Variable-stiffness friction slippage anti-swing three-dimensional shock isolation device and shock absorption method thereof

Abstract

The invention discloses a variable-stiffness friction slippage anti-swing three-dimensional shock isolation device and a shock absorption method thereof, and belongs to the technical field of building shock isolation and shock absorption. According to the technical scheme, the vibration damper comprises a top plate, a horizontal rubber support, a center mass block, a spring support, a limiting plate, a friction plate, a vertical rubber support and a bottom plate. The multi-stage self-adaptive rigidity mechanism has the beneficial effects that the friction material is arranged between the limiting plate and the friction plate, and the friction sliding position and the motion state can be controllably adjusted by adjusting the pre-tightening force of the bolt, the friction coefficient and the rigidity of the vertical rubber support, so that the multi-stage self-adaptive rigidity mechanism is formed; and the shock insulation and self-resetting performance of the structure under the action of horizontal and vertical earthquakes is obviously improved. The device has good three-dimensional shock insulation and swing resistance, and is simple in structure and convenient to install and maintain. The dynamic response of the upper structure applying the device under the earthquake action can be effectively inhibited, so that the structural safety and the use comfort are guaranteed.

Description

Technical Field

[0001] This invention relates to the field of building seismic isolation and vibration reduction technology, and in particular to a variable stiffness friction sliding anti-sway three-dimensional seismic isolation device and its vibration reduction method. Background Technology

[0002] Earthquakes, as highly destructive natural disasters, pose a serious threat to the structural safety of buildings due to their multidimensional seismic characteristics. Traditional seismic isolation technologies, such as laminated rubber bearings, can effectively reduce the horizontal seismic response of structures, but their vertical stiffness is usually much greater than their horizontal stiffness (approximately 1000 times), resulting in weak vertical isolation effects and an inability to effectively attenuate vertical ground motions. Studies have shown that vertical ground motions not only affect the functional use of structures, but their effect may even exceed that of the horizontal component in near-fault earthquakes. Therefore, developing three-dimensional seismic isolation technologies that simultaneously control horizontal and vertical motions has become an important direction for improving the seismic resilience of buildings.

[0003] Current research on three-dimensional seismic isolation largely focuses on theoretical analysis and experimental exploration, while mature, reliable, and economical three-dimensional seismic isolation systems for practical engineering applications remain relatively scarce. Existing three-dimensional seismic isolation schemes, such as three-dimensional spring-damped systems and roller isolation devices, often suffer from problems such as complex construction, insufficient recovery capacity, weak anti-sway performance, or difficulty in coordinating vertical stiffness. This is particularly problematic for high-rise or tall structures, which are prone to swaying and torsion under seismic loads, further exacerbating the risk of structural failure. Therefore, there is an urgent need for a three-dimensional seismic isolation device that can balance horizontal and vertical isolation, possess multi-stage energy dissipation, have good recovery capacity, and effectively suppress structural swaying.

[0004] How to solve the above problems is the research topic of this plan. Summary of the Invention

[0005] To address the aforementioned issues, this invention proposes a rationally constructed and controllable variable stiffness friction sliding anti-sway three-dimensional seismic isolation device and its vibration reduction method. The aim is to overcome the shortcomings of existing seismic isolation technologies and achieve adaptive response and efficient energy dissipation to earthquake excitations of different intensities, such as minor, moderate, and major earthquakes, through the coordinated work of horizontal isolation layers, vertical isolation layers, and the anti-sway device.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: a three-dimensional vibration isolation device with variable stiffness friction sliding anti-sway, comprising an upper horizontal vibration isolation system, a middle vertical vibration isolation and reset system, and a lower integrated vertical energy dissipation anti-sway system;

[0007] The horizontal seismic isolation system includes a top plate, horizontal rubber bearings, and a central mass block; the upper end of the horizontal rubber bearing is connected to the top plate by bolts, and the lower end is connected to the central mass block, forming the first horizontal seismic isolation layer, which mainly filters horizontal seismic energy.

