A three-dimensional vibration reduction structure and vibration reduction device with nonlinear stiffness

Abstract

This invention discloses a three-dimensional vibration damping structure and device with nonlinear stiffness. The three-dimensional vibration damping structure includes an upper end face, a lower end face, and a damping structure. The upper end face and the lower end face are coaxially arranged. The damping structure includes multiple elastic bending rods arranged circumferentially along the line connecting the axes of the upper end face and the lower end face. The cross-section of each elastic bending rod is crescent-shaped. When the three-dimensional vibration damping structure is compressed, nonlinear geometric stiffness is generated. The nonlinear stiffness can be flexibly adjusted through various structural parameters of the rods, thereby allowing for the design of the three-dimensional vibration damping structure according to vibration requirements. Benefiting from the nonlinear stiffness characteristics, the vibration damping performance of the structure is effectively improved. This invention also discloses a damping device that overcomes the shortcomings of existing nonlinear stiffness damping devices, opening up a new direction for the design, analysis, and application of nonlinear stiffness damping devices.

Description

Technical Field

[0001] This invention relates to the field of passive vibration control technology, specifically to a three-dimensional vibration reduction structure and device with nonlinear stiffness. Background Technology

[0002] Vibration problems exist in many engineering and manufacturing fields. Vibration is generally considered a detrimental factor, affecting the performance of mechanical equipment, accelerating localized harmful wear, and shortening equipment lifespan. Therefore, reducing the harm caused by vibration is crucial, and vibration control has always been a key issue that cannot be ignored in the engineering field.

[0003] Vibration control generally refers to controlling the dynamic response or instability of a control system to limit amplitude within acceptable limits. Vibration control methods are broadly classified into active and passive control. Active control methods can adjust in real-time based on the actual excitation conditions using algorithms and are currently used in many engineering practices. However, active control systems have complex technical structures, high manufacturing costs, are difficult to maintain, and require external energy support. In contrast, passive vibration control avoids these drawbacks and has certain advantages.

[0004] Classical passive vibration control employs linear damping systems; however, linear systems have significant limitations in practical applications. To address this issue, nonlinear damping systems have been developed in recent years, with nonlinear stiffness systems being a crucial research area in vibration control. Their main characteristic is that the system's stiffness changes nonlinearly with displacement, and this beneficial nonlinear stiffness variation enables excellent vibration reduction. Nonlinear damping structures have broad application prospects in many key fields, such as precision instrument manufacturing, aerospace, and automotive manufacturing.

[0005] While existing nonlinear stiffness damping devices can reduce the system's natural frequency, improve damping performance, and suppress resonance, some problems remain unresolved. First, the force transmission of these devices requires complex transmission mechanisms, resulting in large size and weight, making them unsuitable for applications with stringent size and weight requirements, such as precision instruments and aerospace. Furthermore, most damping devices typically use bolts or hinges to connect components, leaving tiny gaps between parts. For vibrations with small amplitudes, these devices are ineffective at damping. Summary of the Invention

[0006] The present invention aims to overcome the shortcomings of the prior art and provide a three-dimensional vibration reduction structure with nonlinear stiffness. The three-dimensional vibration reduction structure can be flexibly combined and has a wide range of applications.

[0007] The second objective of this invention is to provide a vibration damping device that utilizes the aforementioned three-dimensional vibration damping structure with nonlinear stiffness. This vibration damping device overcomes the shortcomings of existing nonlinear stiffness vibration damping devices and opens up a completely new direction for the design, analysis, and application of nonlinear stiffness vibration damping devices.

[0008] The technical solution of this invention to solve the problems of the prior art is:

[0009] A three-dimensional vibration damping structure with nonlinear stiffness includes an upper end face, a lower end face, and a vibration damping structure disposed between the upper end face and the lower end face, wherein the upper end face and the lower end face are coaxially arranged; the vibration damping structure includes multiple elastic bending rods, which are arranged circumferentially along the line connecting the axes of the upper end face and the lower end face; the cross-section of the elastic bending rods is crescent-shaped; when the upper end face or the lower end face is subjected to a load, the vibration damping structure generates nonlinear stiffness through compressive deformation.

