Additive Manufacturing-Based Inertial Amplification Nonlinear Low-Frequency Vibration Isolation Metamaterial Structure, Isolation Device, and Performance Control Method

Abstract

This invention discloses an additive manufacturing-based inertial amplification nonlinear low-frequency vibration isolation metamaterial structure, vibration isolation device, and its performance control method. The vibration isolation metamaterial structure includes a rhombic frame structure, an inertial amplification unit, and a square spring structure. The square spring structure is arranged within the rhombic frame structure, with its two ends connected to a pair of opposite corners of the rhombic frame structure. The elastic extension direction of the square spring structure is parallel to the diagonal of this pair of opposite corners of the rhombic frame structure. The inertial amplification unit has a centrally symmetrical structure, including a rigid rod, two counterweights, and two diagonal rods. The center of symmetry of the inertial amplification unit, the center of the rhombic frame structure, and the center of the square spring structure all coincide in projection. Therefore, the vibration isolation metamaterial structure of this invention significantly widens the bandgap range and enhances low-frequency vibration isolation performance, exhibiting excellent performance in suppressing longitudinal waves in the 0-1000Hz low-frequency range, increasing vibration damping, and energy absorption.

Description

Technical Field

[0001] This invention relates to an inertial amplification nonlinear low-frequency vibration isolation metamaterial structure based on additive manufacturing, a vibration isolation device and its performance control method, belonging to the field of inertial amplification vibration isolation technology. Background Technology

[0002] Low-frequency vibrations are widely present in mechanical equipment, transportation, and building structures. They not only affect the precision and lifespan of equipment, but also cause noise pollution and structural fatigue, and in severe cases, even threaten personnel safety.

[0003] Traditional vibration isolation materials (such as rubber and springs) are limited by their inherent properties and are difficult to effectively suppress low-frequency vibrations.

[0004] In recent years, metamaterials have shown great potential in the field of vibration isolation due to their unique bandgap characteristics. However, existing metamaterial structures still have problems such as narrow bandgap range, insufficient nonlinear characteristics, and incomplete utilization of inertial amplification effect, which limit their application in practical engineering. Summary of the Invention

[0005] The purpose of this invention is to provide an additive manufacturing-based inertial amplification nonlinear low-frequency vibration isolation metamaterial structure, vibration isolation device, and its performance control method. By introducing an inertial amplification unit and a nonlinearly designed square spring structure, the bandgap range of the vibration isolation metamaterial structure is significantly widened and the low-frequency vibration isolation performance is enhanced. It has excellent performance in suppressing longitudinal waves in the 0~1000Hz low-frequency range, increasing vibration damping, and energy absorption.

[0006] To achieve the above-mentioned technical objectives, the present invention will adopt the following technical solution: An additive manufacturing-based inertial amplification nonlinear low-frequency vibration isolation metamaterial structure includes a rhombic frame structure and a square spring structure. The square spring structure is arranged inside the rhombic frame structure, and its two ends are respectively connected to one set of diagonals of the rhombic frame structure. At the same time, the elastic extension direction of the square spring structure is parallel to the diagonal of this set of diagonals of the rhombic frame structure. An inertial amplification unit is also arranged inside the rhombic frame structure. The inertial amplification unit has a centrally symmetrical structure and includes a rigid rod, two counterweights, and two diagonal rods. The rigid rod is arranged along the diagonal of one set of diagonals of the rhombic frame structure. The two counterweights are respectively connected to the two ends of the rigid rod. The two diagonal rods are located on both sides of the center of the rigid rod, and one end of each diagonal rod is connected to the rigid rod, while the other end is respectively connected to the remaining set of diagonals of the rhombic frame structure. The center of symmetry of the inertial amplification unit, the center of the rhomboid frame structure, and the center of the square spring structure all coincide in projection.

[0007] Preferably, it also includes two mass blocks; a rhombus frame structure is arranged between the two mass blocks, and one set of opposite corners of the rhombus frame structure is connected to the two mass blocks respectively; a square spring structure is arranged along the diagonal of the remaining set of opposite corners of the rhombus frame structure.

[0008] Preferably, the two diagonal rods of the inertial amplification unit and the two ends of the square spring structure are respectively connected to the same set of diagonals of the rhomboid frame structure.

[0009] Preferably, the middle part of the square spring structure includes a plurality of Z-shaped crease units, which are arranged in a wave-like manner along the axial direction of the square spring structure, and each crease unit has the same size and shape.

[0010] Preferably, the rhombic frame structure includes at least one pair of rhombic frame structure parts of the same size and shape; the two rhombic frame structure parts correspond to a first rhombic frame structure part and a second rhombic frame structure part, and the first rhombic frame structure parts are superimposed to form a whole; the first rhombic frame structure part is provided with a square spring structure, and the center of the first rhombic frame structure part coincides with the center of the square spring structure; the second rhombic frame structure part is provided with an inertial amplification unit, and the center of the second rhombic frame structure part coincides with the symmetry center of the inertial amplification unit.

[0011] Preferably, the rhomboid frame structure is integrally formed with the square spring structure and the inertia amplification unit using additive manufacturing technology.

[0012] The second technical objective of this invention is to provide a vibration isolation device comprising the aforementioned additive manufacturing-based inertial amplification nonlinear low-frequency vibration isolation metamaterial structure.

[0013] Preferably, multiple additive manufacturing-based inertial amplification nonlinear low-frequency vibration isolation metamaterial structures are connected end to end from top to bottom to form a set of vibration isolation structures, and multiple sets of vibration isolation structures are combined to form a vibration isolation device.

