A quasi-zero stiffness unit, a metamaterial vibration isolation structure and a design method suitable for different tensile loads

Abstract

The application relates to the technical field of new materials, and discloses a quasi-zero stiffness unit suitable for different tensile loads, a metamaterial vibration isolation structure and a design method, which comprise a first rigid side wall and a second rigid side wall, a positive stiffness unit is arranged in the center of the first rigid side wall, a negative stiffness unit is arranged at the opening of the top of the first rigid side wall, and one end of the second rigid side wall is connected with the vertex of the positive stiffness unit and extends upwards through the negative stiffness unit. The application realizes the regulation and control of the stiffness response of the structure under the action of different loads by parameterizing the design and multi-level combination of the tensile unit configuration and combining the interaction of the positive stiffness and the negative stiffness, the quasi-zero stiffness platform of the structure can be adjusted with the change of the tensile load, so that the stable low dynamic stiffness characteristics of the structure can be maintained within a wide load range, and then the adaptive regulation and control and flexible control of the low-frequency vibration isolation performance are realized.

Description

Technical Field

[0001] This invention relates to the field of new materials technology, specifically to a quasi-zero stiffness unit, metamaterial vibration isolation structure, and design method that can adapt to different tensile loads. Background Technology

[0002] With the rapid development of marine exploration, deep-sea equipment, and high-precision measurement systems, the low-frequency vibration problem of structures in complex service environments is becoming increasingly prominent. Flexible structures, exemplified by underwater towed linear array systems, not only bear continuously varying tensile loads during service but are also subjected to the coupling effects of multi-source excitations such as flow field disturbances and platform motion. This makes them highly susceptible to significant vibration responses in the low-frequency range, thereby affecting the system's stability and detection accuracy. Therefore, developing structural design methods that combine high load-bearing capacity with low-frequency vibration isolation performance has become a critical issue urgently needing to be addressed in related fields.

[0003] In recent years, metamaterials based on artificial structure design have provided a new technical approach for low-frequency vibration control. Typical metamaterial vibration isolation mechanisms mainly include Bragg scattering and localized resonant vibration. Bragg scattering relies on matching the structural periodicity with the target wavelength; when the operating frequency decreases to the low-frequency range, the required structural size increases significantly, making it difficult to meet the compactness requirements of engineering structures. While localized resonant vibration can achieve subwavelength bandgap, its low-frequency application typically relies on reducing system stiffness or adding mass. This can weaken structural stability or significantly increase system mass under high load or tension conditions, thus limiting its engineering applications.

[0004] Quasi-zero stiffness (QZS) structures have attracted widespread attention due to their high static stiffness and low dynamic stiffness. Existing design methods typically couple positive and negative stiffness elements to create a platform with near-zero equivalent stiffness within a specific operating range, thereby significantly reducing the system's natural frequency and achieving low-frequency vibration isolation. However, existing QZS structures are mostly based on compression configurations, such as bistable structures, magnetic negative stiffness mechanisms, or combined spring structures, primarily suitable for compressive load environments. In contrast, in scenarios such as towed cables, flexible connection structures, and deep-sea suspension systems, structures typically operate under tensile loads, and their stress modes, stability characteristics, and quasi-zero stiffness realization mechanisms differ significantly from those under compression conditions. Therefore, existing compression-type QZS design methods are difficult to directly extend to tensile conditions. Meanwhile, although some research has begun to focus on tensile QZS structures, quasi-zero stiffness structures mostly employ a single configuration or fixed parameter design, and their quasi-zero stiffness characteristics are usually only achieved under specific preload conditions or within a single operating range. When the external tensile load changes, the equivalent stiffness response of the structure will shift accordingly, causing the position of the quasi-zero stiffness plateau to change or even disappear, thus significantly reducing its low-frequency vibration isolation performance. Therefore, traditional quasi-zero stiffness structures have poor adaptability to variable tensile conditions and cannot meet the stable vibration isolation requirements under conditions of continuous tensile force changes in actual engineering. This greatly limits their application in towing systems and flexible load-bearing structures. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention proposes a quasi-zero stiffness structure suitable for different tensile loads. By parametrically designing and combining tensile unit configurations at multiple levels, and by integrating the interaction between positive and negative stiffness, the stiffness response of the structure under different loads can be controlled. Furthermore, the quasi-zero stiffness platform of the structure can be adjusted according to changes in tensile load, maintaining stable low dynamic stiffness characteristics over a wide load range, thereby achieving adaptive adjustment and flexible control of low-frequency vibration isolation performance.