[0010] Preferably, the concave direction of the elastic bending rod is toward the line connecting the axes of the upper end face and the lower end face.

[0011] Preferably, the concave direction of the elastic bending rod is opposite to the line connecting the axes of the upper end face and the lower end face.

[0012] Preferably, the large circle and the small circle in the cross-section of the elastic bending rod intersect to form a small arc and a large arc, wherein the two ends of the small arc and the large arc are connected and have the same concave direction, thereby forming the crescent-shaped cross-section.

[0013] Preferably, the guide line along the length of the elastic bending rod is a two-dimensional curve, represented by a hyperbolic function or a trigonometric function.

[0014] Preferably, the upper end face, the lower end face, and the vibration damping structure are all integrally formed using 3D printing technology, wherein the material used in the 3D printing technology is thermoplastic polyurethane elastomer.

[0015] A vibration damping device includes m vibration damping modules and m+1 connecting plates, where m is a positive integer; wherein the m+1 connecting plates are coaxial and equidistant, and each vibration damping module is disposed between two adjacent connecting plates; each vibration damping module is composed of multiple three-dimensional vibration damping structures with nonlinear stiffness connected in parallel.

[0016] Preferably, multiple three-dimensional vibration damping structures are arranged in a matrix or in a circular arrangement between two adjacent sets of connecting plates.

[0017] Preferably, two adjacent sets of connecting plates constitute the upper and lower end faces of the three-dimensional vibration reduction structure, respectively.

[0018] Preferably, the connecting plate is flat, annular, or cylindrical.

[0019] Compared with the prior art, the present invention has the following advantages:

[0020] 1. This invention manufactures a three-dimensional vibration damping structure with nonlinear stiffness, and the resulting vibration damping device with nonlinear stiffness compensates for the shortcomings of existing nonlinear stiffness. The vibration damping element made of this material has advantages such as small size, light weight, no hinge gap, no need for lubrication, and high motion accuracy, which can meet the requirements of small size, low weight and high reliability in vibration damping scenarios, and provides an innovative solution for the design of nonlinear stiffness.

[0021] 2. The elastic bending rod in this invention has a crescent-shaped cross-section. Compared to rectangular and circular cross-section bending rods, the crescent-shaped cross-section bending rod exhibits stronger nonlinearity in its force-displacement curve: it has greater stiffness in the early stage of compression and less stiffness in the later stage. This stronger nonlinear stiffness enables the structure to provide greater load-bearing capacity and superior vibration reduction performance within its operating range.

[0022] 3. Compared with traditional vibration damping components, using vibration damping components with nonlinear stiffness will achieve a lower natural frequency and excellent wideband vibration damping effect, and can effectively suppress resonance.

[0023] 4. This invention has a wide range of applications, and can be used in the development and design of vibration damping components for precision instruments, aerospace, and other fields with special requirements for size, weight, and reliability, such as UAV gimbals, optical vibration damping tables, and lithography machine vibration damping. Furthermore, this invention has many advantages, including simple structure, small size, light weight, no hinge gaps, no lubrication required, high motion precision, easy installation and use, and low operating costs. It can achieve excellent (optimal) broadband vibration damping and resonance suppression effects in confined spaces.

[0024] 5. The "three-dimensional vibration reduction structure" proposed in this invention can be manufactured through 3D printing technology and other processes, thereby achieving mass production. It can effectively reduce production costs, improve production efficiency, and significantly reduce material waste, thus having significant economic and social benefits.

[0025] 6. Multiple "three-dimensional vibration reduction structures" can be combined in parallel and series to form modules with specific stiffness coefficients and shapes. The modules can also be combined again to form vibration reduction devices to adapt to different engineering application scenarios.

[0026] 7. Three-dimensional vibration reduction structures with nonlinear stiffness can be made from various base materials (metal, rubber, etc.) to create vibration reduction devices of different shapes (shims, bushings, suspensions, supports, etc.). Attached Figure Description

[0027] Figure 1 This is a perspective view of the three-dimensional vibration reduction structure with nonlinear stiffness of the present invention in Example 1.

