Stable friction damper with segmented positive and negative stiffness characteristics and modeling method thereof

Abstract

The invention relates to the technical field of structural engineering, in particular to a stable friction damper with segmented positive and negative stiffness characteristics and a modeling method of the friction damper. The friction damper comprises supports, and a pre-compression spring assembly, a lever assembly, a viscoelastic damper assembly and a rotating friction assembly which are arranged between the supports; the pre-compression spring assembly is used for achieving the negative stiffness effect, the lever assembly plays a role in increasing the force and the negative stiffness effect, and the pre-compression spring assembly and the lever assembly form a stable triangular deformation structure. The rotating friction assembly is used for providing friction damping force and guaranteeing the stability of the structure when the pre-compression spring assembly and the lever assembly rotate relatively. The viscoelastic damper assembly is used for applying vibration reduction control force to the structure when small-amplitude vibration of the structure is not enough to drive the friction surface to slide. The invention further provides a corresponding modeling analysis method, and the dynamic behaviors of the device in different working stages are accurately described.

Description

Technical Field

[0001] This invention relates to the field of structural engineering technology, and in particular to a stable friction damper with segmented positive and negative stiffness characteristics and its modeling method. Background Technology

[0002] With the rapid development of modern civil, transportation, and aerospace engineering, flexible structures such as large-span spatial structures, tall mast structures, and long-span bridges are increasingly widely used, facing higher performance requirements in their construction and operation. These structures typically possess characteristics such as low natural frequencies, dense modal distribution, slender configurations, and lightweight, high-strength materials, resulting in low inherent damping and weak energy dissipation capacity. Under the influence of multiple dynamic sources such as wind, earthquakes, and operational loads, they are prone to large-amplitude, long-duration, and multimodal broadband vibrations, severely affecting the structural service performance and long-term safety. Therefore, the development of efficient and reliable vibration control strategies and devices is of great demand.

[0003] Vibration control of flexible structures primarily employs a synergistic approach of aerodynamic and mechanical control. In wind load control, aerodynamic measures are widely used due to their directness and efficiency, with the core being the optimized design of the structural cross-sectional shape. For example, introducing pressure pits or helical winding treatments on the surface of stay cables or suspension cables can effectively disrupt separated airflow and vortex shedding, thereby reducing aerodynamic excitation loads. For bridge main beam cross-sections, aerodynamic stability can be improved by setting guide vanes, suppression plates, or using separation sections. Although aerodynamic control technology has made significant progress in structural wind engineering, its performance is sensitive to structural geometry and dynamic parameters. During long-term operation, environmental effects such as dust accumulation and snow cover can alter the structural surface morphology, weakening or even destroying the effectiveness of existing aerodynamic control measures and introducing new vibration risks.

[0004] Therefore, in engineering practice, mechanical control measures have gradually become an important supplement to aerodynamic control, effectively suppressing multimodal vibration responses under multi-source excitation by introducing additional damping. The core performance indicators of mechanical damping devices include the damping level they provide and the range of adaptability to structural vibration modes. Currently, widely used passive control devices include tuned mass dampers, viscous dampers, high-damping rubber dampers, friction dampers, and eddy current dampers. Although these devices have achieved certain results in structural vibration control, their performance is limited by material properties, installation conditions, and working environment, and their applicability remains limited. Especially with the increasing development of large-span structures, traditional dampers cannot fully meet the actual engineering requirements in terms of high-mode coverage, low-frequency vibration suppression, and service stability. Therefore, there is an urgent need to develop high-performance, multifunctional new damping devices to achieve more efficient and reliable vibration control of complex flexible structures.

[0005] Among various passive damping devices, friction dampers exhibit promising engineering application prospects due to their excellent damping performance, wide environmental adaptability, lack of liquid leakage risk, and high cost-effectiveness. However, the inherent nonlinearity in their working mechanism also brings certain limitations: under small amplitude excitation, effective damping cannot be provided because sliding friction is not activated; while under large amplitude conditions, significant slippage of the contact surface leads to a decrease or even failure of the damping effect, severely affecting its applicability in multimodal vibration control of flexible structures. Patent CN202210588648.X (Friction-type vibration damping device with force amplification mechanism and negative stiffness effect and its installation) proposes a device that utilizes the negative stiffness effect to enhance friction damping, but it still fails to solve the problem of the friction damper not providing damping when the friction surface adheres; in addition, because the negative stiffness effect and friction force are provided by the preloaded spring, the negative stiffness effect and friction force cannot be adjusted separately, making optimal design difficult; furthermore, the movement of the sliding surface of the device is not directionally constrained, making it difficult to guarantee working stability.