[0014] The third technical objective of this invention is to provide a method for performance control of an additively manufactured, inertial amplification nonlinear low-frequency vibration isolation metamaterial structure, comprising the following steps: S1. Preset the adjustment range of the geometric parameters of the inertial amplification unit and preliminarily determine the geometric parameters of the inertial amplification unit based on the preset adjustment range; the preset adjustment range of the geometric parameters of the inertial amplification unit includes the adjustment range of the side length of the counterweight, the adjustment range of the connection angle, and the adjustment range of the wall thickness. S2. By adjusting the wall thickness, connection angle, and side length of the counterweight, the local stiffness and inertial amplification effect of the inertial amplification unit can be changed, thereby controlling the width and depth of the bandgap of the inertial amplification nonlinear low-frequency vibration isolation metamaterial structure. S3. Use finite element analysis software to establish a dynamic model of the inertial amplified nonlinear low-frequency vibration isolation metamaterial structure, simulate the energy band diagram of the structure under different geometric parameters, determine the starting frequency, cutoff frequency and width of the band gap, and combine the quasi-static tensile test results of the vibration isolation metamaterial structure under different geometric parameters to select the optimal combination of geometric parameters. S4. An inertial amplification nonlinear low-frequency vibration isolation metamaterial structure with optimal geometric parameter combination is formed using laser 3D printing technology. The printed inertial amplification nonlinear low-frequency vibration isolation metamaterial structure is installed on a vibration test bench. External excitation is applied through a vibrator, and the displacement response curve of the inertial amplification nonlinear low-frequency vibration isolation metamaterial structure is measured using a laser vibrometer to verify its actual vibration isolation performance.

[0015] Preferably, in step S1, the side length of the counterweight is adjusted in the range of 2~8mm, the connection angle is adjusted in the range of 76~88°, and the wall thickness ε is adjusted in the range of 0.7~1.5mm.

[0016] Based on the above-mentioned technical objectives, the present invention has the following advantages compared with the prior art: 1. The additive manufacturing-based inertial amplification nonlinear low-frequency vibration isolation metamaterial structure of this invention further optimizes the existing vibration isolation metamaterial structure with a square spring structure arranged within a rhombic frame structure. It not only arranges a square spring structure with nonlinear characteristics within the rhombic frame structure but also an inertial amplification unit with a specific structural form (the inertial amplification unit has a centrally symmetrical structure, including a rigid rod, two counterweights, and two diagonal rods). Therefore, the synergistic effect of the nonlinear characteristics of the square spring structure and the inertial effect of the inertial amplification unit optimizes the metamaterial structure of this invention. The low-frequency vibration isolation effect allows the square spring structure to achieve low stiffness characteristics through its geometric flexibility while providing stable restoring force, enabling the rhomboid frame structure to produce controllable deformation under low-frequency excitation and avoiding instability of the metamaterial structure described in this invention due to excessive softness. The inertial amplification unit, through the leverage of the rigid rod and the inclined rod (a connecting rod arranged at an angle relative to the rigid rod, hence denoted as the inclined rod), significantly amplifies the inertial effect of the counterweight, thereby enhancing the energy absorption and dissipation capability of the metamaterial structure described in this invention against low-frequency vibrations. Specifically, when subjected to low-frequency vibration, the inclined rod amplifies the displacement caused by the low-frequency vibration into a larger displacement and acceleration at the end of the counterweight through geometric transformation, causing the counterweight to generate an inertial reaction force much greater than that caused by direct excitation. This amplified inertial reaction force is fed back to the matrix through the metamaterial structure described in this invention (formed by the coupling of the rhomboid frame structure, the square spring structure, and the inertial amplification unit), thereby strongly suppressing low-frequency input vibrations and achieving the inertial amplification effect.

[0017] Furthermore, the metamaterial structure described in this invention, given that the inertial amplification unit can amplify inertial forces to counteract vibration energy and prevent the transmission and accumulation of vibration, exhibits excellent vibration isolation effects, particularly for low-frequency vibrations with longer wavelengths and more concentrated energy. In addition, the introduction of the square spring structure further enhances the nonlinear stiffness characteristics of the metamaterial structure. Through periodically distributed zigzag units, nonlinear elastic deformation can be generated during vibration, thereby widening the bandgap range of the metamaterial structure and enhancing its low-frequency vibration isolation performance. The synergistic effect of the square spring structure and the inertial amplification unit not only increases the dissipation paths of vibration energy but also delays fatigue damage to the metamaterial structure, extending the service life of the vibration isolation device.

[0018] This invention, through its inertial amplification nonlinear low-frequency vibration isolation metamaterial structure, demonstrates exceptional adaptability in a variety of complex environments. Whether subjected to prolonged low-frequency vibrations or instantaneous high-amplitude impacts, the structure provides effective vibration isolation and energy dissipation.

[0019] 2. The metamaterial structure described in this invention arranges a rhombic frame structure between two mass blocks, with one set of diagonals of the rhombic frame structure connected to the two mass blocks respectively. A square spring structure is arranged along the diagonal of the remaining set of diagonals of the rhombic frame structure. Therefore, when low-frequency vibrations are input from the two mass blocks, the rhombic frame structure mainly bears shear deformation rather than direct tension and compression, thereby significantly reducing the equivalent stiffness and providing motion space for the inertial amplification unit, ensuring the feasibility and effectiveness of the inertial amplification effect.

[0020] 3. The metamaterial structure described in this invention connects the two diagonal rods of the inertial amplification unit and both ends of the square spring structure to the same set of diagonals of the rhombic frame structure. This effectively promotes the optimization of the overall stiffness distribution of the metamaterial structure by the inertial amplification unit. Due to the lower stiffness of the inertial amplification unit, the counterweight can undergo greater displacement, effectively enhancing the amplification effect of the inertial amplification unit. On the other hand, the higher stiffness of the other set of diagonals of the rhombic frame structure restricts the free movement of the counterweight, resulting in a weaker inertial amplification effect. Furthermore, connecting the two diagonal rods of the inertial amplification unit and both ends of the square spring structure to the same set of diagonals of the rhombic frame structure avoids early stiffening or nonlinear interference phenomena, making the inertial reaction force more controllable and stable, thereby further enhancing the low-frequency vibration isolation performance.