[0006] To achieve the above objectives, the present invention employs the following technical solution:

[0007] According to one aspect of the present invention, a quasi-zero stiffness unit adaptable to different tensile loads is provided, comprising a first rigid sidewall and a second rigid sidewall. A positive stiffness unit is disposed in the center of the interior of the first rigid sidewall, and a negative stiffness unit is disposed at the top opening of the first rigid sidewall. One end of the second rigid sidewall is connected to the vertex of the positive stiffness unit and extends upward through the negative stiffness unit. The positive stiffness unit and the negative stiffness unit are arranged in parallel and abut against the first rigid sidewall and the second rigid sidewall together to provide quasi-zero stiffness characteristics when subjected to axial tensile load.

[0008] Furthermore, the positive stiffness unit is a symmetrically arranged hyperbolic positive stiffness elastic body.

[0009] Furthermore, the negative stiffness element is a symmetrically arranged buckling negative stiffness elastic body.

[0010] Furthermore, the negative stiffness unit includes at least two sub-units, which extend smoothly downward along the first rigid sidewall to the second rigid sidewall, and each pair of sub-units is axially symmetrical along the second rigid sidewall.

[0011] Furthermore, the first rigid sidewall is a hollow frame structure.

[0012] Furthermore, the second rigid sidewall is T-shaped.

[0013] Furthermore, the structural parameters of the negative stiffness unit include length l1, height h1, and thickness t1, and the structural parameters of the positive stiffness unit include height l2, width h2, and thickness t2. By adjusting the above structural parameters individually or in combination, different threshold tensile load ranges can be matched to adapt to the quasi-zero stiffness vibration reduction requirements of various working conditions.

[0014] According to another aspect of the present invention, a quasi-zero stiffness metamaterial vibration isolation structure adaptable to different tensile loads is provided, comprising a plurality of quasi-zero stiffness units, wherein the plurality of quasi-zero stiffness units are connected in series or in parallel, or mixed together to form a metamaterial vibration isolation structure.

[0015] According to another aspect of the present invention, a design method for a quasi-zero stiffness metamaterial vibration isolation structure adaptable to different tensile loads is provided, comprising the following steps:

[0016] First, determine the target tensile load range and its variation interval. Based on this, design the parametric configuration and combination form of the quasi-zero stiffness element. Assuming that the structure works within a certain target tensile load range, construct the corresponding element force-displacement response characteristics by adjusting the geometric parameters such as the length and thickness of the curved beam.

[0017] The overall structure is segmented according to different tensile load ranges, and the mechanical behavior of each sub-unit is matched in a targeted manner within the corresponding load range so that it can enter the quasi-zero stiffness working state at the corresponding stage.

[0018] A local mechanical model is established for each sub-unit, and its equivalent stiffness expression is obtained by combining nonlinear mechanical analysis. Based on this, the parameter matching relationship and combination method of the multi-unit are determined.

[0019] The equivalent dynamic modeling method is adopted to transform the multi-unit combined structure into an overall system with target dynamic characteristics, thereby obtaining quasi-zero stiffness structural design parameters that can adapt to different tensile load conditions.

[0020] When the tensile load changes, different sub-units sequentially enter the quasi-zero stiffness working state, so that the structure can maintain the characteristic of quasi-zero stiffness vibration reduction in different load ranges.

