CN107327194B - Supporting type negative-stiffness friction damper - Google Patents

Supporting type negative-stiffness friction damper Download PDF

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CN107327194B
CN107327194B CN201710684602.7A CN201710684602A CN107327194B CN 107327194 B CN107327194 B CN 107327194B CN 201710684602 A CN201710684602 A CN 201710684602A CN 107327194 B CN107327194 B CN 107327194B
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curved surface
friction
box body
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CN107327194A (en
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纪晓东
苗增辉
张峻山
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Tsinghua University
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    • EFIXED CONSTRUCTIONS
    • E04BUILDING
    • E04HBUILDINGS OR LIKE STRUCTURES FOR PARTICULAR PURPOSES; SWIMMING OR SPLASH BATHS OR POOLS; MASTS; FENCING; TENTS OR CANOPIES, IN GENERAL
    • E04H9/00Buildings, groups of buildings or shelters adapted to withstand or provide protection against abnormal external influences, e.g. war-like action, earthquake or extreme climate
    • E04H9/02Buildings, groups of buildings or shelters adapted to withstand or provide protection against abnormal external influences, e.g. war-like action, earthquake or extreme climate withstanding earthquake or sinking of ground
    • E04H9/021Bearing, supporting or connecting constructions specially adapted for such buildings
    • EFIXED CONSTRUCTIONS
    • E04BUILDING
    • E04HBUILDINGS OR LIKE STRUCTURES FOR PARTICULAR PURPOSES; SWIMMING OR SPLASH BATHS OR POOLS; MASTS; FENCING; TENTS OR CANOPIES, IN GENERAL
    • E04H9/00Buildings, groups of buildings or shelters adapted to withstand or provide protection against abnormal external influences, e.g. war-like action, earthquake or extreme climate
    • E04H9/02Buildings, groups of buildings or shelters adapted to withstand or provide protection against abnormal external influences, e.g. war-like action, earthquake or extreme climate withstanding earthquake or sinking of ground
    • E04H9/021Bearing, supporting or connecting constructions specially adapted for such buildings
    • E04H9/023Bearing, supporting or connecting constructions specially adapted for such buildings and comprising rolling elements, e.g. balls, pins

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  • Engineering & Computer Science (AREA)
  • Architecture (AREA)
  • Business, Economics & Management (AREA)
  • Emergency Management (AREA)
  • Environmental & Geological Engineering (AREA)
  • Civil Engineering (AREA)
  • Structural Engineering (AREA)
  • Buildings Adapted To Withstand Abnormal External Influences (AREA)
  • Vibration Prevention Devices (AREA)

Abstract

The invention provides a supporting type negative stiffness friction damper, which belongs to the technical field of energy dissipation and vibration reduction of civil engineering structures and comprises a transverse deformation constraint box body, curved surface friction components and axial connecting supports, wherein the curved surface friction components are respectively positioned in the box body and at the left side and the right side of the box body; the curved surface friction member comprises a laminated rubber spring, a sliding box, a curved surface self-adaptive sliding hinge and an outward convex friction curved surface plate, wherein the sliding box, the curved surface self-adaptive sliding hinge and the outward convex friction curved surface plate are respectively arranged at two ends of the laminated rubber spring from near to far in sequence and are coaxial with the laminated rubber spring; the convex friction curved plate is fixedly connected with an end plate of the transverse deformation restraint box body, two end plates of the transverse deformation restraint box body are fixed through a pair of lead screws, and pre-tightening force is applied to the laminated rubber spring through the pair of lead screws; the invention is arranged in a building structure, can reduce the equivalent rigidity of the structure, increases the structural damping, can control the displacement and acceleration response of the structure under the action of an earthquake, and reduces the earthquake damage of the building.

Description

Supporting type negative-stiffness friction damper
Technical Field
The invention relates to the technical field of energy dissipation and vibration reduction of civil engineering structures, in particular to a supporting type negative-stiffness friction damper.