[0006] In summary, multimodal vibration control of long-span structures remains a pressing problem to be solved. There is a significant need for the development of new high-performance dampers. Friction damping devices still have the aforementioned adaptability issues, and there is a lack of adaptable friction dampers and their modeling and analysis methods. Summary of the Invention

[0007] To address the issues of insufficient damping in small amplitude and inadequate damping in large amplitude friction dampers, the present invention aims to provide a stable friction damper with segmented positive and negative stiffness characteristics and its modeling method, which greatly improves its applicability and stability in vibration reduction of flexible structures such as bridge cables and main beams.

[0008] The objective of this invention can be achieved through the following technical solutions:

[0009] The first objective of this invention is to provide a stable friction damper with segmented positive and negative stiffness characteristics, comprising a support, and a pre-compression spring assembly, a lever assembly, a viscoelastic damper assembly, and a rotational friction assembly disposed between the supports.

[0010] The bracket is fixed to the external damper support structure. One end is allowed to be connected to the end of the pre-compression spring assembly via a connecting assembly, or a connecting assembly and a rotational friction assembly. The end of the pre-compression spring assembly away from the connecting assembly is allowed to be connected to the lever assembly via a rotational friction assembly. The end of the lever assembly away from the pre-compression spring assembly is allowed to be connected to the other end of the bracket via a rotational friction assembly.

[0011] The lever assembly is provided with a viscoelastic damper assembly at its end perpendicular to its length direction, and is connected to the external structure to be damped (e.g., external cable, the same below) through the viscoelastic damper assembly;

[0012] The pre-compression spring assembly is used to achieve the negative stiffness effect, the lever assembly plays the role of amplifying force and negative stiffness effect, the pre-compression spring assembly and the lever assembly form a stable triangular deformation structure, the rotational friction assembly is used to provide frictional damping force when the pre-compression spring assembly and the lever assembly rotate relative to each other while ensuring the stability of the structure; the viscoelastic damper assembly is used to apply vibration reduction control force to the structure when the sliding friction is not activated during small vibrations of the structure.

[0013] In practical vibration reduction applications, this friction damper exhibits an adhesive state on the friction surface during the small amplitude phase of the structural response, with the vibration control force primarily provided by the viscoelastic damper assembly possessing positive stiffness characteristics. However, during the large amplitude phase of the structural response, the friction surface slips, providing frictional damping force, while the negative stiffness effect of the pre-compression spring enhances the vibration reduction performance. Furthermore, the static friction design of the friction assembly ensures the stability of the pre-compression spring at its critical equilibrium position, facilitating installation.

[0014] In one embodiment of the present invention, in the initial equilibrium state, the hinge points connecting the pre-compression spring assembly, the lever assembly, and the bracket are located on the same straight line; the rotational friction assembly provides static friction to improve the stability of the pre-compression spring assembly.

[0015] When the pre-compression spring assembly and the lever assembly rotate about their hinge points with the bracket, the axial force of the pre-compression spring assembly has a thrust along the direction perpendicular to the connection between the two hinge points on the bracket, which promotes the rotation of the lever assembly and produces a negative stiffness effect. The rotating friction assembly provides sliding friction to dissipate energy.

[0016] In one embodiment of the present invention, the pre-compression spring assembly includes a spring guide frame and a spring sleeved on the outside of the spring guide frame;

[0017] The spring guide frame is a spring guide frame that allows for axial extension and contraction, with one end connected to a support and the other end connected to a lever assembly via a rotational friction assembly.

[0018] In one embodiment of the present invention, the spring guide frame includes a spring receiving portion, limiting plates disposed at both ends of the spring receiving portion, and a connector disposed on the side of the limiting plates away from the spring receiving portion.

[0019] In one embodiment of the present invention, the connector on one side of the spring guide frame is connected to the support via a connecting hinge, and the connector on the other side is connected to the lever assembly via a connecting hinge.