[0021] According to another aspect of the present invention, a quasi-zero stiffness metamaterial vibration isolation structure adaptable to different tensile loads is provided, characterized in that it comprises a plurality of quasi-zero stiffness units, wherein the plurality of quasi-zero stiffness units are connected in series or in parallel, or mixed together to form a metamaterial vibration isolation structure.

[0022] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0023] 1. This invention constructs a tensile quasi-zero stiffness element based on geometric nonlinear effects to parametrically design the structure. By combining multi-element collaboration and hierarchical combination, it achieves stiffness response control of the structure under different tensile load conditions. Specifically, by adjusting the element configuration parameters and their combinations, different elements enter a quasi-zero stiffness working state in different tensile ranges, thus forming a quasi-zero stiffness platform covering a wide load range. Simultaneously, by adjusting structural parameters or prestress state, adaptive changes in equivalent stiffness characteristics can be achieved, allowing the quasi-zero stiffness range to be dynamically adjusted with changes in tensile load.

[0024] 2. This invention effectively improves upon the limitation of traditional quasi-zero stiffness structures, which are only applicable to a single load condition. It achieves the ability to maintain low dynamic stiffness characteristics under different tensile load conditions, thereby significantly improving the low-frequency vibration isolation performance and adaptability of the structure. This invention can achieve stable vibration isolation within a wide load range while ensuring high static load-bearing capacity, avoiding the problem of vibration isolation performance failure due to load changes.

[0025] 3. The structural design proposed in this invention comprehensively considers the mechanical response characteristics under different tensile load conditions. Through coordinated control of positive and negative stiffness and multi-unit hierarchical combination, it achieves the adjustability and scalability of the quasi-zero stiffness platform. Compared with the limitations of traditional structures that only have good performance under local conditions, this invention maintains a stable vibration isolation effect over a wide load range, and has the advantages of simple structural form, strong adaptability, and great potential for engineering applications. Attached Figure Description

[0026] Figure 1 This is a schematic diagram of the quasi-zero stiffness unit structure of the present invention, adapted to different tensile loads. Figure 1 ;

[0027] Figure 2 This is a schematic diagram of the quasi-zero stiffness unit structure of the present invention, adapted to different tensile loads. Figure 2 ;

[0028] Figure 3This is a schematic diagram of the geometric parameters of the quasi-zero stiffness unit structure adapted to different tensile loads according to the present invention. (a) is the structural parameters of the positive stiffness unit, and (b) is the structural parameters of the negative stiffness unit.

[0029] Figure 4 This is a three-dimensional diagram of the tensile quasi-zero stiffness sub-unit of the present invention and a schematic diagram of its force-displacement response;

[0030] Figure 5 This is a schematic diagram of vibration isolation of a quasi-zero stiffness metamaterial composed of quasi-zero stiffness units connected in series, and a schematic diagram of its overall response.

[0031] Figure 6 This is a schematic diagram of the vibration isolation of a quasi-zero stiffness metamaterial composed of quasi-zero stiffness units and a schematic diagram of its overall response.

[0032] The labels in the figure are: 1. First rigid sidewall; 2. Second rigid sidewall; 3. Positive stiffness element; 4. Negative stiffness element. Detailed Implementation

[0033] The present invention will be further illustrated below with reference to specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. Furthermore, it should be understood that after reading the teachings of this invention, those skilled in the art can make various alterations or modifications to the invention, and these equivalent forms also fall within the scope defined in this application.

[0034] like Figure 1-3 As shown, a quasi-zero stiffness unit adaptable to different tensile loads is illustrated, comprising a first rigid sidewall 1 and a second rigid sidewall 2. A positive stiffness unit 3 is disposed in the center of the interior of the first rigid sidewall 1, and a negative stiffness unit 4 is disposed at the top opening of the first rigid sidewall 1. One end of the second rigid sidewall 2 is connected to the vertex of the positive stiffness unit 3 and extends upward through the negative stiffness unit 4. The positive stiffness unit 3 and the negative stiffness unit 4 are arranged in parallel and abut against the first rigid sidewall and the second rigid sidewall together to provide quasi-zero stiffness characteristics when subjected to axial tensile loads.