[0021] 4. The inertial amplification nonlinear low-frequency vibration isolation metamaterial structure of this invention integrates the rhombic frame structure with the square spring structure or the inertial amplification unit into a single structure; this significantly improves the overall reliability and stability, avoids structural weaknesses that may arise from connecting parts or assembly processes, and thus reduces the risk of stress concentration and fatigue failure. It ensures that the structure maintains its efficient vibration isolation performance under long-term and complex load conditions.

[0022] 5. The inertial amplification nonlinear low-frequency vibration isolation metamaterial structure of this invention has mass blocks at both ends of the rhombic frame structure; the mass blocks can change the inertial characteristics of the structure, causing changes in the structure's natural frequency and vibration mode. The mass blocks can increase the structure's damping, reduce the vibration amplitude, and improve the structure's stability and vibration resistance.

[0023] 6. The performance control method of the inertial amplification nonlinear low-frequency vibration isolation metamaterial structure described in this invention achieves precise control of the vibration isolation performance of the structure by optimizing key geometric parameters.

[0024] This invention selects wall thickness, connection angle, and counterweight side length as key control parameters because they directly affect the local stiffness, inertial amplification effect, and bandgap characteristics of the structure. Wall thickness determines the stiffness distribution of the frame structure; increasing wall thickness improves local stiffness and narrows the bandgap, while decreasing wall thickness reduces stiffness and widens the bandgap range. The connection angle, by adjusting the inclination of the diagonal brace, affects the strength of the inertial amplification effect; a smaller connection angle enhances the lever effect of the diagonal brace, significantly amplifying the inertial effect of the counterweight, thereby improving vibration isolation performance in the 0-1000Hz low-frequency range. The counterweight side length directly determines the magnitude of the inertial force; increasing the side length enhances the inertial amplification effect and improves the energy absorption capacity for low-frequency vibrations. To accurately realize the above complex geometric structure, this invention selects laser additive manufacturing technology for fabrication.

[0025] This technology enables high-precision layer-by-layer construction of the structure, ensuring the integrated molding of the frame structure, square spring structure, and inertial amplification unit, thereby further improving the vibration isolation performance and durability of the vibration isolation metamaterial structure. Attached Figure Description

[0026] 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 only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0027] Figure 1This is a schematic diagram of the inertial amplification nonlinear low-frequency vibration isolation metamaterial structure (Example 1, with horizontal arrangement of inertial amplification units) described in this invention. Figure 2 This is a schematic diagram of the inertial amplification nonlinear low-frequency vibration isolation metamaterial structure described in this invention (Example 14, with the inertial amplification unit arranged vertically). Figure 3 This diagram illustrates the complete production process of the inertial amplification nonlinear low-frequency vibration isolation metamaterial structure described in this invention, which is integrally formed using additive manufacturing technology.

[0028] Figure 4 This is a band structure diagram showing the side length a of the counterweight of the inertial amplification unit, the connection angle θ of the diagonal rod, and the wall thickness e of the rhombic frame structure in the inertial amplification nonlinear low-frequency vibration isolation metamaterial structure described in Example 1; wherein: (a) represents a structural schematic diagram of the inertial amplification nonlinear low-frequency vibration isolation metamaterial structure in Example 1; (b) represents a comparison diagram of the band gap changes in the metamaterial structure caused by changes in the side length of the counterweight (a=2mm, 4mm, 6mm, 8mm); (c) represents a comparison diagram of the band gap changes in the metamaterial structure caused by changes in the connection angle θ of the diagonal rod (θ=76°, 80°, 84°, 88°); (d) represents a comparison diagram of the band gap changes in the metamaterial structure caused by changes in the wall thickness e of the rhombic frame structure (e=0.7mm, 0.8mm, 0.9mm, 1.5mm); Figure 5 The test results for verifying the mechanical properties of the inertial amplification nonlinear low-frequency vibration isolation metamaterial structure described in this invention are as follows: (a) shows the load-displacement curve of the inertial amplification nonlinear low-frequency vibration isolation metamaterial structure described in Example 1; (b) shows the load-displacement curve of the inertial amplification nonlinear low-frequency vibration isolation metamaterial structure described in Example 14; (c) shows the load-displacement curve of the inertial amplification nonlinear low-frequency vibration isolation metamaterial structure described in Example 1 at different connection angles (θ=76°, 80°, 84°, 88°); (d) shows the load-displacement curve of the inertial amplification nonlinear low-frequency vibration isolation metamaterial structure described in Example 1 at different wall thicknesses (e=0.7mm, 0.8mm, 0.9mm, 1.5mm).

[0029] Figure 6 The experimental results of the low-frequency vibration isolation performance test of the inertial amplification nonlinear low-frequency vibration isolation metamaterial structure described in Embodiment 1 of the present invention are as follows, from left to right: a schematic diagram of the longitudinal bandgap of the vibration isolation metamaterial structure; a simulated harmonic response curve of the vibration isolation metamaterial structure; and a harmonic response curve of the experimental verification of the vibration isolation metamaterial structure.

[0030] Figure 7The experimental results of the low-frequency vibration isolation performance test of the inertial amplification nonlinear low-frequency vibration isolation metamaterial structure described in Embodiment 14 of the present invention are as follows, from left to right: a schematic diagram of the longitudinal bandgap of the vibration isolation metamaterial structure; a simulated harmonic response curve of the vibration isolation metamaterial structure; and a harmonic response curve of the experimental verification of the vibration isolation metamaterial structure.