[0008] The vertical isolation and reset system includes multiple spring supports and a bottom plate;

[0009] The upper end of the spring support is connected to the central mass block, and the lower end is connected to the bottom plate, providing the initial vertical stiffness, elastic restoring force, and the main vertical isolation function for the structure;

[0010] The anti-sway system includes anti-sway units arranged on each side of the left and right of the central mass block;

[0011] The anti-sway unit includes a limit plate, a friction plate, a vertical rubber bearing, the side of the bottom plate, and friction material; on one side of the limit plate in the anti-sway unit is connected to the side of the central mass block, the lower end of the side of the bottom plate is connected to the bottom plate, the friction plate is connected to the side of the bottom plate through a vertical rubber bearing, and friction material is arranged between the limit plate and the friction plate. By adjusting the pre-tightening force of the connecting bolts, the friction force between the sliding surfaces can be changed; by selecting friction materials with different friction coefficients and designing vertical rubber bearings with different stiffnesses, the comprehensive control of the vertical friction slip threshold, the stiffness after slip, and the energy dissipation capacity of the device can be achieved, forming a multi-stage adaptive working mechanism of "no slip in small earthquakes, slip in medium earthquakes, large slip and energy dissipation in large earthquakes".

[0012] The vertical rubber bearing is connected to the side of the bottom plate through bolts. By tightening or loosening the bolts, the pre-tightening force acting on the friction material can be adjusted, thereby changing the slip friction threshold. The vertical rubber bearing not only provides the lateral stiffness required for anti-sway, but its vertical deformation is also coupled with friction slip and participates in energy dissipation.

[0013] By reasonably selecting friction materials, rubber hardness, spring parameters, and pre-tightening force, the mechanical properties of the device can be flexibly "customized" to meet different seismic requirements from ordinary buildings to important projects.

[0014] Multiple horizontal rubber bearings can be provided, arranged evenly or at intervals along the circumferential direction, jointly constituting a horizontal isolation layer.

[0015] Multiple spring supports are provided, and the multiple spring supports are evenly distributed at intervals in the vertical isolation and reset system, mainly providing the initial vertical stiffness and elastic reset force.

[0016] Multiple vertical rubber bearings are provided, arranged around the sides of the central mass block, integrated with the anti-sway system, jointly providing anti-sway stiffness and additional vertical energy dissipation.

[0017] The limit plate is set in a U-shaped shape, and a fixing groove is opened on the inner side of the limit plate, and the fixing groove is matched with the friction material.

[0018] Working process:

[0019] When there is a minor earthquake or frequent wind load: the vertical force is less than the static friction force, the device works as a whole, the stiffness is relatively large K1, and it restricts the minor vibration of the structure.

[0020] During a moderate earthquake: the vertical force exceeds the static friction force, the friction interface begins to slip, the vertical stiffness of the device drops to K2, and it enters the seismic isolation and energy dissipation state. At the same time, the vertical rubber bearing deforms and dissipates energy.

[0021] During a major earthquake: the slip displacement increases, and the springs and vertical rubber supports continue to provide restoring force and energy dissipation, effectively extending the structural period, significantly reducing the transmission of seismic forces, and suppressing the overall swaying of the structure.

[0022] Post-earthquake: Under the elastic restoring force of the spring supports and vertical rubber supports, the central mass block drives the upper structure to automatically reset.

[0023] The vibration reduction method based on the aforementioned variable stiffness friction sliding anti-sway three-dimensional vibration isolation device includes the following steps:

[0024] S1, Design during minor earthquakes, i.e., no-slip condition

[0025] At this point, the entire device is in an elastic working state, and no slippage occurs at the friction interface; the total vertical stiffness K1 is provided by the parallel stiffness of all spring supports and vertical rubber supports:

[0026] (1)

[0027] In the formula This represents the number of vertical rubber supports and spring supports (assuming they are equal). and The vertical stiffness of a single vertical rubber bearing and a single spring bearing are respectively.

[0028] (2)

[0029] In the formula , , These are the shear modulus, cross-sectional area, and thickness of the rubber body, respectively.