[0028] Figure 2 This is a front view of the three-dimensional vibration reduction structure with nonlinear stiffness of the present invention in Example 1.

[0029] Figure 3 for Figure 1 A schematic diagram of the elastic bending rod of the vibration damping structure.

[0030] Figure 4 for Figure 3 Enlarged view of point A in the image.

[0031] Figure 5 for Figure 4 A front view of the crescent-shaped cross-section in the image.

[0032] Figure 6 This is a schematic diagram of the compression deformation of the three-dimensional vibration reduction structure with nonlinear stiffness of the present invention in Example 1.

[0033] Figure 7 This is a perspective view of the three-dimensional vibration reduction structure with nonlinear stiffness of the present invention in Example 2.

[0034] Figure 8 This is a perspective view of the three-dimensional vibration reduction structure with nonlinear stiffness of the present invention in Example 3.

[0035] Figure 9 This is a schematic diagram of the vibration damping device of the present invention in Example 4.

[0036] Figure 10 This is a schematic diagram of the vibration damping device of the present invention in Example 5.

[0037] Figure 11 This is a schematic diagram of the vibration damping device of the present invention in Example 6.

[0038] Figure 12 This is a schematic diagram of the vibration reduction device of the present invention in Example 7.

[0039] Figure 13 This is a schematic diagram of the vibration damping device of the present invention in Example 8.

[0040] Figure 14 This is a schematic diagram of the vibration damping device of the present invention in Example 9.

[0041] Figure 15 This is a perspective view of the gasket in Example 10.

[0042] Figure 16This is a perspective view of the bushing in Example 11.

[0043] Figure 17 This is a schematic diagram of a vibration damping element with nonlinear stiffness.

[0044] Figure 18 This is a dynamic model diagram of a vibration damping element with nonlinear stiffness.

[0045] Figure 19 This is a graph showing the theoretical and calculated displacement transmissivity of the vibration damping element.

[0046] Figure 20 This is a stress contour plot of the elastic bending rod before and after deformation.

[0047] Figure 21 This is a stress contour plot of the crescent-shaped section at the midpoint of the elastic bending bar before and after deformation.

[0048] Figure 22 Comparison of force-displacement curves for different cross-sectional shapes.

[0049] Wherein, 1-upper end face; 2-lower end face; 3-elastic bending rod; 4-vibration damping structure; 5-outer convex surface of elastic bending rod; 6-inner concave surface of elastic bending rod; 7-crescent-shaped cross-section; 8-small arc; 9-large arc; 10-three-dimensional vibration damping structure before compression; 11-three-dimensional vibration damping structure after compression; 12-middle end face; 13-outer end face; 14-inner end face; 15-load mass; 16-base; 17-nonlinear elastic force; 18-hysteresis damping force. Detailed Implementation

[0050] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings, but the embodiments of the present invention are not limited thereto.

[0051] Example 1

[0052] Reference Figures 1-6 This embodiment provides a three-dimensional vibration damping structure with nonlinear stiffness, including an upper end face 1, a lower end face 2, and a vibration damping structure 4; wherein, in the length direction (i.e., Figure 2 In the vertical direction, the vibration damping structure 4 is disposed between the upper end face 1 and the lower end face 2. The vibration damping structure 4 is composed of four elastic bent rods 3, and the concave direction of each elastic bent rod 3 is toward the line connecting the axes of the upper end face 1 and the lower end face 2. The multiple elastic bent rods 3 are evenly distributed in a circle along the line connecting the axes of the upper end face 1 and the lower end face 2.

[0053] Reference Figures 1-6 The guide line along the length of the bent rod 3 is a two-dimensional curve, represented by trigonometric functions.