[0031] Figure 8 This is an exploded view of the inertial amplification nonlinear low-frequency vibration isolation metamaterial structure in Embodiment 1 of the present invention.

[0032] Figure 9 This is a three-dimensional structural diagram of the inertial amplification nonlinear low-frequency vibration isolation metamaterial structure in Embodiment 1 of the present invention.

[0033] Figure 10 This is a perspective view of the vibration isolation device in an embodiment of the present invention.

[0034] Explanation of the labels in the diagram: 1. Mass block; 2. Inertial amplification unit; 3. Rhomboid frame structure; 4. Upper structure; 5. Lower structure; 41. Square spring structure; 51. Counterweight; 52. Diagonal bar; 53. Rigid bar. Detailed Implementation

[0035] 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. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention. Unless otherwise specifically stated, the relative arrangement, expressions, and values ​​of components and steps set forth in these embodiments do not limit the scope of the present invention. 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.

[0036] For ease of description, spatial relative terms such as "above," "over," "on the upper surface of," "above," etc., are used here to describe the spatial positional relationship of a device or feature as shown in the figure with 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 figure. For example, if the device in the figure 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).

[0037] To suppress low-frequency vibrations, the research team of this invention developed a metamaterial structure as shown in Chinese Patent CN119196206A, which exhibits relatively excellent vibration isolation performance in low-frequency vibrations. However, on the one hand, this metamaterial structure does not introduce an inertial amplification unit 2 to further optimize the vibration isolation performance; on the other hand, its bandgap range is relatively narrow, which has significant limitations in engineering practice.

[0038] To this end, the research and development team of this invention further optimized the metamaterial structure shown in Chinese Patent CN119196206A. On the one hand, it retained the overall frame structure (rhomboid frame structure) of the original metamaterial structure and its included square spring structure 41, a nonlinear vibration damping component. On the other hand, it introduced an inertial amplification unit 2. Therefore, the technical problems faced by the research and development team of this invention include at least the following two: one is how the inertial amplification unit 2 is coupled with the rhomboid frame structure and the square spring structure 41 to optimize the vibration isolation performance of the resulting metamaterial structure and broaden its bandgap range; the other is what structural form of the inertial amplification unit 2, after coupling with the rhomboid frame structure and the square spring structure 41, can optimize the vibration isolation performance of the resulting metamaterial structure and further broaden its bandgap range.

[0039] Based on this current technological situation, the research and development team of this invention has developed the following... Figure 1 , Figure 2 , Figure 8 and Figure 9The inertial amplification nonlinear low-frequency vibration isolation metamaterial structure shown includes a rhombus frame structure 3, an inertial amplification unit 2, and a square spring structure 41. The two ends of the square spring structure 41 are respectively connected to one set of opposite corners of the rhombus frame structure 3, and the elastic extension direction of the square spring structure 41 is parallel to the diagonal of this set of opposite corners of the rhombus frame structure 3. The inertial amplification unit 2 is a centrally symmetrical structure with two connecting ends, each corresponding to one set of opposite corners of the rhombus frame structure 3. The center of symmetry of the inertial amplification unit 2, the center of the rhombus frame structure 3, and the center of the square spring structure 41 all project to coincide.

[0040] In this invention, to increase the damping of the vibration isolation metamaterial structure, reduce its vibration amplitude, and improve its stability and vibration resistance, a rhomboid frame structure 3 is arranged between two mass blocks 1. One set of diagonals of the rhomboid frame structure 3 (in the attached drawing, this set of diagonals is 120°) is connected to each of the two mass blocks 1. A square spring structure 41 is arranged along the diagonal of the remaining set of diagonals of the rhomboid frame structure 3 (in the attached drawing, this set of diagonals is 60°). The mass blocks 1 can alter the inertial characteristics of the structure, causing changes in its natural frequency and vibration mode. The mass blocks 1 can increase the damping of the structure, reduce the vibration amplitude, and improve its stability and vibration resistance.

[0041] The inertial amplification unit 2 used in this invention includes a rigid rod 53, two counterweights 51, and two diagonal rods 52. The rigid rod 53 is arranged along one diagonal line of a set of opposite corners of the rhomboid frame structure 3. The two counterweights 51 are respectively connected to both ends of the rigid rod 53. The two diagonal rods 52 are located on both sides of the center of the rigid rod 53, with one end of each diagonal rod 52 connected to the rigid rod 53 and the other end connected to the remaining set of opposite corners of the rhomboid frame structure 3. Therefore, the ends of the two diagonal rods 52 in this invention are the two connecting ends of the inertial amplification unit 2.

[0042] The square spring structure 41 used in this invention includes a plurality of zigzag crease units in its middle part. The crease units are arranged in a wave-like manner along the axial direction of the square spring structure 41, and each crease unit has the same size and shape.

[0043] The following will describe in detail the inertial amplification nonlinear low-frequency vibration isolation metamaterial structure of the present invention with reference to several embodiments. Example 1

[0044] like Figure 1 , Figures 8 to 9 As shown, the inertial amplification nonlinear low-frequency vibration isolation metamaterial structure based on additive manufacturing disclosed in this embodiment is formed by 3D printing process and is formed by melting and forming two layers.

[0045] The upper structure 4 includes an upper mass block component A, a first rhomboid frame structure component, a square spring structure 41, and a lower mass block component A. The lower structure 5 includes an upper mass block component B, a first rhomboid frame structure component, an inertial amplification unit 2, and a lower mass block component B. The upper mass block components A and B are the same size and shape, and they are fused together to form the upper mass block. The lower mass block components A and B are the same size and shape, and they are fused together to form the lower mass block. The upper and lower mass blocks together constitute the two mass blocks. The first and second rhomboid frame structure components are the same size and shape, and they are fused together to form the rhomboid frame structure 3.