[0035] Specifically, the rigid sidewalls, in contrast to the positive and negative stiffness units, provide support, connection, and guidance. Therefore, they can be made of materials with minimal deformation under working loads, such as metals, high-strength engineering plastics, composite materials, or additive manufacturing materials. The rigid sidewalls can employ U-shaped, T-shaped, frame-shaped, plate-shaped, or other equivalent support structures. The positive and negative stiffness units primarily generate corresponding equivalent stiffness responses through their geometric configurations. They can be integrally formed with the rigid walls using the same material or a combination of different materials. The positive stiffness unit 3 is a symmetrically arranged hyperbolic positive stiffness elastic body, which can be a rhomboid, arc-shaped beam, straight beam, broken-line beam, or ring-shaped structure capable of generating positive equivalent stiffness. The negative stiffness unit 4 is a symmetrically arranged buckling negative stiffness elastic body, which can be an arc-shaped beam, arch beam, S-shaped beam, buckling beam, or bistable beam capable of generating a negative equivalent stiffness range.

[0036] The negative stiffness unit 4 includes at least two sub-units, which extend smoothly downwards along the first rigid sidewall to the second rigid sidewall. Each pair of sub-units is axially symmetrical about the second rigid sidewall. The number and layers of negative stiffness sub-units can be adjusted according to the target tensile load, bearing capacity, and the width of the quasi-zero stiffness platform. In this embodiment, the negative stiffness unit includes four sub-units.

[0037] Specifically, the height, length, and thickness of the negative stiffness element are denoted as h1, l1, and t1, respectively; the height, length, and thickness of the positive stiffness element are denoted as h2, l2, and t2, respectively. Figure 4 The diagram shows a tensile quasi-zero stiffness sub-element and its force-displacement response. When the structure operates under tensile load, the sub-element can form an approximately horizontal plateau region near the target load, corresponding to the working range where the equivalent stiffness is close to zero. Its characteristic load is denoted as F0, and the corresponding displacement range is denoted as d0.

[0038] Example 1: A quasi-zero stiffness metamaterial vibration isolation structure adaptable to different tensile loads

[0039] like Figure 5 As shown, in this embodiment, the working tensile load range of the target structure is assumed to be F1-F3, and this range is divided into low load interval, medium load interval, and high load interval. Sub-unit A, sub-unit B, and sub-unit C are designed for each of these different load intervals, as follows: Figure 3 As shown on the left. Sub-unit A corresponds to the low load range, with its target platform load close to F1; sub-unit B corresponds to the medium load range, with its target platform load close to F2; and sub-unit C corresponds to the high load range, with its target platform load close to F3. By adjusting the dimensions of the curved beam, such as length, height, and thickness, the quasi-zero stiffness design requirements under different tensile load ranges can be met.

[0040] In terms of structural arrangement, sub-unit A, sub-unit B, and sub-unit C are connected in series along the tensile direction to form a structure as shown in the figure. Figure 5 The overall series structure is shown. After being connected in series, the force-displacement response curve of the overall structure is characterized by multiple local plateau regions connected sequentially. Figure 5 In the diagram, F1, F2, and F3 represent the characteristic load levels of the overall structure at different stages. The displacement intervals corresponding to each shaded area can be considered as quasi-zero stiffness working intervals, with their width denoted as d0. When the external tensile load gradually increases from low to high, sub-unit A first enters the quasi-zero stiffness working state. When the load continues to increase and exceeds the main working range of sub-unit A, sub-unit B enters the working interval and undertakes the stiffness adjustment role in the intermediate load stage. When the load further increases to the high load range, sub-unit C enters the quasi-zero stiffness working state. Thus, the three sub-units play their roles sequentially at different tensile load stages, enabling the overall structure to maintain low dynamic stiffness characteristics over a wide load range. Furthermore, by increasing the number of sub-units and adjusting the geometric parameters of each sub-unit, a wide and continuous adaptive load quasi-zero stiffness vibration reduction performance can be achieved.