Background
A plurality of large earthquake damages in recent years show that the modern buildings designed for earthquake resistance can basically realize large earthquake but the earthquake damage repair of structural members (such as beams, columns, shear walls and the like) has high cost and long time consumption, and is difficult to repair after earthquake or uneconomical to repair, so that a large number of earthquake damaged buildings are forcedly dismantled; in addition, non-structural members (e.g., infill walls, ceilings, etc.) and equipment are damaged severely, which affects the continued use of important buildings (e.g., hospitals) after earthquakes. The seismic loss of the structural member is related to the overlarge interlayer displacement of the building, and the seismic loss of the non-structural member is related to the overlarge interlayer displacement of the building or the overlarge floor acceleration. Therefore, to achieve rapid recovery of the functions of important buildings after earthquake, it is necessary to achieve double control of the inter-storey displacement and floor acceleration while reducing the earthquake damage of structural and non-structural members.
At present, the earthquake resistance of a building structure is improved mainly by arranging a passive control damping device in engineering. The traditional passive control device mainly comprises an anti-buckling support, a viscous damper, a friction damper and the like, and the mechanical principle of the traditional passive control device is that the interlayer displacement response of a building structure under the action of an earthquake is reduced by adding damping and rigidity to the structure. However, the conventional passive control devices are unable to effectively reduce the floor acceleration response of the building structure under the action of an earthquake, and therefore, unable to reduce the earthquake damage of a large number of acceleration-dependent non-structural members.
Disclosure of Invention
In order to realize double control of interlayer displacement and floor acceleration, the invention aims to provide a support type negative stiffness friction damper, which adds large damping to a structure, can increase the energy consumption capability and the equivalent damping ratio of the structure under the action of an earthquake, and controls the interlayer displacement response of the structure under the strong earthquake; meanwhile, the negative stiffness is introduced into the structure, the equivalent stiffness of the structure can be reduced, and the total restoring force of the structure is reduced under the same displacement, so that the floor acceleration response of the structure is effectively reduced. The support type negative stiffness friction damper has the characteristics of simple structure, large output force, easiness in design, flexibility in layout and the like, can simultaneously control interlayer displacement and floor acceleration response of a structure under the action of an earthquake, and improves the quick recovery capability of the building structure after the earthquake.
In order to achieve the purpose, the invention adopts the technical scheme that:
a supporting type negative stiffness friction damper is characterized by comprising a transverse deformation restraining box body, a curved surface friction member positioned in the transverse deformation restraining box body and axial connecting supports positioned on the left side and the right side of the transverse deformation restraining box body; the transverse deformation restraint box body comprises an upper end plate, a lower end plate, a left cover plate and a right cover plate; the curved surface friction member comprises a laminated rubber spring, a sliding box, a curved surface self-adaptive sliding hinge and an outward convex friction curved surface plate, wherein the sliding box, the curved surface self-adaptive sliding hinge and the outward convex friction curved surface plate are respectively positioned at two ends of the laminated rubber spring from near to far; the damper also comprises an outer box, the sliding box and the laminated rubber spring are both positioned in the outer box, the outer wall of the sliding box is attached to the inner walls of the two ends of the outer box, and the sliding box and the outer box can slide relatively along the axial direction of the laminated rubber spring; the end plates of the transverse deformation restraint box body are fixedly connected with the convex friction curved plate through friction type high-strength bolts, the upper end plate and the lower end plate of the transverse deformation restraint box body are fixed through a pair of lead screws, and pre-pressure is applied to the laminated rubber spring through the pair of lead screws; after the pre-pressure is applied in place, connecting the end plates and the cover plate of the transverse deformation restraint box body by using friction type high-strength bolts so as to fix the relative positions of the two end plates; one end of an axial connecting support positioned on the right side of the transverse deformation restraining box body is fixed with a right cover plate of the transverse deformation restraining box body, and the other end of the axial connecting support is fixed with a node of the building structure; one end of an axial connecting support positioned on the left side of the transverse deformation restraint box body is fixed with the left side wall of the curved surface friction member middle outer box, and the other end of the axial connecting support is fixed with a node of the building structure.
The convex friction curved plate of the negative-stiffness friction damper is provided with a convex circular curved surface, and the surface of the circular curved surface is rough.
The sliding box and the curved surface self-adaptive sliding hinge are arranged in a matched mode, a curved surface groove is formed in the surface of the sliding box, and the curved surface self-adaptive sliding hinge is formed by sectioning two curved surfaces; the concave curved surface of the curved surface self-adaptive sliding hinge is attached to the convex round curved surface of the convex friction curved plate and slides relatively; the convex curved surface of the curved surface self-adaptive sliding hinge is attached to the curved surface groove of the sliding box and rotates relatively; the sliding box keeps translation during the motion process of the negative-rigidity friction damper.