[0046] The upper and lower mass blocks A are respectively located at the upper and lower ends of the first rhomboid frame structure and are respectively connected to the upper and lower ends of the first rhomboid frame structure. The square spring structure 41 is arranged within the first rhomboid frame structure and along the transverse direction of the first rhomboid frame structure (i.e., attached). Figure 1 The square spring structure 41 is arranged diagonally in a horizontal direction, and the two ends of the square spring structure 41 are respectively connected to a set of diagonals in the horizontal direction of the first rhomboid frame structure.

[0047] The upper and lower mass block components B are respectively located at the upper and lower ends of the second rhomboid frame structure component and are respectively connected to the upper and lower ends of the second rhomboid frame structure component. The inertial amplification unit 2 is arranged inside the second rhomboid frame structure component, and the two ends of the inertial amplification unit 2 are respectively connected to the second rhomboid frame structure component laterally (i.e., attached). Figure 1 A pair of diagonally corresponding connections (in the horizontal direction).

[0048] Meanwhile, in this embodiment, the center of the square spring structure 41 coincides with the center of the first rhomboid frame structure, while the center of symmetry of the inertial amplification unit 2 coincides with the center of the second rhomboid frame structure. (The last sentence appears to be incomplete and possibly refers to a different embodiment.) Figure 1 The center of the square spring structure 41, the center of symmetry of the inertial amplification unit 2, and the center of the rhomboid frame structure 3 are coincident when projected onto the plane of the drawing.

[0049] In addition, in this embodiment, the inertial amplification unit 2 includes a rigid rod 53 and two counterweights 51. The two ends of the rigid rod 53 are respectively connected to a counterweight 51, and the middle part is connected to the left and right corners of the frame structure 3 through two diagonal rods 52 that are centrally symmetrically distributed. This design significantly amplifies the inertial effect of the counterweights 51 through the lever effect of the rigid rod 53 and the diagonal rods 52, thereby enhancing the structure's ability to absorb and dissipate energy from low-frequency vibrations.

[0050] The inertial amplification nonlinear low-frequency vibration isolation metamaterial structure described in this embodiment is formed by laser 3D printing and implemented using the DiMetal-100H laser powder bed melting equipment (manufactured by Guangzhou Leijia Additive Manufacturing Technology Co., Ltd.). The specific steps include: S101. Control the oxygen content in the forming cavity to be below 10 ppm; S102. Control the powder feeding device to supply 3D printing metal powder to the forming cylinder, and then use the automatic powder spreading device to evenly spread the aforementioned 3D printing metal powder on the forming substrate. The 3D printing metal powder used is gas-atomized AlSi7Mg alloy powder (chemical composition: 92.43 at.%, 7.23 at.% Si, 0.34 at.% Mg), produced by Jiangsu Weilai New Material Technology Co., Ltd., with a particle size range of 15-53 μm. AlSi7Mg alloy powder was chosen for LPBF fabrication of the vibration-damping metamaterial structure described in this invention because it possesses low density and high ductility, along with certain strength and corrosion resistance. Parts manufactured using AlSi7Mg alloy powder exhibit higher stability and reliability, making them particularly suitable for high-performance mechanical systems in vibration damping applications.

[0051] S103. Control the laser scanning of the 3D printed metal powder on the substrate until it is completely melted to form a single-layer cross-section of the inertial amplification nonlinear low-frequency vibration isolation metamaterial structure sample; the laser line energy of the laser used has a scanning speed v of 800 mm / s, a laser power P set to a fixed value of 200 W, an interlayer thickness of 30 μm, and a scanning spacing of 60 μm. S104. After each layer is processed, the forming cavity is lowered by the thickness of one layer of powder. Based on the scanning model of the nonlinear low-frequency vibration isolation metamaterial structure amplified by inertia, steps S2 and S3 are repeated to finally obtain the target sample forming part.

[0052] To obtain a low-frequency vibration isolation metamaterial structure with excellent vibration reduction performance due to inertial amplification nonlinearity, this embodiment provides a method for performance control of this vibration isolation metamaterial structure, which specifically includes the following steps: S1. Preset the adjustment range of the geometric parameters of the inertial amplification unit 2 and preliminarily determine the geometric parameters of the inertial amplification unit 2 based on the preset adjustment range of the geometric parameters; the preset adjustment range of the geometric parameters of the inertial amplification unit 2 includes the adjustment range of the side length of the counterweight 51, the adjustment range of the connection angle, and the adjustment range of the wall thickness ε; the adjustment range of the side length of the counterweight 51 is 2~8mm, the adjustment range of the connection angle is 76~88°, and the adjustment range of the wall thickness ε is 0.7~1.5mm.

[0053] S2. By adjusting the wall thickness, connection angle, and side length, the local stiffness and inertial amplification effect of the vibration isolation metamaterial structure are changed, thereby controlling the band gap width and depth of the vibration isolation metamaterial structure. Specifically, different side lengths a, connection angles θ, and wall thicknesses ε are set for the inertial amplification unit 2 to obtain different inertial amplification nonlinear low-frequency vibration isolation metamaterial structures, so as to control the band gap width and depth of the vibration isolation metamaterial structure. See Examples 2 to 13 for details.