[0041] Compared to a single sub-unit structure, this embodiment uses a multi-sub-unit series design along the tensile direction to sequentially connect the local quasi-zero stiffness intervals corresponding to F1, F2, and F3, thereby forming an overall quasi-zero stiffness platform covering a wider load range. This design can effectively improve the structure's adaptability to variable tensile load conditions and maintain stable low-frequency vibration isolation performance over a wider operating range.

[0042] Example 2: A quasi-zero stiffness metamaterial vibration isolation structure adaptable to different tensile loads

[0043] Building upon Example 1, this example further proposes a multi-unit series-parallel combination design method for different load ranges. For application scenarios with large load variations, high load-bearing requirements, or higher requirements for vibration isolation and stability, a parallel combination method is introduced on the basis of series design to improve the overall load-bearing capacity of the structure and enhance the stiffness response characteristics within different load ranges.

[0044] like Figure 6As shown in (a), the overall tensile load range is first divided into several load intervals according to the working requirements of the target structure, and tensile quasi-zero stiffness sub-units corresponding to each interval are designed. Taking four sub-units as an example, sub-units A and B correspond to the low load interval, and sub-units C and D correspond to the high load interval. Each sub-unit adopts a tensile curved beam nonlinear configuration, and its curved beam length, thickness, height and other parameters are determined according to the target load interval, so that it exhibits an equivalent stiffness close to zero in the corresponding interval. In terms of combination, sub-units A and B are first set in parallel to improve the bearing capacity in the low load interval; then sub-units C and D are set in parallel to improve the bearing capacity in the high load interval; then the above two sets of parallel modules are connected in series along the tensile direction to form a series-parallel structure.

[0045] like Figure 6 As shown in (b), the overall force-displacement response curve of this series-parallel structure exhibits two plateau regions that appear sequentially. F4 and F5 represent the characteristic load levels corresponding to the two parallel modules, respectively, and the shaded area represents the quasi-zero stiffness operating range, with a typical width of 2d0. When the external tensile load gradually increases, the first parallel module first enters the quasi-zero stiffness operating state; as the load further increases, the second parallel module enters the operating range, thus enabling the overall structure to maintain low dynamic stiffness characteristics even under higher load levels. In this structure, the series connection is mainly used to expand the load coverage of the overall quasi-zero stiffness platform, while the parallel connection is mainly used to improve the load-bearing capacity within a specific load range. Compared to structures using only a series design, this embodiment not only expands the coverage of the quasi-zero stiffness platform but also ensures a higher static load-bearing capacity, making it more suitable for engineering scenarios with large variable tensile load amplitudes or complex operating conditions.

[0046] This invention also discloses a design method for quasi-zero stiffness structures adaptable to different tensile loads. Taking a tensile curved beam element as an example, the range of tensile loads borne by the structure and its variation interval are first determined, and the parametric configuration and combination form of the quasi-zero stiffness element are designed accordingly. Assuming that the structure operates within a certain target tensile load range, the corresponding element force-displacement response characteristics are constructed by adjusting the geometric parameters such as the length and thickness of the curved beam.

[0047] Based on this, the overall structure is segmented according to different tensile load ranges, and the mechanical behavior of each sub-unit is specifically matched within the corresponding load range, enabling it to enter a quasi-zero stiffness working state at the corresponding stage. Furthermore, a local mechanical model is established for each sub-unit, and its equivalent stiffness expression is obtained by combining nonlinear mechanical analysis, thereby determining the parameter matching relationship and combination method of the multi-unit structure. Based on this, an equivalent dynamic modeling method is used to transform the multi-unit combined structure into an equivalent overall system with target dynamic characteristics, thus obtaining quasi-zero stiffness structural design parameters adapted to different tensile load conditions. When the tensile load changes, different sub-units sequentially enter the quasi-zero stiffness working state, achieving the characteristic of maintaining quasi-zero stiffness vibration reduction in different load ranges.

