylindrical structure formed by connecting six curved structural unit cells end to end in sequence; each curved structural unit cell includes a circular ring body and an arc ligament assembly disposed on the outer periphery of the circular ring body.

[0094] The basic geometric parameters of the unit cell of this curved structure are as follows: Figure 5 As shown in Table 1, including the central angle of the arcuate ligament The central angle of the main body of the ring Circular arc radius of curvature Circular ring main feature radius , width of the arc band Circular body ring width The cell length corresponding to the unit cell of the curved surface structure in its unbent state. and cell height ,in, and Both are π. It is 16 mm. It is 4 mm. and All are 1 mm. It is 21 mm. It is 20 mm.

[0095] Table 1. Basic geometric parameters of the unit cell of the curved surface structure

[0096]

[0097] It should be noted that the above dimensions are only a preferred embodiment of the present invention and are not intended to limit the scope of protection of the present invention. In practical applications, the load-bearing strength and energy absorption and vibration reduction effect of the structure can be adjusted by changing the thickness of the compression-torsion structural unit, the thickness of the annular connecting panel, and the number of axial layers. In this embodiment, SolidWorks 2024 is used for three-dimensional modeling (the three-dimensional modeling software is software with solid modeling, circumferential array, and solid bending functions, preferably SolidWorks 2024), and multi-jet fusion molding 3D printing technology is used to prepare the sample. The printing material is nylon PA12. Of course, the matrix material can also be selected from resin, metal, or ceramic materials according to the usage environment, and the molding method can also adopt 3D printing processes such as photopolymerization molding, laser melting molding, or fused deposition modeling.

[0098] Furthermore, to verify the impact of structural parameters on performance, metamaterial structures with thicknesses of 2 mm, 4 mm, and 6 mm were designed, respectively, under the condition of the same number of axial layers. Figure 6-7 As shown in Table 2, under the same thickness (2 mm), 4-layer and 8-layer metamaterial structures were designed respectively, and simulation and experimental tests were conducted on them under axial static compression of 25 mm.

[0099] Table 2. Wall thickness and number of layers in four different models

[0100]

[0101] Simulation and experimental test results are as follows Figure 8The results show that the simulation and experimental results (printed with PA12 material; material defects, contact friction, and boundary deviations introduce nonlinearity and printing errors, but the trend is the same as the simulation, exhibiting two stages) show the same trend. The curves clearly show that the model exhibits two elastic characteristics in the elastic stage. Analysis reveals that the mechanical response in the first stage is generated by the overall macroscopic structural deformation of the model. The metamaterial has low overall stiffness but large deformation, effectively absorbing energy during compression, demonstrating good energy absorption. When the displacement reaches a certain level, the second stage begins. At this point, the internal unit cells of the model contact and compress each other, working together to resist the load, significantly increasing the overall resistance to axial forces. The contact and interaction mechanism between unit cells endows the structure with a segmented elastic response and good energy absorption characteristics, providing performance support for its application in engineering scenarios such as buffering and energy absorption. Under the same material and loading conditions, the 4-layer metamaterial structure with a thickness of 6mm exhibits higher load-bearing strength and energy absorption effect, and its force-displacement curve shows good consistency with the simulation results.

[0102] In addition, such as Figure 9 As shown, a four-layer, 6 mm thick metamaterial structure is glued to a platform directly above a modal exciter. A 100 Hz sinusoidal excitation signal is generated using an arbitrary function generator and amplified by one, two, and three times, respectively, to drive the exciter to apply a mechanical load. Under the same excitation amplitude, acceleration response data at the excitation end and the other end of the model are collected using a high-precision accelerometer. Experimental results show that the vibration reduction effect of this invention can reach up to 70%. Figure 10 As shown.

[0103] In addition, such as Figure 11 As shown in Table 3, modal analysis was performed on the metamaterial structure of this invention and a conventional thin-walled cylinder with the same wall thickness of 2 mm. The results show that the first six eigenvalues ​​of the metamaterial structure of this invention are significantly lower than those of the conventional thin-walled cylinder. This indicates that the introduction of the circular arc ligament and the circular ring body reduces the equivalent stiffness of the structure, and lower-order modes are more easily excited in the form of local bending, local buckling, and compression-torsion coupling deformation. The conventional thin-walled cylinder has higher eigenvalues, indicating its greater overall stiffness and deformation mode that is more biased towards the overall structural response. In contrast, the metamaterial structure of this invention can preferentially generate local recoverable deformation under lower loads or vibration inputs, which is beneficial for dispersing external energy input and improving the structure's vibration damping and energy absorption capacity. Furthermore, the first few eigenvalues ​​appear in pairs, indicating that the structure has good circumferential symmetry, and the modal response exhibits similar deformation characteristics in different directions.