[0020] In one embodiment of the present invention, the lever assembly includes levers arranged at parallel intervals;

[0021] One end of the lever is connected to a pre-compression spring assembly via a rotational friction assembly, and the other end is connected to a bracket via the pre-compression spring assembly.

[0022] A viscoelastic damper assembly is provided along the middle of the lever, perpendicular to its length, and on the side of the lever that is far apart from each other.

[0023] In one embodiment of the present invention, the rotating friction assembly includes an independently disposed friction disk and a disc spring;

[0024] When the rotating friction assembly is positioned at the connection point between the bracket and the pre-compression spring assembly, the friction discs are located on both sides of the joint, with the bracket joint and the disc spring arranged sequentially on the outer side of each side of the joint; and they are connected via a connecting hinge.

[0025] When the rotating friction assembly is positioned at the connection point between the pre-compression spring assembly and the lever assembly, the friction disc is positioned on the side of the lever that is close to each other, and the disc spring is positioned on the side of the lever that is far from the friction disc. The friction disc, lever, and disc spring are connected by a connecting hinge.

[0026] When the rotating friction assembly is positioned at the location where the lever assembly and the bracket are connected, the friction disc is positioned on the side where the levers are close to each other, and the disc spring is positioned on the side of the levers away from the friction disc. The friction disc, lever, and disc spring are connected by a connecting hinge.

[0027] The friction coefficient between the friction disk and the adjacent plate is greater than 0, which is used to provide friction force;

[0028] The disc spring is used between the friction disc and the adjacent plate.

[0029] In one embodiment of the invention, the friction disc is aligned with the central axis of the disc spring.

[0030] In one embodiment of the present invention, the viscoelastic damper assembly includes a first viscoelastic damper and a second viscoelastic damper respectively disposed on the opposite side of two levers and movably connected to the levers, and a damper connecting plate for connecting the first viscoelastic damper and the second viscoelastic damper.

[0031] The damper connecting plate is connected to the external structure that needs vibration reduction.

[0032] In one embodiment of the present invention, the first viscoelastic damper and the second viscoelastic damper simultaneously possess positive stiffness and damping characteristics, and are each independently selected from one of a high-damping rubber damper, a metal damper, or a viscoelastic damper.

[0033] In this invention, the pre-compression spring assembly and the rotational friction assembly form a negative stiffness friction damping assembly, and the viscoelastic damper assembly is connected in series with the negative stiffness friction damping assembly. When the structural amplitude is small, the negative stiffness friction damping assembly does not deform under the action of static friction force, and the deformation of the viscoelastic damper assembly provides vibration reduction control force. When the structural amplitude is large, the negative stiffness friction damping assembly provides negative stiffness-sliding friction force.

[0034] When the viscoelastic damper assembly vibrates parallel to the lever axis at the connection point with the structure, the viscoelastic damper provides vibration reduction control force.

[0035] The connection position between the viscoelastic damper assembly and the lever assembly can be adjusted along the lever axis, thereby adjusting the magnitude of the negative stiffness and the amplification factor of the friction force.

[0036] In summary, this invention utilizes a pre-compression spring assembly to achieve a negative stiffness effect, a rotating friction assembly to provide frictional damping force, a lever assembly to amplify both the frictional damping force and the negative stiffness force, and a viscoelastic damper assembly to provide both positive stiffness and energy dissipation capacity. These components are integrated into a single unit via connectors. In practical vibration reduction applications, during the small amplitude phase of the structural response, the friction surface remains in an adhesive state, with the vibration control force primarily provided by the viscoelastic damper assembly exhibiting positive stiffness. During the large amplitude phase of the structural response, the friction surface slips, providing frictional damping force, while the negative stiffness effect of the pre-compression spring enhances vibration reduction performance. Furthermore, the static friction design of the friction assembly ensures the stability of the pre-compression spring at its critical equilibrium position, facilitating installation. This invention also proposes a modeling and analysis method based on the LuGre friction model, accurately describing the dynamic behavior of the device at different operating stages, providing a theoretical basis and engineering guidance for evaluating the device's vibration reduction effect and optimizing its parameters.