[0054] The vibration isolation metamaterial structures corresponding to each embodiment have different structural parameters, as shown in Tables 1 to 3 below: Table 1 Different side lengths a

[0055]

[0056] Table 2 Different connection angles θ

[0057] Table 3 Different wall thicknesses ε

[0058] Referring to Table 1, it can be seen that the only difference between the inertial amplification nonlinear low-frequency vibration isolation metamaterial structures described in Examples 1 to 4 is the side length a of the counterweight 51. Specifically, in Example 1, a = 2 mm; in Example 2, a = 4 mm; in Example 3, a = 6 mm; and in Example 4, a = 8 mm.

[0059] Referring to Table 2, it can be seen that the only difference between the inertial amplification nonlinear low-frequency vibration isolation metamaterial structures described in Examples 5 to 8 is the connection angle θ. Specifically, in Example 5, θ = 76°; in Example 6, θ = 80°; in Example 7, θ = 84°; and in Example 8, θ = 88°.

[0060] Referring to Table 3, it can be seen that the only difference between Examples 9 to 12 is the wall thickness ε. Specifically, in Example 9, ε = 0.7 mm; in Example 10, ε = 0.8 mm; in Example 11, ε = 0.9 mm; and in Example 12, ε = 1.5 mm.

[0061] S3. Use finite element analysis software to establish a dynamic model of the inertial amplified nonlinear low-frequency vibration isolation metamaterial structure, simulate the energy band diagram of the structure under different geometric parameters, determine the starting frequency, cutoff frequency and width of the band gap, and combine the quasi-static tensile test results of the vibration isolation metamaterial structure under different geometric parameters to select the optimal combination of geometric parameters. Based on the geometric parameters of the inertial amplification nonlinear low-frequency vibration isolation metamaterial structure set in Examples 2-13, a dynamic model of the corresponding vibration isolation metamaterial structure was established using finite element analysis software to simulate the structural energy band diagram under different geometric parameters. See the appendix for details. Figure 4 (b), (c), (d).

[0062] from Figure 4 As can be seen in (b), as the side length of counterweight 51 increases, the starting frequency of the first bandgap gradually decreases, which indicates that the inertial amplification effect of counterweight 51 is significantly enhanced, thereby improving the low-frequency vibration isolation performance of the structure.

[0063] Figure 4 Figure (c) shows the band structure diagram of the structure at different connection angles. As the connection angle increases, the band gap range below 500 Hz gradually decreases. Especially when the connection angle reaches 88°, the band gap almost disappears completely. This indicates that a smaller connection angle is more conducive to enhancing the inertial amplification effect and widening the low-frequency band gap.

[0064] Figure 4 (d) reveals the influence of wall thickness on the energy band characteristics of the structure. The wall thickness directly determines the stiffness distribution of the structure. As the wall thickness increases, the structural stiffness increases significantly, but the vibration isolation performance decreases significantly. This indicates that the wall thickness needs to achieve a balance between stiffness and vibration isolation performance.

[0065] Based on the analysis results in (b), (c), and (d) of section 4, it can be concluded that by optimizing the side length, connection angle, and wall thickness of counterweight 51, the bandgap characteristics of the structure can be significantly controlled, thereby achieving excellent low-frequency vibration isolation performance.

[0066] Based on the geometric parameters of the inertial amplification nonlinear low-frequency vibration isolation metamaterial structure set in Examples 2-13, the corresponding test pieces were printed using 3D printing technology to conduct quasi-static tensile tests in order to evaluate the mechanical properties of each test piece.

[0067] The quasi-static tensile test was performed using an electronic universal testing machine (CMT4304-5-KN, SANS Corporation, China). The sample was placed on a horizontal platform on the base of the testing machine and fixed and leveled by a steel clamp. The testing machine applied a uniform upward displacement to the upper surface of the sample through the upper clamp. At the same time, the upper clamp accurately obtained the force applied during the uniform displacement through a sensor. The magnitude of the force was equivalent to the downward reaction force during the tensile process of the vibration isolation metamaterial structure. After the tensile test was completed, the force-displacement curve during the tensile process was automatically plotted. The tensile speed was set to 0.05 mm / s.

[0068] Figure 5Figure (c) shows the load-displacement curves at different connection angles (data obtained through quasi-static tensile testing). It can be observed that the elongation of the structure gradually decreases with increasing angle, especially at 88°, where the structure fails when the displacement reaches 17 mm. With increasing connection angle, the connection points of the structure gradually move closer to the rotation center of the inertial amplification unit 2. The inertial amplification unit 2 consists of two diagonal braces 52 connecting the left and right points of the frame structure 3. When the structure is subjected to vertical tension, the relative elongation of the frame structure 3 causes the rotating arm to shorten. With increasing connection angle, the shortening of the rotating arm increases rotational resistance, thereby enhancing rotational damping and improving the overall stiffness of the structure. Specifically, the shorter the rotating arm, the greater the resistance generated by rotation, which improves the structure's ability to resist external loads, thus increasing its overall stiffness. Therefore, increasing the connection angle not only affects the effect of inertial amplification but also enhances the stiffness of the structure by increasing rotational damping.

[0069] Figure 5 Figure (d) shows the load-displacement curves (data obtained through quasi-static tensile testing) for wall thicknesses of 0.7 mm, 0.9 mm, 1.0 mm, and 1.5 mm. The results show that wall thickness has a significant impact on structural stiffness. Particularly when the wall thickness is 1.5 mm, the load increases sharply with increasing tensile displacement. The structure begins to yield at approximately 280 N and fails at 368 N. Further analysis indicates that increasing wall thickness directly leads to enhanced structural stiffness, enabling the structure to withstand higher loads under the same tensile displacement, exhibiting stronger load-bearing capacity. This phenomenon demonstrates that increasing wall thickness not only enhances structural rigidity but also improves its resistance to deformation.