[0054] Reference Figures 1-6The cross-sectional shape of the bent rod 3 is crescent-shaped; wherein, the large circle and the small circle in the cross-section intersect to form a small arc 8 and a large arc 9, the two ends of the small arc 8 and the large arc 9 are connected and have the same concave direction, thus forming a crescent-shaped cross-section 7; the length of the two ends of the small arc 8 or the large arc 9 is the width of the crescent-shaped cross-section 7, and the length of the bottom end of the small arc 8 and the bottom end of the large arc 9 is the thickness of the crescent-shaped cross-section 7.

[0055] Reference Figures 1-6 The upper end face 1, the lower end face 2, and the vibration damping structure 4 are all integrally formed by 3D printing technology, wherein the material used in the 3D printing technology is thermoplastic polyurethane elastomer.

[0056] Reference Figure 6 and Figure 20 When the upper end face 1 is compressed under load, a relative displacement occurs between the upper end face 1 and the lower end face 2, transmitting the external force to the vibration damping structure 4, causing the elastic rod 3 to bend and deform. During the deformation process, due to the trigonometric function of the guide line of the elastic rod 3 and its crescent-shaped cross-section, the curvature of the middle part of the elastic rod 3 decreases significantly, resulting in a larger force, while the curvature change at both ends of the elastic rod is not significant, resulting in a smaller force. This indicates that the elastic force generated by the compression of the elastic rod mainly originates from the bending deformation in the middle of the rod. During compression, the outer convex surface 5 of the elastic rod 3 is in a tensile state, generating tensile stress; while the inner concave surface 6 of the elastic rod 3 is in a compressive state, generating compressive stress. To restore the original state of the elastic rod 3, the internal material of the elastic rod 3 generates a nonlinear elastic force to resist the tensile and compressive stresses.

[0057] like Figure 21 As shown, the stress during deformation is concentrated in the middle part of the upper and lower circular arcs of the cross-section, while the stress in the middle layer is smaller. Comparing the cross-sectional shapes before and after deformation, it can be seen that after the elastic bending rod 3 is bent and deformed, the upper and lower circular arcs are stretched, increasing the curvature. This change in the crescent-shaped cross-sectional shape makes the elastic bending rod 3 easier to compress compared to its initial state.

[0058] like Figure 22 As shown, compared to rectangular and circular cross-section bending rods, the crescent-shaped cross-section elastic bending rod 3 can generate stronger nonlinear elastic force, exhibiting greater stiffness in the early stage of compression and less stiffness in the later stage. This stronger nonlinear stiffness enables the vibration damping structure to have greater load-bearing capacity and lower resonant frequency within its operating range, effectively improving vibration damping performance. The three-dimensional vibration damping structure utilizes the elastic deformation of the elastic bending rod 3 itself to achieve the transmission and conversion of motion, force, and energy, thereby realizing vibration damping. After the external load is removed, the vibration damping structure 4, the upper end face 1, and the lower end face 2 can all be reset.

[0059] Example 2

[0060] Reference Figure 7 This embodiment provides a three-dimensional vibration reduction structure with nonlinear stiffness. The difference between this embodiment and Embodiment 1 is that the vibration reduction structure 4 in this embodiment is composed of six elastic bending rods 3. The concave direction of each elastic bending rod 3 is towards the line connecting the axis of the upper end face 1 and the lower end face 2. The multiple elastic bending rods 3 are evenly distributed in a circle along the line connecting the axis of the upper end face 1 and the lower end face 2.

[0061] When the upper end face 1 is compressed under load, a relative displacement occurs between the upper end face 1 and the lower end face 2, transmitting the external force to the vibration damping structure 4. This causes the elastic bending rod 3 to bend and deform, generating nonlinear stiffness, which provides the structure with a certain load-bearing capacity, ensures a low resonant frequency, and effectively improves vibration damping performance. The three-dimensional vibration damping structure utilizes the elastic deformation of the elastic bending rod 3 itself to achieve the transmission and conversion of motion, force, and energy, thereby achieving vibration damping. After the external load is removed, the vibration damping structure 4, the upper end face 1, and the lower end face 2 can all be reset.