[0037] The second objective of this invention is to provide a modeling and analysis method based on the LuGre friction model, which describes the dynamic behavior of the aforementioned friction damper at different operating stages, providing a theoretical basis and engineering guidance for the evaluation of the device's vibration reduction effect and parameter optimization design.

[0038] In one embodiment of the present invention, the vibration reduction control force of the above-mentioned device is calculated using the following formula:

[0039]

[0040] Among them, F d To reduce vibration control force, v d This represents the displacement at the connection point between the viscoelastic damper assembly and the structure. Represents the corresponding velocity, u d This represents the displacement of the viscoelastic damper assembly and lever connection point relative to the support. and Representing the corresponding velocity and acceleration, z is the state variable in the LuGre friction model. Its first derivative with respect to time, k d c d F represents the stiffness and viscous damping coefficient of the viscoelastic component. ns For the expression of negative stiffness force, m d For the moving mass of the pre-compressed spring assembly and the lever movable assembly, F c For static friction, F s Let σ0 be the sliding friction force, σ0 be the friction surface stiffness coefficient, and σ1 be the friction surface viscosity coefficient. Let γ be a characteristic velocity, and γ be a coefficient.

[0041] Compared with the prior art, the present invention has the following beneficial effects:

[0042] (1) This invention proposes a stable damper with segmented positive and negative stiffness characteristics, which retains the advantages of friction damping and solves the problem of no damping effect of traditional friction dampers when the structure vibrates at small amplitude by using the series vibratory damping method.

[0043] (2) This invention proposes a stable damper with segmented positive and negative stiffness characteristics, which uses a pre-compressed spring to achieve negative stiffness, thereby greatly improving the vibration reduction effect of friction damping when the structure vibrates at a large amplitude.

[0044] (3) This invention proposes a stable damper with segmented positive and negative stiffness characteristics, which combines the advantages of negative stiffness and friction damper, and uses static friction to improve the stability of negative stiffness in the initial equilibrium state.

[0045] (4) This invention proposes a stable damper with segmented positive and negative stiffness characteristics and its modeling and analysis method, providing a tool for the vibration reduction effect analysis and parameter optimization design of the damper. Attached Figure Description

[0046] Figure 1 This is a schematic diagram of the structure of a stable damper with segmented positive and negative stiffness characteristics according to Example 1.

[0047] Figure 2 This is an exploded view of a stable damper with segmented positive and negative stiffness characteristics according to Example 1.

[0048] Figure 3 A calculation diagram of a stable damper with segmented positive and negative stiffness characteristics;

[0049] Figure 4 The mechanical properties of a stable damper with segmented positive and negative stiffness characteristics under different deformation amplitudes are studied.

[0050] Figure 5 A calculation diagram illustrating the use of a stable damper with segmented positive and negative stiffness characteristics for cable-stayed bridge vibration reduction.

[0051] Figure 6 The time history of the location of maximum amplitude during the vibration decay process of a stable damper with segmented positive and negative stiffness characteristics installed on a cable-stayed bridge;

[0052] Figure 7 The deformation time history of a stable damper with segmented positive and negative stiffness characteristics when it is installed on a cable-stayed bridge during the vibration decay stage.

[0053] Figure 8 The damping effect of a stable damper with segmented positive and negative stiffness characteristics during the free decay process of cable vibration;

[0054] The following are the labeling elements in the diagram: 1. Pre-compression spring assembly; 2. Lever assembly; 3. Rotational friction assembly; 4. Viscoelastic damper assembly; 5. Bracket; 6. Connecting hinge; 1-1. Spring; 1-2. Spring guide tube; 1-3. Limiting plate; 1-4. First connector; 1-5. Second connector; 2-1. Lever; 3-1. Friction disc; 3-2. Disc spring; 4-1. Viscoelastic damper; 4-2. Damper connecting plate. Detailed Implementation

[0055] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0056] In the description of this invention, unless otherwise explicitly specified and limited, the terms "connected," "linked," and "fixed" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0057] In this invention, unless otherwise explicitly specified and limited, "above" or "below" the second feature can include direct contact between the first and second features, or contact between the first and second features through another feature between them. Furthermore, "above," "over," and "on top" of the second feature includes the first feature directly above or diagonally above the second feature, or simply indicates that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature includes the first feature directly below or diagonally below the second feature, or simply indicates that the first feature is at a lower horizontal level than the second feature.