[0070] based on Figure 5 The analysis of results (c) and (d) shows that optimizing the connection angle and wall thickness of the structure according to different application requirements can effectively control its mechanical properties, thereby achieving the best vibration isolation and load-bearing capacity.

[0071] Based on Examples 2-13, the optimal geometric parameter combination of the inertial amplification unit 2 in the inertial amplification nonlinear low-frequency vibration isolation metamaterial structure of the present invention is obtained: the connection angle is 80°, and the side length of the counterweight 51 is 6mm. The thicknesses of the first and second rhomboid frame structures, the square spring structure 41, and the rigid rod 53 are all 0.8mm.

[0072] The optimal structural parameter of 0.8 mm for the thickness of the rhombic frame structure 3 was chosen based on a comprehensive consideration of simulation results from the structural band diagram and experimental verification. Numerical simulations revealed that reducing the thickness of the rhombic frame structure 3 significantly improves vibration isolation performance. However, in early experiments, samples with a thickness less than 0.8 mm exhibited poor formability and were more prone to damage during cutting from the substrate due to residual stress. On the other hand, while samples with a thickness exceeding 0.8 mm showed better structural stability, their low-frequency absorption capacity decreased significantly, and their low-frequency bandgap range narrowed. Therefore, the 0.8 mm thickness of the rhombic frame structure 3 achieved the best balance between formability, structural stability, and vibration isolation performance, and was thus determined as the optimal parameter.

[0073] S4. An inertial amplification nonlinear low-frequency vibration isolation metamaterial structure with optimal geometric parameter combination is formed using laser 3D printing technology. The printed inertial amplification nonlinear low-frequency vibration isolation metamaterial structure is installed on a vibration test bench. External excitation is applied through a vibrator, and the displacement response curve of the inertial amplification nonlinear low-frequency vibration isolation metamaterial structure is measured using a laser vibrometer to verify its actual vibration isolation performance.

[0074] Low-frequency vibration isolation performance tests were conducted on the inertial amplification nonlinear low-frequency vibration isolation metamaterial structure formed by laser 3D printing with optimal geometric parameter combinations. The test results are shown in the appendix. Figure 6 The results in the figure indicate that, using appropriate structural parameters, an inertial amplification forming component manufactured with a rhomboid frame structure 3 (thickness 0.8 mm), a connection angle of 80°, and an inertial amplification counterweight 51 (side length 6 mm) can form an ultra-wide low-frequency longitudinal bandgap. Multiple longitudinal bandgaps exist within the observed frequency range, accounting for over 60% of the total bandgap (refer to...). Figure 6 (Left figure). Furthermore, the frequency response function obtained from finite element analysis ( Figure 6 The intermediate graph) and the experimentally measured transfer rate ( Figure 6 A comparison with the right figure shows that, in the low transmission frequency range, the experimental data and the finite element analysis results are highly consistent, indicating that both methods have high reliability in vibration damping effects. Furthermore, the transmissibility measured in this frequency range agrees well with the finite element analysis results, further verifying the consistency between the experiment and the numerical simulation. Example 14

[0075] like Figure 2As shown, the inertial amplification nonlinear low-frequency vibration isolation metamaterial structure described in this embodiment differs from the inertial amplification nonlinear low-frequency vibration isolation metamaterial structure described in Embodiment 1 only in that the two ends of the inertial amplification unit 2 described in this embodiment are respectively connected to a set of diagonals (angle of 60°) in the vertical direction of the second rhomboid frame structure. At this time, the rigid rod 53 is arranged along the diagonal line of a set of diagonals (angle of 120°) in the horizontal direction of the second rhomboid frame structure.

[0076] Quasi-static tensile tests were conducted on the inertial amplification nonlinear low-frequency vibration isolation metamaterial structures described in Example 1 and this example, and the obtained data are referenced in the appendix. Figure 5 (a) and (b).

[0077] analyze Figure 5 As shown in (a) and (b), under the same tensile conditions, there are significant differences in the load-displacement curves of the two structures. This is mainly due to the design of the horizontal connection (the vibration-isolation metamaterial structure described in Example 1), which allows for more effective stress distribution and greater deformation under vertical tensile loads, thereby optimizing its low-frequency vibration isolation performance. This flexible design gives the structure lower stiffness, contributing to its excellent vibration isolation performance. In contrast, the vertical connection (the vibration-isolation metamaterial structure described in Example 14) results in higher overall stiffness and shorter displacement during tension. The higher stiffness causes the structure to reach its yield point more quickly, and its deformation capacity is limited, leading to poorer vibration isolation performance. Therefore, the vertical connection method, due to its higher stiffness, directly affects its vibration isolation performance, making it less effective in low-frequency vibration isolation than the horizontal connection.

[0078] The inertial amplification nonlinear low-frequency vibration isolation metamaterial structure described in this embodiment was subjected to low-frequency vibration isolation performance tests. The test results are referenced. Figure 7 Through analysis Figure 6 , Figure 7 The test results suggest that the vibration isolation performance of the vertically connected structure (the vibration isolation metamaterial structure described in Example 14) is far inferior to that of the horizontally connected structure (the vibration isolation metamaterial structure described in Example 1), especially in the low-frequency range below 500 Hz, where the vibration isolation effect of the vertically connected structure decreases significantly, exhibiting a narrower bandgap and higher vibration transmissibility. In contrast, the horizontally connected structure demonstrates a wider bandgap and lower vibration transmissibility in the low-frequency range, thus achieving superior vibration isolation performance. This result is highly consistent with previous numerical simulations and experimental data, fully demonstrating the significant advantages of the horizontally connected structure in low-frequency vibration isolation. Example 15

[0079] Parameters attached Figure 10This embodiment provides a vibration isolation device, which is constructed based on the metamaterial structure described in Embodiment 1. Specifically, the vibration isolation device includes several rows of independent vibration isolation structures, each vibration isolation structure being formed by connecting several of the above-mentioned metamaterial structures end to end.