Compared with the prior art, the invention has the following advantages:
(1) "negative stiffness" characteristic: the force-displacement curve of the invention has obvious negative rigidity characteristic, namely, the sliding friction force between the self-adaptive sliding hinge and the outward convex friction curved plate is gradually reduced along with the increase of the relative motion of the self-adaptive sliding hinge and the outward convex friction curved plate. Due to the negative stiffness characteristic, the damper can reduce the equivalent stiffness of a building structure and reduce the floor acceleration response of the building under the action of an earthquake. By controlling the floor acceleration response of the building structure, the earthquake damage of a large number of acceleration-related non-structural members is effectively reduced, and the quick recovery capability of the building after the earthquake is improved.
(2) The energy consumption ability is strong, and anti-seismic performance is superior: the invention dissipates the seismic energy by the sliding friction force, which belongs to coulomb damping. Unlike the conventional viscous damping which exponentially attenuates the free vibration of the system, the Coulomb damping can linearly attenuate the free vibration of the system, and the damping efficiency is higher. Therefore, the invention can add larger equivalent damping to the building structure, reduce the vibration response of the building structure and improve the anti-seismic performance of the building structure.
(3) The node has good stress: according to the invention, as the relative displacement between the curved surface self-adaptive sliding hinge and the convex friction curved plate is increased, the output of the damper is reduced; at maximum displacement, the damper output is zero. Therefore, the stress of the connecting joint of the invention and the building structure can avoid the problems of coupling of the maximum bending moment of the joint and the maximum axial force of the support and complex stress of the joint in the traditional support-frame structure.
The invention realizes the effective combination of negative rigidity and large damping, can realize double control of interlayer displacement and floor acceleration of the building structure, reduces the damage of structural members and non-structural members under the action of earthquake, improves the quick recovery capability of the building structure after the earthquake, and has good market popularization and application prospect.
Drawings
Fig. 1 is a schematic view of the overall structure of the present invention.
Fig. 2 is a schematic cross-sectional view of the overall structure of the present invention.
Fig. 3 is a force diagram of the convex friction curved plate of the invention.
Fig. 4 is a schematic view of the geometric relationship between the convex friction curved plate and the curved self-adaptive sliding hinge according to the present invention.
FIG. 5 is a graph of restoring force of an embodiment of the present invention.
Detailed Description
The technical solution of the present invention is further described in detail with reference to the accompanying drawings and specific embodiments.
The whole structure of the supporting type negative-stiffness friction damper is shown in figure 1, the section structure is shown in figure 2, and the damper comprises a transverse deformation restraining box body (the transverse deformation restraining box body is opened front and back, and a closed box body can be adopted in practical use), a curved-surface friction member positioned in the transverse deformation restraining box body and axial connecting supports positioned on the left side and the right side of the transverse deformation restraining box body; the transverse deformation restraint box body comprises an upper end plate 5-1, a lower end plate 5-2, a right cover plate 6-1 and a left cover plate 6-2; the curved surface friction member comprises a laminated rubber spring 4, a sliding box 3, a curved surface self-adaptive sliding hinge 2 and an outward convex friction curved surface plate 1, wherein the sliding box 3, the curved surface self-adaptive sliding hinge 2 and the outward convex friction curved surface plate 1 are respectively arranged at two ends of the laminated rubber spring 4 from near to far in sequence and are coaxial with the laminated rubber spring; the damper also comprises an outer box 7, the sliding box 3 and the laminated rubber spring 4 are both positioned in the outer box, the outer wall of the sliding box 3 is attached to the inner walls of the two ends of the outer box, and the sliding box 3 and the outer box 7 can slide relatively along the axial direction of the laminated rubber spring 4; the end plate of the transverse deformation restraint box body is fixedly connected with the convex friction curved plate 1 through a friction type high-strength bolt, the upper end plate and the lower end plate of the transverse deformation restraint box body are fixed through a pair of lead screws 9, and prepressing force is applied to the laminated rubber spring 4 through the pair of lead screws 9; after the pre-pressure is applied in place, connecting the end plates and the cover plate of the transverse deformation restraint box body by using friction type high-strength bolts so as to fix the relative positions of the two end plates; one end of an axial connecting support 8-1 positioned on the right side of the transverse deformation restraining box body is fixed with a right cover plate of the transverse deformation restraining box body, the other end of the axial connecting support 8-1 is fixed with a node (such as a beam column node, a shear wall-coupling beam node and the like) of a building structure, one end of an axial connecting support 8-2 positioned on the left side of the transverse deformation restraining box body is fixed with the left side wall of the middle and outer box 7 of the curved surface friction member, and the other end of the axial connecting support 8-2 is fixed with the node of the building structure.