[0058] In the description of this embodiment, the terms "upper," "lower," "left," and "right," etc., refer to the orientation or positional relationship shown in the accompanying drawings. They are used only for ease of description and simplification of operation, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the present invention. In addition, the terms "first" and "second" are used only for distinction in description and have no special meaning.

[0059] In the following embodiments, unless otherwise specified, the structures or components used are conventional structures or components in the art, as long as they can achieve the corresponding functions.

[0060] Example 1

[0061] This embodiment provides a stable friction damper with segmented positive and negative stiffness characteristics, such as... Figures 1-2 As shown, the device includes a support 5, and a pre-compression spring assembly 1, a lever assembly 2, a viscoelastic damper assembly 4, and a rotational friction assembly 3 disposed between the support 5. The support 5 is fixed to an external damper support structure. One end of the support 5 is allowed to be connected to the end of the pre-compression spring assembly 1 via a connecting assembly, or the connecting assembly and the rotational friction assembly 3. The end of the pre-compression spring assembly 1 away from the connecting assembly is allowed to be connected to the lever assembly 2 via the rotational friction assembly 3. The end of the lever assembly 2 away from the pre-compression spring assembly 1 is allowed to be connected to the other end of the support 5 via the rotational friction assembly 3. The lever assembly 2 is provided with a viscoelastic damper assembly 4 at its end perpendicular to its length direction and is connected to an external cable via the viscoelastic damper assembly 4.

[0062] In this embodiment, the rotational friction assembly 3 is only provided at the connection positions of the pre-compression spring assembly 1 and the lever assembly 2, and at the connection positions of the lever assembly 2 and the bracket 5. The pre-compression spring assembly 1 is used to achieve a negative stiffness effect. The pre-compression spring assembly 1 and the lever assembly 2 form a stable triangular deformation structure. The rotational friction assembly 3 provides frictional damping force, which is used to provide frictional damping force when the pre-compression spring assembly 1 and the lever assembly 2 rotate relative to each other, while ensuring the stability of the structure. The lever assembly 2 plays the role of amplifying the frictional damping force and the negative stiffness effect. The viscoelastic damper assembly 4 is used to apply vibration control force (providing positive stiffness and energy dissipation capacity) to the structure when it vibrates.

[0063] Furthermore, in the initial equilibrium state, the hinge points connecting the pre-compression spring assembly 1, the lever assembly 2, and the bracket 5 are located on the same straight line; the rotational friction assembly 3 provides static friction to improve the stability of the pre-compression spring assembly 1; when the pre-compression spring assembly 1 and the lever assembly 2 rotate around their hinge points with the bracket 5, the axial force of the pre-compression spring assembly 1 has resistance along the direction perpendicular to the connection of the two hinge points on the bracket 5, promoting the rotation of the spring 1-1 assembly and producing a negative stiffness effect.

[0064] Furthermore, the pre-compression spring assembly 1 includes a spring guide frame 1-2 and a spring 1-1 sleeved on the outside of the spring guide frame 1-2; the spring guide frame 1-2 is a spring guide frame 1-2 that allows for axial extension and contraction, one end of which is connected to the support 5, and the other end is connected to the lever assembly 2 through the rotational friction assembly 3.

[0065] Furthermore, the spring guide frame 1-2 includes a spring receiving part, limiting pieces 1-3 disposed at both ends of the spring receiving part, and connectors (including a first connector 1-4 and a second connector 1-5) disposed on the side of the limiting pieces 1-3 away from the spring receiving part; the first connector 1-4 on one side of the spring guide frame 1-2 is connected to the bracket 5 through a connecting hinge 6, and the second connector 1-5 on the other side is connected to the lever assembly 2 through a connecting hinge 6.

[0066] Furthermore, the lever assembly 2 includes levers 2-1 arranged in parallel intervals; one end of the lever 2-1 is connected to the pre-compression spring assembly 1 through the rotational friction assembly 3, and the other end is connected to the bracket 5 through the pre-compression spring assembly 1; a viscoelastic damper assembly 4 is provided along the middle of the lever 2-1 perpendicular to its length direction and on the side of the levers 2-1 that are far apart from each other.