[0080] In the description of this specification, the use of terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refers to a specific feature, structure, material, or characteristic described in connection with that embodiment or example, which is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0081] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. An additive manufacturing-based inertial amplification nonlinear low-frequency vibration isolation metamaterial structure, comprising a rhombic frame structure and a square spring structure; the square spring structure is arranged within the rhombic frame structure, and both ends of the square spring structure are respectively connected to a pair of opposite corners of the rhombic frame structure, while the elastic extension direction of the square spring structure is parallel to the diagonal of this pair of opposite corners of the rhombic frame structure, characterized in that, The rhomboid frame structure also houses an inertial amplification unit; the inertial amplification unit has a centrally symmetrical structure, including a rigid rod, two counterweights, and two diagonal rods, wherein: The rigid rods are arranged along one of the diagonal lines of the rhomboid frame structure. Two counterweights are connected to the two ends of the rigid rods respectively. Two diagonal rods are set on both sides of the center of the rigid rods. One end of each diagonal rod is connected to the rigid rod, and the other end is connected to the remaining diagonal line of the rhomboid frame structure respectively. The center of symmetry of the inertial amplification unit, the center of the rhomboid frame structure, and the center of the square spring structure all coincide in projection.

2. The inertial amplification nonlinear low-frequency vibration isolation metamaterial structure based on additive manufacturing according to claim 1, characterized in that, It also includes two mass blocks; a rhombus frame structure is arranged between the two mass blocks, and one set of opposite corners of the rhombus frame structure is connected to the two mass blocks respectively; a square spring structure is arranged along the diagonal of the remaining set of opposite corners of the rhombus frame structure.

3. The inertial amplification nonlinear low-frequency vibration isolation metamaterial structure based on additive manufacturing according to claim 2, characterized in that, The two diagonal rods of the inertial amplification unit and the two ends of the square spring structure are respectively connected to the same set of diagonals of the rhomboid frame structure.

4. The inertial amplification nonlinear low-frequency vibration isolation metamaterial structure based on additive manufacturing according to claim 3, characterized in that, The square spring structure contains several zigzag crease units in the middle. These crease units are arranged in a wave-like pattern along the axial direction of the square spring structure, and each crease unit has the same size and shape.

5. The inertial amplification nonlinear low-frequency vibration isolation metamaterial structure based on additive manufacturing according to claim 3, characterized in that, The rhomboid frame structure includes at least one pair of rhomboid frame structure parts of the same size and shape; The two rhomboid frame structures are respectively called the first and second rhomboid frame structures, and the first and second rhomboid frame structures are combined to form a whole; The first rhomboid frame structure has a square spring structure inside, and the center of the first rhomboid frame structure coincides with the center of the square spring structure. The second rhomboid frame structure contains an inertial amplification unit, and the center of the second rhomboid frame structure coincides with the center of symmetry of the inertial amplification unit.

6. The additive manufacturing-based inertial amplification nonlinear low-frequency vibration isolation metamaterial structure according to claim 5, characterized in that, The rhomboid frame structure is integrally formed with the square spring structure and the inertia amplification unit using additive manufacturing technology.

7. A vibration isolation device, characterized in that: Including the additive manufacturing-based inertial amplification nonlinear low-frequency vibration isolation metamaterial structure as described in any one of claims 1-6.

8. The vibration isolation device according to claim 7, characterized in that: Multiple additive manufacturing-based inertial amplification nonlinear low-frequency vibration isolation metamaterial structures are connected end to end from top to bottom to form a set of vibration isolation structures, and multiple sets of vibration isolation structures are combined to form a vibration isolation device.

9. A method for performance control of an additively manufactured, inertial amplification nonlinear low-frequency vibration isolation metamaterial structure, comprising the following steps: S1. Preset the adjustment range of the geometric parameters of the inertial amplifier unit and preliminarily determine the geometric parameters of the inertial amplifier unit based on the preset adjustment range; The preset adjustment range of the geometric parameters of the inertial amplification unit includes the adjustment range of the side length of the counterweight, the adjustment range of the connection angle, and the adjustment range of the wall thickness. S2. By adjusting the wall thickness, connection angle, and side length of the counterweight, the local stiffness and inertial amplification effect of the inertial amplification unit can be changed, thereby controlling the width and depth of the bandgap of the inertial amplification nonlinear low-frequency vibration isolation metamaterial structure. S3. Use finite element analysis software to establish a dynamic model of the inertial amplified nonlinear low-frequency vibration isolation metamaterial structure, simulate the energy band diagram of the structure under different geometric parameters, determine the starting frequency, cutoff frequency and width of the band gap, and combine the quasi-static tensile test results of the vibration isolation metamaterial structure under different geometric parameters to select the optimal combination of geometric parameters. S4. An inertial amplification nonlinear low-frequency vibration isolation metamaterial structure with optimal geometric parameter combination is formed using laser 3D printing technology. The printed inertial amplification nonlinear low-frequency vibration isolation metamaterial structure is installed on a vibration test bench. External excitation is applied through a vibrator, and the displacement response curve of the inertial amplification nonlinear low-frequency vibration isolation metamaterial structure is measured using a laser vibrometer to verify its actual vibration isolation performance.

10. The performance control method for the inertial amplification nonlinear low-frequency vibration isolation metamaterial structure according to claim 9, characterized in that: In step S1, the side length of the counterweight is adjusted from 2 to 8 mm, the connection angle is adjusted from 76 to 88°, and the wall thickness ε is adjusted from 0.7 to 1.5 mm.

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