[0062] Example 3

[0063] Reference Figure 8 This embodiment provides a three-dimensional vibration reduction structure with nonlinear stiffness. The difference between this embodiment and Embodiment 1 is that the vibration reduction structure 4 in this embodiment is composed of four elastic bending rods 3. Each elastic bending rod 3 is concave and faces away from the line connecting the axes of the upper end face 1 and the lower end face 2. The line connecting the axes of the upper end face 1 and the lower end face 2 of the multiple elastic bending rods 3 is evenly distributed in a circle.

[0064] When the upper end face 1 is compressed under load, a relative displacement occurs between the upper end face 1 and the lower end face 2, transmitting the external force to the vibration damping structure 4. This causes the elastic bending rod 3 to bend and deform, generating nonlinear stiffness, which provides the structure with a certain load-bearing capacity, ensures a low resonant frequency, and effectively improves vibration damping performance. The three-dimensional vibration damping structure utilizes the elastic deformation of the elastic bending rod 3 itself to achieve the transmission and conversion of motion, force, and energy, thereby achieving vibration damping. After the external load is removed, the vibration damping structure 4, the upper end face 1, and the lower end face 2 can all be reset.

[0065] Example 4

[0066] Reference Figure 9 This embodiment provides a vibration damping device with nonlinear stiffness. The figure only shows the constituent modules, and their area size will be determined according to product requirements. This vibration damping device connects multiple three-dimensional vibration damping structures of Embodiment 1 in parallel to form a vibration damping module. The vibration damping device in this embodiment includes two vibration damping modules, an upper end face 1, a lower end face 2, and a middle end face 12. In the length direction, the end faces are connected by vibration damping modules.

[0067] Among them, the upper end face 1, the lower end face 2 and the middle end face 12 are flat plates; in the vibration reduction module, multiple three-dimensional vibration reduction structures are arranged in a rectangular array on a plane perpendicular to the length direction, and the figure shows a 2×2 arrangement.

[0068] The vibration reduction principle of the vibration reduction device with nonlinear stiffness of the present invention is as follows:

[0069] Please refer to Figures 17-18 The figure shows a single-degree-of-freedom vibration damping element consisting of harmonic excitation, a vibration damping device with nonlinear stiffness, and mass. Based on the principle of nonlinear dynamics, the vibration damping element is simplified into a dynamic model of nonlinear elastic force and hysteretic damping force. Here, x and y represent the displacements of the harmonic excitation and the load mass 15, respectively, M is the mass, and F... k (x r ), These are functions of the nonlinear elastic force 17 and the hysteretic damping force 18, respectively, where x r It is the displacement difference between the harmonic excitation and the load mass displacement, i.e., x r =yx. It is x r The first derivative with respect to time t, It is x r The second derivative with respect to time t.

[0070] Using the Lagrange method, the differential equations of motion for this system are as follows:

[0071]

[0072] Where d is the differential operator, is the partial differential operator, t is time, and D is the non-conservative generalized force. It is the first derivative of y with respect to time t, where T and V are the total kinetic energy and total potential energy of the system, respectively.

[0073] Solving the system's differential equations of motion yields:

[0074]

[0075] in, This is the second derivative of y with respect to time t. Based on the above function model, the displacement transmissibility of the vibration damping element can be calculated through the ratio of response to excitation. Taking a module composed of a "three-dimensional vibration damping structure" as an example, its transmissibility is tested and compared with the calculated value. The results are as follows: Figure 19 As shown.

[0076] The results show that the vibration reduction device with nonlinear stiffness of the present invention has good vibration reduction performance and can effectively suppress the system resonance peak.

[0077] Example 5

[0078] Reference Figure 10 This embodiment provides a vibration damping device with nonlinear stiffness. The figure only shows the constituent modules, and their area size will be determined according to product requirements. The vibration damping device connects multiple three-dimensional vibration damping structures of Embodiment 1 in parallel to form a vibration damping module. The vibration damping device includes three vibration damping modules and four end faces (upper end face 1, lower end face 2, and two middle end faces 12). In the length direction, the end faces are connected by vibration damping modules.

[0079] The upper end face 1, the lower end face 2, and the two middle end faces 12 are all flat.