[0067] Further, the rotating friction assembly 3 includes an independently arranged friction disc 3-1 and a disc spring 3-2; when the rotating friction assembly 3 is positioned where the bracket 5 is connected to the pre-compression spring assembly 1, the friction disc 3-1 is positioned on both sides of the joint, with the bracket joint and the disc spring 3-2 sequentially located on the outer side of one side of the joint; and they are connected via a connecting hinge 6; when the rotating friction assembly 3 is positioned where the pre-compression spring assembly 1 is connected to the lever assembly 2, the friction disc 3-1 is positioned on the side of the lever 2-1 that is close to each other, and the disc spring 3-2 is positioned on the side of the lever 2-1 that is away from the friction disc 3-1, and so on. The friction disc 3-1, lever 2-1, and disc spring 3-2 are connected by a connecting hinge 6. When the rotating friction assembly 3 is positioned where the lever assembly 2 is connected to the bracket 5, the friction disc 3-1 is positioned on the side of the lever 2-1 that is close to it, and the disc spring 3-2 is positioned on the side of the lever 2-1 that is away from the friction disc 3-1. The friction disc 3-1, lever 2-1, and disc spring 3-2 are connected by a connecting hinge 6. The friction coefficient between the friction disc 3-1 and the adjacent plate is greater than 0, which is used to provide friction force. The disc spring 3-2 is used to provide friction between the friction disc 3-1 and the adjacent plate.

[0068] Among them, the friction disc 3-1 and the disc spring 3-2 have the same central axis.

[0069] Furthermore, the viscoelastic damper assembly 4 includes a first viscoelastic damper and a second viscoelastic damper respectively disposed on opposite sides of the two levers 2-1 and movably connected to the levers 2-1, and a damper connecting plate 4-2 for connecting the first viscoelastic damper and the second viscoelastic damper; the damper connecting plate 4-2 is connected to an external cable.

[0070] Preferably, the first viscoelastic damper and the second viscoelastic damper both have positive stiffness and damping characteristics, and are each independently selected from one of a high-damping rubber damper, a metal damper, or a viscoelastic damper.

[0071] In this embodiment, the pre-compression spring assembly 1 and the rotational friction assembly 3 form a negative stiffness friction damping assembly, and the viscoelastic damper assembly 4 is connected in series with the negative stiffness friction damping assembly. When the structural amplitude is small, the negative stiffness friction damping assembly does not deform under the action of static friction force, and the deformation of the viscoelastic damper assembly 4 provides vibration reduction control force. When the structural amplitude is large, the negative stiffness friction damping assembly provides negative stiffness-sliding friction force.

[0072] When the viscoelastic damper assembly 4 vibrates parallel to the axis of lever 2-1 at the connection point with the structure, the viscoelastic damper 4-1 provides vibration reduction control force.

[0073] The connection position between the viscoelastic damper assembly 4 and the lever assembly 2 can be adjusted along the axis of lever 2-1, thereby adjusting the magnitude of the negative stiffness and the amplification factor of the friction force.

[0074] Example 2

[0075] This embodiment provides a stable friction damper with segmented positive and negative stiffness characteristics. Figure 1 The modeling method for the friction damper shown is as follows: Figure 3 As shown, the damping control force of the damper is calculated using the following formula:

[0076]

[0077] Wherein: F d To reduce vibration control force, v d This represents the displacement at the connection point between the viscoelastic damper assembly 4 and the structure. Represents the corresponding velocity, u d The displacement of the connection point between the viscoelastic damper assembly 4 and lever 2-1 relative to the bracket 5. and Representing the corresponding velocity and acceleration, z is the state variable in the LuGre friction model. Its first derivative with respect to time, k d c d F represents the stiffness and viscous damping coefficient of the viscoelastic component. ns For the expression of negative stiffness force, m d For the moving mass of the pre-compressed spring assembly 1 and the movable component of lever 2-1, F c For static friction, F s Let σ0 be the sliding friction force, σ0 be the friction surface stiffness coefficient, and σ1 be the friction surface viscosity coefficient. Let γ be a characteristic velocity, γ be a coefficient, and t be time.