The convex friction curved plate 1 has a convex circular curved surface, and the surface of the circular curved surface is rough (the sliding friction coefficient of the circular curved surface can be determined according to the use requirement of the damper, in the embodiment, the sliding friction coefficient is 0.40), and the stable sliding friction coefficient can be kept under the condition of high pressure bearing (in the embodiment, the average surface pressure of the contact part between the convex friction curved plate and the curved surface adaptive sliding hinge is up to 25 MPa). The convex friction curved plate is connected with the transverse deformation restraint end plate through bolts, and is convenient to detach, replace and repair. The convex friction curved plate 1 of the embodiment is formed by casting an organic friction material mold, the sliding friction coefficient of the curved surface is 0.40, the maximum bearable surface pressure reaches 30MPa, and in order to facilitate the assembly of the curved plate, a steel lining plate with the thickness of 10mm is arranged on the bottom surface of the curved plate.
The sliding box 3 is matched with the curved surface self-adaptive sliding hinge 2, as shown in fig. 2; the surface of the sliding box 3 is provided with a curved surface groove; the curved surface self-adaptive sliding hinge 2 is formed by sectioning two curved surfaces, an inner concave curved surface of the curved surface self-adaptive sliding hinge 2 is attached to an outer convex circular curved surface of the outer convex friction curved plate 1, and the curved surface self-adaptive sliding hinge 2 and the outer convex friction curved plate 1 slide relatively to each other to generate sliding friction force; the convex curved surface of the curved surface self-adaptive sliding hinge 2 is attached to the curved surface groove of the sliding box 3, an anti-friction material is sprayed on the surface of the convex curved surface of the curved surface self-adaptive sliding hinge 2 (in the embodiment, a polytetrafluoroethylene spraying material is adopted, the sliding friction coefficient of the surface is less than 0.05), the curved surface self-adaptive sliding hinge 2 and the sliding box 3 rotate relatively, and the friction force of the contact part is basically zero; in the motion process of the negative-rigidity friction damper, the curved-surface self-adaptive sliding hinge 2 is always tightly attached to and slides on the convex friction curved plate 1, and the sliding box 3 is always kept in translation without rotating. The sliding box 3 and the curved surface self-adaptive sliding hinge 2 of the embodiment are both made of common steel materials and are machined by a numerical control machine; in the present embodiment, the surface roughness of the convex curved surface of the curved surface adaptive sliding hinge 2 and the surface roughness of the curved surface groove of the sliding box 3 are ra1.6, and the surface roughness of the concave curved surface of the curved surface adaptive sliding hinge 2 is ra6.3. Meanwhile, the surface of the convex curved surface of the curved surface self-adaptive sliding hinge 2 is coated with a polytetrafluoroethylene antifriction material, and the sliding friction coefficient of the convex curved surface is less than 0.05.
The laminated rubber spring 4 has the characteristics of large axial rigidity and high axial bearing capacity, and ensures that enough positive pressure is provided for the outward convex friction curved plate 1. The pre-pressure of the laminated rubber spring is applied by the transverse deformation restraint box body, and the adjustment and the control of the pre-pressure can be realized by controlling the external force applied to the opposite-threading rod 9. In this embodiment, the laminated rubber spring is formed by connecting 4 laminated rubber supports commonly used in engineering in series, and the laminated rubber supports are according to the national standard GB 20688.3-2006 rubber support-third part: the design and manufacture of the building shock insulation rubber support comprise laminated rubber with a lead core and steel connecting plates at two ends of the laminated rubber, wherein the vertical rigidity of a single laminated rubber support reaches 100kN/mm, and the limit surface pressure reaches more than 30 MPa.