[0104] Table 3. Magnitude of Eigenvalues ​​for Thick-Walled Metamaterials and Rings

[0105]

[0106] Based on the axial static compression simulation and experimental testing, harmonic response analysis was performed on the vibration-damping metamaterial structure of this invention to evaluate its dynamic response characteristics under periodic vibration loads. During the simulation, ABAQUS finite element software was used to perform frequency sweep analysis on four models with different parameters, covering a frequency range of 0-300 Hz, and displacement response curves for each model at different excitation frequencies were extracted. The results are as follows: Figure 12 The results show that all four models exhibit displacement response peaks at specific frequencies, indicating that the structure resonates near these frequencies. The different models exhibit varying numbers, distribution ranges, and peak response frequencies, suggesting that structural thickness and the number of layers significantly affect the dynamic performance of the vibration-damping metamaterial structure. Specific simulation results are shown in Table 4. Therefore, this invention not only achieves energy absorption through static compression but also allows for the control of its frequency response characteristics through structural parameters, making it suitable for vibration damping and protection scenarios with periodic vibrations or impact loads.

[0107] Table 4 Resonance Frequency Table for Four Models

[0108]

[0109] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the scope of the technology disclosed in the present invention, and such modifications or substitutions should all be covered within the scope of protection of the present invention.

Claims

1. A locally elastically buckling vibration damping metamaterial structure, characterized by: The vibration-damping metamaterial structure is a cylindrical structure formed by stacking M compression-torsion structural units sequentially along the axial direction, where M ranges from 1 to 10. The adjacent compression-torsion structural units are connected by annular connecting panels, and the entire vibration-damping metamaterial structure has annular connecting panels coaxially arranged at both ends. The compression-torsion structural unit is a cylindrical structure formed by connecting N curved structural unit cells end to end in sequence, where N is 4-8; the angle of bending of each curved structural unit cell in the circumference of the cylinder is 360° / N. The curved structure unit cell includes a circular ring body and an arcuate ligament assembly disposed on the outer periphery of the circular ring body; the circular ring body is bent circumferentially along the cylinder; the arcuate ligament assembly extends along the outer periphery of the circular ring body and includes an upper arcuate ligament group, a lower arcuate ligament group, a right arcuate ligament, and a left arcuate ligament; wherein, the upper arcuate ligament group and the lower arcuate ligament group each include two arcuate ligaments; the connection positions of all arcuate ligaments to the circular ring body are evenly distributed circumferentially along the outer periphery of the circular ring body, and each arcuate ligament is bent and arranged in the same direction of rotation; the right arcuate ligament and the left arcuate ligament are both located between the upper arcuate ligament group and the lower arcuate ligament group, and are rotationally symmetrical about the geometric center of the circular ring body; the upper arcuate ligament group and the lower arcuate ligament group are rotationally symmetrical about the geometric center of the circular ring body; Each of the upper and lower circular arc ligament groups comprises an arc segment and a straight connecting segment; the arc segment extends and curves along the outer circumferential surface of the ring body, and the straight connecting segment is tangentially connected to the end of the arc segment; wherein, the straight connecting segment in the upper circular arc ligament group extends upward and connects to the annular connecting panel located above it, and the straight connecting segment in the lower circular arc ligament group extends downward and connects to the annular connecting panel located below it; the right circular arc ligament comprises an arc segment connected to the outer circumferential surface of the ring body and a right straight connecting segment connected to the end of the arc segment, the right straight connecting segment being used to connect to the adjacent curved surface structure unit cell on the right; the left circular arc ligament comprises an arc segment connected to the outer circumferential surface of the ring body and a left straight connecting segment connected to the end of the arc segment, the left straight connecting segment being used to connect to the adjacent curved surface structure unit cell on the left.