[0048] Overall, this design process comprehensively considers the structural response characteristics under different tensile load conditions, overcoming the shortcomings of traditional quasi-zero stiffness structures that only perform well in a single load range but whose performance weakens significantly under other load conditions. This enables the structure to maintain stable low dynamic stiffness characteristics over a wide load range, thereby achieving stable maintenance of low-frequency vibration isolation performance.

[0049] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A quasi-zero stiffness element adaptable to different tensile loads, characterized in that, It includes a first rigid sidewall and a second rigid sidewall. A positive stiffness unit is provided in the center of the first rigid sidewall, and a negative stiffness unit is provided at the top opening of the first rigid sidewall. One end of the second rigid sidewall is connected to the vertex of the positive stiffness unit and extends upward through the negative stiffness unit. The positive stiffness unit and the negative stiffness unit are arranged in parallel and abut against the first rigid sidewall and the second rigid sidewall together to provide quasi-zero stiffness characteristics when subjected to axial tensile load.

2. The quasi-zero stiffness element adaptable to different tensile loads according to claim 1, characterized in that, The positive stiffness element is a symmetrically arranged hyperbolic positive stiffness elastic body.

3. The quasi-zero stiffness element adaptable to different tensile loads according to claim 1, characterized in that, The negative stiffness element is a symmetrically arranged buckling negative stiffness elastic body.

4. A quasi-zero stiffness element adaptable to different tensile loads according to claim 3, characterized in that, The negative stiffness element includes at least two sub-elements, which extend smoothly downward along the first rigid sidewall to the second rigid sidewall, and each pair of sub-elements is axially symmetrical along the second rigid sidewall.

5. A quasi-zero stiffness element adaptable to different tensile loads according to claim 1, characterized in that, The first rigid sidewall is a hollow frame structure.

6. A quasi-zero stiffness element adaptable to different tensile loads according to claim 1, characterized in that, The second rigid sidewall is T-shaped.

7. A quasi-zero stiffness element adaptable to different tensile loads according to any one of claims 1-6, characterized in that, The structural parameters of the negative stiffness unit include length l1, height h1, and thickness t1, and the structural parameters of the positive stiffness unit include height l2, width h2, and thickness t2. By adjusting the above structural parameters individually or in combination, different threshold tensile load ranges can be matched to meet the quasi-zero stiffness vibration reduction requirements of various working conditions.

8. A quasi-zero stiffness metamaterial vibration isolation structure adaptable to different tensile loads, characterized in that, It includes multiple quasi-zero stiffness units as described in any one of claims 1-7, wherein the multiple quasi-zero stiffness units are connected in series or in parallel, or are mixed together to form a metamaterial vibration isolation structure.

9. A design method for quasi-zero stiffness metamaterial vibration isolation structures adaptable to different tensile loads, characterized in that, Includes the following steps: First, determine the target tensile load range and its variation interval. Based on this, design the parametric configuration and combination form of the quasi-zero stiffness element. Assuming that the structure works within a certain target tensile load range, construct the corresponding element force-displacement response characteristics by adjusting the geometric parameters such as the length and thickness of the curved beam. The overall structure is segmented according to different tensile load ranges, and the mechanical behavior of each sub-unit is matched in a targeted manner within the corresponding load range so that it can enter the quasi-zero stiffness working state at the corresponding stage. A local mechanical model is established for each sub-unit, and its equivalent stiffness expression is obtained by combining nonlinear mechanical analysis. Based on this, the parameter matching relationship and combination method of the multi-unit are determined. The equivalent dynamic modeling method is adopted to transform the multi-unit combined structure into an overall system with target dynamic characteristics, thereby obtaining quasi-zero stiffness structural design parameters that can adapt to different tensile load conditions. When the tensile load changes, different sub-units sequentially enter the quasi-zero stiffness working state, so that the structure can maintain the characteristic of quasi-zero stiffness vibration reduction in different load ranges.

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