[0078] Furthermore, based on the known damper parameters and the known v d (t) and the corresponding u was calculated using numerical methods d And z, and thus the control force F of the damper can be obtained. d .

[0079] like Figure 4 As shown, when v d When (t) is a sinusoidal function, the relationship between the control force and displacement of a typical damper can be seen when v d When the amplitude of (t) is small, the damper provides viscoelastic damping force (with positive stiffness). When the amplitude increases, the damper mainly provides negative stiffness friction force.

[0080] Example 3

[0081] like Figure 5 As shown, when using Example 1 ( Figure 1 When the friction damper shown provides a stable damper with segmented positive and negative stiffness characteristics to control the vibration of the stay cable, the modeling and analysis method provided in Example 2 can be used to calculate the free decay curve of the stay cable under the damper's vibration reduction control, as shown in the example. Figure 6 and Figure 7 As shown in the figure, when the amplitude of the stay cable is large, the response decays according to frictional damping; after the vibration amplitude decays to a certain value, it decays according to viscous damping. Figure 8 The damping is calculated based on the attenuation curve. It can be seen that even when the amplitude is very small, the friction damper can still provide a damping effect, which solves the problem that traditional friction dampers cannot provide damping when the friction surfaces are stuck together. Furthermore, it can be seen that the negative stiffness effect greatly improves the maximum damping effect provided by the damper.

[0082] The above description of the embodiments is provided to enable those skilled in the art to understand and use the invention. It will be apparent to those skilled in the art that various modifications can be made to these embodiments, and the general principles described herein can be applied to other embodiments without inventive effort. Therefore, the present invention is not limited to the above embodiments, and any improvements and modifications made by those skilled in the art based on the interpretation of the present invention, without departing from the scope of the invention, should be within the protection scope of the present invention.

Claims

1. A stable friction damper with segmented positive and negative stiffness characteristics, characterized in that, It includes a support (5), and a pre-compression spring assembly (1), a lever assembly (2), a viscoelastic damper assembly (4), and a rotational friction assembly (3) disposed between the support (5); The bracket (5) is fixed to the external damper support structure. One end is allowed to be connected to the end of the pre-compression spring assembly (1) through a connecting assembly, or a connecting assembly and a rotating friction assembly (3). The end of the pre-compression spring assembly (1) away from the connecting assembly is allowed to be connected to the lever assembly (2) through the rotating friction assembly (3). The end of the lever assembly (2) away from the pre-compression spring assembly (1) is allowed to be connected to the other end of the bracket (5) through the rotating friction assembly (3). The lever assembly (2) is provided with a viscoelastic damper assembly (4) at its end perpendicular to its length direction, and is connected to the external structure to be damped through the viscoelastic damper assembly (4). Among them, the pre-compression spring assembly (1) is used to achieve the negative stiffness effect, the lever assembly (2) plays the role of amplifying force and negative stiffness effect, the pre-compression spring assembly (1) and the lever assembly (2) form a stable triangular deformation structure, the rotational friction assembly (3) is used to provide frictional damping force when the pre-compression spring assembly (1) and the lever assembly (2) rotate relative to each other, while ensuring the stability of the structure; the viscoelastic damper assembly (4) is used to provide positive stiffness and energy dissipation capacity.

2. The stable friction damper with segmented positive and negative stiffness characteristics according to claim 1, characterized in that, In the initial equilibrium state, the hinge points connecting the pre-compression spring assembly (1), the lever assembly (2), and the bracket (5) are located on the same straight line; the rotational friction assembly (3) provides static friction and improves the stability of the pre-compression spring assembly (1); When the pre-compression spring assembly (1) and the lever assembly (2) rotate about the hinge point between them and the bracket (5), the axial force of the pre-compression spring assembly (1) has a thrust along the direction perpendicular to the connection between the two hinge points on the bracket (5), which promotes the rotation of the lever assembly (2) and produces a negative stiffness effect. The rotating friction assembly (3) provides sliding friction to dissipate energy.

3. The stable friction damper with segmented positive and negative stiffness characteristics according to claim 1, characterized in that, The pre-compression spring assembly (1) includes a spring guide frame (1-2) and a spring (1-1) sleeved on the outside of the spring guide frame (1-2); The spring guide frame (1-2) is a spring guide frame (1-2) that allows for extension and retraction along its axial direction. One end of the spring guide frame (1-2) is connected to the support (5), and the other end is connected to the lever assembly (2) via the rotating friction assembly (3).