[0080] In the vibration reduction module, multiple three-dimensional vibration reduction structures are arranged in a rectangular array on a plane perpendicular to the length direction, as shown in the figure in a 3×3 arrangement.

[0081] Example 6

[0082] Reference Figure 11 This embodiment provides a vibration damping device with nonlinear stiffness. The figure only shows the constituent modules, and their area size will be determined according to product requirements. The vibration damping device connects multiple three-dimensional vibration damping structures of Embodiment 1 in parallel to form a vibration damping module. The vibration damping device includes four vibration damping modules and five end faces (upper end face 1, lower end face 2, and three intermediate end faces 12). In the length direction, the end faces are connected by vibration damping modules.

[0083] Among them, the upper end face 1, the lower end face 2 and the three intermediate end faces 12 are flat.

[0084] In the vibration reduction module, multiple three-dimensional vibration reduction structures are arranged in a rectangular array on a plane perpendicular to the length direction, as shown in the figure in a 4×4 arrangement.

[0085] Example 7

[0086] Reference Figure 12 This embodiment provides a vibration damping device with nonlinear stiffness. The figure only shows the constituent modules, and their area size will be determined according to product requirements. The vibration damping device connects multiple three-dimensional vibration damping structures of Embodiment 1 in parallel to form a vibration damping module. The vibration damping device includes three vibration damping modules and four end faces (upper end face 1, lower end face 2, and two middle end faces 12). In the length direction, the end faces are connected by vibration damping modules.

[0087] Among them, the upper end face 1, the lower end face 2, and the two middle end faces 12 are flat plates, specifically circular rings.

[0088] In the vibration reduction module, multiple three-dimensional vibration reduction structures are arranged in a circular array on a plane perpendicular to the length direction. The figure shows an arrangement of six in a circle.

[0089] Example 8

[0090] Reference Figure 13 This embodiment provides a vibration damping device with nonlinear stiffness. The figure only shows the constituent modules, and their area size will be determined according to product requirements. This vibration damping device connects multiple three-dimensional vibration damping structures of Embodiment 2 in parallel to form a vibration damping module. The vibration damping device includes three vibration damping modules and four end faces (upper end face 1, lower end face 2, and two middle end faces 12). In the length direction, the end faces are connected by vibration damping modules.

[0091] Among them, the upper end face 1, the lower end face 2 and the two middle end faces 12 are flat.

[0092] In the vibration reduction module, multiple three-dimensional vibration reduction structures are arranged in a rectangular array on a plane perpendicular to the length direction, as shown in the figure in a 3×3 arrangement.

[0093] Example 9

[0094] Reference Figure 14 This embodiment provides a vibration damping device with nonlinear stiffness. The figure only shows the constituent modules, and their area size will be determined according to product requirements. The vibration damping device connects multiple three-dimensional vibration damping structures of Embodiment 3 in parallel to form a vibration damping module. The vibration damping device includes three vibration damping modules and four end faces (upper end face 1, lower end face 2, and two middle end faces 12). In the length direction, the end faces are connected by vibration damping modules.

[0095] Among them, the upper end face 1, the lower end face 2 and the two intermediate end faces 12 are flat.

[0096] In the vibration reduction module, multiple three-dimensional vibration reduction structures are arranged in a rectangular array on a plane perpendicular to the length direction, as shown in the figure in a 3×3 arrangement.

[0097] Example 10

[0098] Reference Figure 15 This embodiment provides a vibration damping device with nonlinear stiffness, used for making gaskets.

[0099] In this vibration damping element, the vibration damping device connects multiple three-dimensional vibration damping structures with nonlinear stiffness in parallel to form a vibration damping module; the vibration damping device includes a vibration damping module, an upper end face 1 and a lower end face 2; in the length direction, the end faces are connected by the vibration damping module.

[0100] Among them, the upper end face 1 and the lower end face 2 are flat plates, specifically circular rings.

[0101] In the vibration reduction module, multiple three-dimensional vibration reduction structures are arranged in a circular array on a plane perpendicular to the length direction.