The assembly process of the supporting type negative stiffness friction damper is as follows: the laminated rubber spring 4 is connected with the sliding box 3 through a common bolt and is arranged in the outer box 7; the convex friction curved plate 1 is firmly connected with the transverse deformation restraint box body end plates (5-1 and 5-2) through friction type high-strength bolts; the laminated rubber spring 4, the sliding box 3, the curved surface self-adaptive sliding hinge 2 and the convex friction curved plate 1 are stacked in sequence, and precompression is applied to the laminated rubber spring 4 through a pair of lead screws 9; after the pre-pressure is applied in place, the friction type high-strength bolt is used for connecting the end plates (5-1 and 5-2) and the cover plates (6-1 and 6-2) of the transverse deformation restraint box body so as to fix the relative positions of the two end plates and prevent the two end plates from rotating relatively in the working process of the damper. So far, the assembly of the support type negative-stiffness friction damper is completed, as shown in fig. 1.
After the supporting type negative-stiffness friction damper is assembled into a whole, the whole is transported to the site, and two ends of the axial connecting support are respectively and reliably connected with nodes of a building structure through bolts. The damper is applied to a building structure in a supporting mode, can be obliquely arranged, and is flexible in angle between the axial direction (namely the direction of a connecting line connecting two nodes of the building structure of the damper) and a building floor.
The working principle of the supporting type negative stiffness friction damper is introduced as follows:
under the action of earthquake, two nodes of the building structure connected with the damper are relatively displaced in the connecting line direction, and the outer box 7 is driven by the axial connecting support to move along the axial direction of the damper, so that the curved surface self-adaptive sliding hinge 2 slides on the convex friction curved plate 1. In the relative motion process of the curved surface self-adaptive sliding hinge and the convex friction curved plate, the laminated rubber spring 4 is always kept in a compressed state, so that the relative sliding of the curved surface self-adaptive sliding hinge 2 and the convex friction curved plate 1 generates sliding friction force and dissipates seismic energy along with the reciprocating motion of the damper.
The interaction between the curved surface self-adaptive sliding hinge 2 and the convex friction curved plate 1The axial force F of the invention can be obtained by simplifying the method into single-point concentrated contact and combining the stress sketch diagrams of figures 3 and 4 and taking the curved surface self-adaptive sliding hinge 2 as a stress analysis object (simplified into a rectangular sliding block on the figures) H The functional relation with the relative axial displacement x, namely the restoring force model of the supporting type negative stiffness friction damper is specifically deduced as follows. The X-axis in the figure is parallel to the present damper axis.
According to the force diagram shown in fig. 3, the positive pressure F of the vertically pre-stressed laminated rubber spring 4 in different directions of movement can be listed V And axial force F of the supporting type negative-stiffness friction damper H The satisfied relational expressions are respectively shown as formula (1) and formula (2):
F v =F σ ·cosα+sgn(x·v)·F τ ·sinα (1)
F H =-sgn(x·v)·F σ ·sinα+F τ ·cosα (2)
in the formula, F V Showing the positive pressure, F, to which the laminated rubber spring 4 is subjected H The axial output of the supporting type negative-stiffness friction damper is represented; f σ The positive pressure acting on one point of the convex friction curved plate 1 acting on the curved self-adaptive sliding hinge 2 is represented; f τ Representing the sliding friction force of the curved surface self-adaptive sliding hinge 2 acted on by the convex friction curved plate 1 in the motion process of the curved surface self-adaptive sliding hinge; x represents the relative displacement of the curved surface self-adaptive sliding hinge and the outward convex friction curved plate, 1 is taken as the positive direction of the X axis, and-1 is taken if the positive direction of the X axis is not the positive direction; v represents the motion direction of the curved surface self-adaptive sliding hinge, 1 is taken out when the motion direction is consistent with the positive direction of the X axis, and-1 is taken out when the motion direction is not consistent with the positive direction of the X axis; sgn (x · v) represents the sign of the product of the displacement and the motion direction of the curved surface adaptive sliding hinge, and the product is a positive number, and is 1, otherwise, is-1.