4. A stable friction damper with segmented positive and negative stiffness characteristics according to claim 3, characterized in that, The spring guide frame (1-2) includes a spring receiving part, limiting pieces (1-3) disposed at both ends of the spring receiving part, and a connector disposed on the side of the limiting piece (1-3) away from the spring receiving part.

5. A stable friction damper with segmented positive and negative stiffness characteristics according to claim 1, characterized in that, The lever assembly (2) includes levers (2-1) arranged in parallel at intervals; One end of the lever (2-1) is connected to the pre-compression spring assembly (1) via a rotational friction assembly (3), and the other end is connected to the bracket (5) via the pre-compression spring assembly (1); A viscoelastic damper assembly (4) is provided along the middle of the lever (2-1) perpendicular to its length direction and on the side of the lever (2-1) that is far apart from each other.

6. A stable friction damper with segmented positive and negative stiffness characteristics according to claim 5, characterized in that, The rotating friction assembly (3) includes an independently configured friction disc (3-1) and a disc spring (3-2); When the rotating friction assembly (3) is positioned at the location where the bracket (5) and the pre-compression spring assembly (1) are connected, the friction disc (3-1) is positioned on both sides of the joint, and the bracket joint and the disc spring (3-2) are located on the outer side of one side of the joint in sequence; and are connected by the connecting hinge (6); When the rotating friction assembly (3) is positioned where the pre-compression spring assembly (1) and the lever assembly (2) are connected, the friction disc (3-1) is positioned on the side where the lever (2-1) is close to each other, and the disc spring (3-2) is positioned on the side of the lever (2-1) away from the friction disc (3-1). The friction disc (3-1), the lever (2-1), and the disc spring (3-2) are connected by a connecting hinge (6). When the rotating friction assembly (3) is positioned where the lever assembly (2) and the bracket (5) are connected, the friction disc (3-1) is positioned on the side where the lever (2-1) is close to each other, and the disc spring (3-2) is positioned on the side of the lever (2-1) away from the friction disc (3-1). The friction disc (3-1), the lever (2-1), and the disc spring (3-2) are connected by a connecting hinge (6). The friction coefficient between the friction disk (3-1) and the adjacent plate is greater than 0.

7. A stable friction damper with segmented positive and negative stiffness characteristics according to claim 6, characterized in that, The friction disc (3-1) and the disc spring (3-2) share the same central axis.

8. A stable friction damper with segmented positive and negative stiffness characteristics according to claim 1, characterized in that, The viscoelastic damper assembly (4) includes a first viscoelastic damper and a second viscoelastic damper, which are respectively disposed on the opposite sides of the two levers (2-1) and fixedly connected to the levers (2-1). And a damper connecting plate (4-2) for connecting the first viscoelastic damper and the second viscoelastic damper; The damper connecting plate (4-2) is connected to the external structure that needs vibration reduction.

9. A modeling and analysis method based on the LuGre friction model, characterized in that, This method is used to describe the dynamic behavior of a stable friction damper with segmented positive and negative stiffness characteristics as described in any one of claims 1 to 8 at different operating stages.

10. The modeling and analysis method based on the LuGre friction model according to claim 9, characterized in that, The vibration reduction control force of the device is calculated using the following formula: Among them, F d To reduce vibration control force, v d The displacement is the point of connection between the viscoelastic damper assembly (4) and the structure. Represents the corresponding velocity, u d The displacement of the connection point between the viscoelastic damper assembly (4) and the lever (2-1) relative to the support (5) is given. and Representing the corresponding velocity and acceleration, z is the state variable in the LuGre friction model. Its first derivative with respect to time, k d c d F represents the stiffness and viscous damping coefficient of the viscoelastic component. ns For the expression of negative stiffness force, m d For the moving mass of the pre-compressed spring assembly (1) and the movable component of the lever (2-1), F c For static friction, F s Let σ0 be the sliding friction force, σ0 be the friction surface stiffness coefficient, and σ1 be the friction surface viscosity coefficient. Let γ be a characteristic velocity, and γ be a coefficient.

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