[0102] Example 11

[0103] Reference Figure 16 This embodiment provides a vibration damping device with nonlinear stiffness, used for manufacturing bushings.

[0104] In this vibration damping element, the vibration damping device connects multiple three-dimensional vibration damping structures with nonlinear stiffness in parallel to form a vibration damping module; the vibration damping device includes two vibration damping modules and three end faces (outer end face 13, inner end face 14 and middle end face 12); in the length direction, the end faces are connected by vibration damping modules.

[0105] Among them, the inner end face 14, the middle end face 12 and the outer end face 13 are cylindrical and arranged in sequence from the inside to the outside.

[0106] In the vibration reduction module, multiple three-dimensional vibration reduction structures are evenly distributed on the cylindrical surface, with their length direction set along the radial direction of the cylinder.

[0107] In addition to the methods mentioned in the above embodiments, the following modifications can be made:

[0108] In three-dimensional vibration reduction structures, the number, shape, size, and materials of the vibration reduction structures can be flexibly selected according to needs, which can meet the engineering requirements for different shapes and specific stiffness.

[0109] In vibration damping devices, the quantity, shape, size, material selection, and stacking method of vibration damping modules and end faces can be flexibly selected according to needs, which can meet the requirements of different shapes and specific stiffness in engineering. By stacking and combining vibration damping modules, vibration damping elements with specific shapes are formed and applied to actual engineering vibration damping environments.

[0110] The above are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above content. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A three-dimensional vibration reduction structure with nonlinear stiffness, characterized in that, The device includes an upper end face, a lower end face, and a vibration damping structure disposed between the upper end face and the lower end face, wherein the upper end face and the lower end face are coaxially arranged; the vibration damping structure includes multiple elastic bending rods arranged circumferentially along the line connecting the axes of the upper end face and the lower end face; the cross-section of the elastic bending rods is crescent-shaped; when the upper end face or the lower end face is subjected to a load, the vibration damping structure generates nonlinear stiffness through compressive deformation; The guide line along the length of the elastic bending rod is a two-dimensional curve. The large circle and small circle in the cross-section of the elastic bending rod intersect to form a small arc and a large arc. The two ends of the small arc and the large arc are connected and their concave directions are consistent, thus forming the crescent-shaped cross-section.

2. The three-dimensional vibration reduction structure with nonlinear stiffness according to claim 1, characterized in that, The concave direction of the elastic bending rod is toward the line connecting the axes of the upper end face and the lower end face.

3. The three-dimensional vibration reduction structure with nonlinear stiffness according to claim 1, characterized in that, The concave direction of the elastic bending rod is opposite to the line connecting the axes of the upper end face and the lower end face.

4. The three-dimensional vibration reduction structure with nonlinear stiffness according to claim 1, characterized in that, The two-dimensional curve is represented by a hyperbolic function or a trigonometric function.

5. The three-dimensional vibration reduction structure with nonlinear stiffness according to claim 1, characterized in that, The upper end face, the lower end face, and the vibration damping structure are all integrally formed using 3D printing technology, wherein the material used in the 3D printing technology is thermoplastic polyurethane elastomer.

6. A vibration damping device using a three-dimensional vibration damping structure with nonlinear stiffness as described in any one of claims 1-5, characterized in that, It includes m vibration damping modules and m+1 connecting plates, where m is a positive integer; the m+1 connecting plates are coaxial and equidistant, and each vibration damping module is set between two adjacent connecting plates; each vibration damping module is composed of multiple three-dimensional vibration damping structures with nonlinear stiffness connected in parallel.

7. The vibration damping device according to claim 6, characterized in that, Multiple three-dimensional vibration damping structures are arranged in a matrix or in a circular pattern between two adjacent sets of connecting plates.

8. The vibration damping device according to claim 6, characterized in that, The two adjacent sets of connecting plates respectively constitute the upper and lower end surfaces of the three-dimensional vibration reduction structure.

9. The vibration damping device according to claim 6, characterized in that, The connecting plate can be flat, circular, or cylindrical.

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