Mechanical model by sliding friction force, F σ And F τ There is a relationship shown in formula (3), wherein μ represents a sliding friction coefficient of the curved convex friction plate 1:
F τ =μ·F σ (3)
the support type is derived by combining the formulas (1) to (3)Axial force F of negative-stiffness friction damper H Positive pressure F of vertically pre-pressed rubber spring V Is expressed by the formula (4):
Figure BDA0001376372320000061
according to the working principle of the supporting type negative stiffness friction damper, the positive pressure F of the vertically pre-pressed laminated rubber spring 4 V The included angle alpha between the normal direction and the vertical direction of one point on the convex friction curved plate 1 is a function of the relative horizontal displacement x and is respectively represented by F V (x) And alpha (x). According to FIG. 4, F can be deduced V (x) And α (x) are respectively expressed by the following formulas (5) and (6):
Figure BDA0001376372320000062
Figure BDA0001376372320000063
in the formula, P 0 The positive pressure of the vertically pre-pressed laminated rubber spring 4 is represented when the relative displacement between the curved surface self-adaptive sliding hinge and the outward convex friction curved plate is zero; k represents the vertical stiffness of the pre-pressed laminated rubber spring 4; r represents the radius of the circle on which the convex circular curved surface of the convex frictional curved plate 1 is located.
By combining formula (4), formula (5) and formula (6), the axial force F is obtained by sorting H Functional relationship F with relative axial displacement x H (x) As shown in formula (7):
Figure BDA0001376372320000064
FIG. 5 depicts P 0 The restoring force curve when the value is =1000kn, k =50kn/mm, R =500mm, and μ =0.40 shows that the restoring force curve of the supported negative-stiffness friction damper of the present invention is formed by superposing the negative stiffness and the damping. Therefore, under the action of earthquake, the invention can reduceThe equivalent rigidity of the structure is low, and the acceleration response of the structure is reduced; meanwhile, the earthquake energy is dissipated through sliding friction, the vibration response of the structure is reduced, and the earthquake-resistant performance of the structure is improved.

Claims (4)

1. A supporting type negative stiffness friction damper is characterized by comprising a transverse deformation restraining box body, a curved surface friction member positioned in the transverse deformation restraining box body and axial connecting supports positioned on the left side and the right side of the transverse deformation restraining box body; the transverse deformation restraint box body comprises an upper end plate, a lower end plate, a left cover plate and a right cover plate; the curved surface friction member comprises a laminated rubber spring, a sliding box, a curved surface self-adaptive sliding hinge and an outward convex friction curved surface plate, wherein the sliding box, the curved surface self-adaptive sliding hinge and the outward convex friction curved surface plate are respectively positioned at two ends of the laminated rubber spring from near to far; the damper also comprises an outer box, the sliding box and the laminated rubber spring are both positioned in the outer box, the outer wall of the sliding box is attached to the inner walls of the two ends of the outer box, and the sliding box and the outer box can slide relatively along the axial direction of the laminated rubber spring; the end plates of the transverse deformation restraint box body are fixedly connected with the convex friction curved plate through friction type high-strength bolts, the upper end plate and the lower end plate of the transverse deformation restraint box body are fixed through a pair of lead screws, and pre-pressure is applied to the laminated rubber spring through the pair of lead screws; after the pre-pressure is applied in place, connecting the end plates and the cover plate of the transverse deformation restraint box body by using friction type high-strength bolts so as to fix the relative positions of the two end plates; one end of an axial connecting support positioned on the right side of the transverse deformation restraining box body is fixed with a right cover plate of the transverse deformation restraining box body, and the other end of the axial connecting support is fixed with a node of the building structure; one end of an axial connecting support positioned on the left side of the transverse deformation restraint box body is fixed with the left side wall of the curved surface friction member middle outer box, and the other end of the axial connecting support is fixed with a node of the building structure.
2. The negative stiffness friction damper according to claim 1, wherein the convex friction curved plate has a convex circular curved surface, and the surface of the circular curved surface is rough.
3. The negative-stiffness friction damper as claimed in claim 2, wherein the sliding box is matched with a curved self-adaptive sliding hinge, a curved groove is arranged on the surface of the sliding box, and the curved self-adaptive sliding hinge is formed by cutting two curved surfaces; the concave curved surface of the curved surface self-adaptive sliding hinge is attached to the convex circular curved surface of the convex friction curved plate, and relative sliding occurs; the convex curved surface of the curved surface self-adaptive sliding hinge is attached to the curved surface groove of the sliding box and rotates relatively; the sliding box keeps translation during the motion process of the negative-rigidity friction damper.
4. The negative stiffness friction damper of claim 3, wherein the surface of the convex curved surface of the curved adaptive sliding hinge is coated with a friction reducing material.
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