2. The vibration-damping metamaterial structure with localized elastic buckling according to claim 1, characterized in that: The inner diameter of the compression-torsion structure unit is 30-45 mm, the thickness is 2-8 mm, and the height is 20 mm; The inner and outer diameters of the annular connecting panel match the inner and outer diameters of the pressure-torsion structure unit, and its height is 1-3mm. The outer diameter of the main body of the ring is 6-12 mm, the inner diameter is 4-10 mm, and the ring width is 1-3 mm; The unit cell of the curved structure in its unbent state has a cell length of 21 mm and a cell height of 20 mm. The radius of curvature of the arc segment is 12-18 mm, and the width is 1-2 mm; The central angle between the connection points of two adjacent circular arc ligaments and the main body of the circular ring is 60°.

3. The vibration-damping metamaterial structure with local elastic buckling according to claim 2, characterized in that: M takes values ​​from 4 to 6, and N takes a value of 6.

4. The locally elastically buckling vibration damping metamaterial structure according to any one of claims 1-3, characterized in that: The material is nylon (PA12).

5. A method of making a locally elastically buckling vibration damping metamaterial structure, characterized by, Includes the following steps: 1) Draw the unit cell model of the curved surface structure. Using 3D modeling software, sketches of curved surface structure unit cells are drawn, and curved surface structure unit cell models are generated. The curved structure unit cell is the curved structure unit cell in the locally elastic buckling vibration-damping metamaterial structure described in claim 1 or 2; 2) Draw the compression-torsion structural unit model Using 3D modeling software, with the central axis of the outer curved surface of the curved structure unit cell model as the reference axis, N curved structure unit cell models are arranged in a circular array around the reference axis, and adjacent curved structure unit cells are connected end to end to form a cylindrical compression-torsion structure unit model. The compression-torsion structural unit is the compression-torsion structural unit in the locally elastic buckling vibration-damping metamaterial structure as described in claim 1 or 2; 3) Draw a vibration-damping metamaterial structure model with local elastic buckling. Using 3D modeling software, first, draw an intermediate annular connecting panel model on the upper end of the compression-torsion structural unit model obtained in step 2), which is coaxial with the compression-torsion structural unit model and has a matching inner and outer diameter; then, according to the layer requirements of the compression-torsion structural unit in the target structure, continue to copy and add the compression-torsion structural unit model and the intermediate annular connecting panel model along the axial direction on the upper end, so that adjacent compression-torsion structural unit models are connected by a shared intermediate annular connecting panel model; finally, draw end annular connecting panel models on both ends of the overall structure, which are coaxial with the compression-torsion structural unit model and have a matching inner and outer diameter, to obtain a vibration-damping metamaterial structure model with local elastic buckling. 4) Printing vibration-damping metamaterial structures with localized elastic buckling Using the locally elastic buckling damping metamaterial structure model obtained in step 3) as input, the structure is directly printed using 3D printing technology to obtain the locally elastic buckling damping metamaterial structure.

6. The preparation method according to claim 5, characterized in that, Step 1) Specifically: Use 3D modeling software to draw a rectangular sketch with length a and width b. Generate a cuboid with a target thickness t by using the extrude boss function. Draw a curved surface structure unit cell sketch with the front face of the cuboid as the reference face. Draw two concentric circles with the center of the front face as the center to form an annulus with a width of d. Then draw six circular arc ligaments with the same width d on the outer circumference of the annulus. The flat curved structure unit cell model is obtained by stretching and cutting; then the flat curved structure unit cell model is bent 360° / N by solid bending to obtain the curved structure unit cell model.

7. The preparation method according to claim 6, characterized in that, Step 3) specifically involves: 1) Using 3D modeling software, draw a ring with the same inner and outer diameters as the upper surface of the compression-torsion structural unit model on the plane containing the upper surface of the compression-torsion structural unit model, with the intersection of the reference axis and the plane as the center. Then, generate the intermediate annular connecting panel model of the target thickness by using the extrude boss function. 2) Based on the layer requirement of the compression-torsion structural unit in the target structure, continue to copy and alternately add the compression-torsion structural unit model and the new intermediate annular connecting panel model along the axial direction at the upper end of the intermediate annular connecting panel model, so that adjacent compression-torsion structural unit models are fixedly connected by the shared intermediate annular connecting panel model until the required number of layers is reached. 3) At both ends of the overall structure, draw rings in the same way as in step 3.1), and generate the end ring connection panel model of the target thickness through the extrude boss function to obtain the vibration reduction metamaterial structure model with local elastic buckling.

8. The preparation method according to claim 5, characterized in that: The 3D modeling software used is SolidWorks 2024.

9. The preparation method according to claim 5, characterized in that: In step 4), the 3D printing technology is multi-flow melt fusion 3D printing technology, and the printing substrate material is nylon (PA12).

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