[0030] (3)

[0031] In the formula , , , These are the shear modulus of the spring, the diameter of the spring wire, the mean diameter of the spring, and the number of effective coils, respectively.

[0032] At this point, the maximum vertical yield force is also known as the slip initiation force.

[0033] (4)

[0034] In the formula This represents the maximum vertical yield force of the device. For first-order stiffness, The vertical displacement of the device at the instant when the friction plate and the limiting plate slide together is the device's yield displacement. The sliding of the friction plate and the limiting plate is considered as the device yielding. It is derived from geometric relationships and material properties and is related to the initial gap between the vertical rubber support and the limiting plate, as well as the compressive deformation caused by the bolt preload.

[0035] (5)

[0036] In the formula 静 Let be the static friction coefficient between the friction plate and the limiting plate. In order to apply preload, The distance between the vertical rubber support and the limiting plate baffle;

[0037] (6)

[0038] In the formula For pressure, The area under stress;

[0039] Solve equations (1)-(6) simultaneously to obtain the maximum vertical yield force Q of the support. d K1:

[0040] (7)

[0041] (8)

[0042] S2, moderate and major earthquake stages, i.e., slip state design

[0043] When the vertical force exceeds Q d Afterwards, the friction interface begins to slip, and the device enters the second working stage; at this time, the vertical stiffness K2 is mainly provided by the spring support:

[0044] (9)

[0045] Vertical force is

[0046] (10)

[0047] in, For the restoring force of the rubber bearing, The dynamic friction force between the friction plate and the limiting plate;

[0048]

[0049] In the formula This represents the vertical displacement of the device;

[0050] (11)

[0051] In the formula 动 The coefficient of dynamic friction between the friction plate and the limiting plate of the device;

[0052] By combining equations (3), (9)-(11), the vertical forces Q and K2 of the support are obtained, and then it is verified whether the bearing capacity and stiffness of the device under large displacement meet the safety requirements and the seismic isolation target:

[0053] (12)

[0054] (13)

[0055] In summary, the vertical second-order stiffness and maximum vertical yield force of the device are:

[0056] (14)

[0057] (15)

[0058] S3, Parameter Optimization and Iteration

[0059] During the design process, it is necessary to consider the static friction coefficient, dynamic friction coefficient, and preload P. h Vertical rubber bearing stiffness k r and spring stiffness k s Comprehensive adjustments and iterative calculations are performed until the stiffness K1, K2 and yield force Q of the device at each level are reached. d It fully meets the seismic design requirements of the installation structure; the final design ensures that the structure remains basically elastic under common earthquakes, enters the friction slip energy dissipation stage under the design earthquake, has sufficient deformation and energy dissipation capacity under rare earthquakes, and guarantees post-earthquake recovery.

[0060] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0061] (1) The present invention adopts three-dimensional synergistic vibration isolation and anti-sway integration: the horizontal rubber bearing is responsible for attenuating horizontal ground motion; the spring bearing and the vertical rubber bearing work together to provide adjustable vertical stiffness and vibration isolation capability; the anti-sway device effectively suppresses the swaying and torsional response of the structure through frictional sliding and deformation coupling with the vertical rubber bearing, thereby realizing the comprehensive control of three-dimensional ground motion.

[0062] (2) Multi-level variable stiffness and adaptive energy dissipation in the present invention: The device uses the friction slip mechanism to achieve a sudden change in stiffness. By adjusting the preload, friction coefficient and support stiffness, the yield force and the stiffness after slip can be precisely controlled to form a multi-level seismic isolation line to adapt to earthquakes of different intensities and efficiently dissipate energy through friction and rubber deformation during earthquakes.

[0063] (3) The present invention has good self-resetting ability: after an earthquake, the elastic restoring force of the spring support and the vertical rubber support work together to drive the central mass block and the upper structure back to the initial position, reducing residual displacement.

[0064] (4) The parameters of the present invention are highly designable and widely applicable: the key performance parameters of the device (such as initial stiffness, yield force, second stiffness, etc.) can be designed in a targeted manner through calculation, which can meet the requirements of different building structure forms and seismic fortification.

[0065] (5) The invention has a simple structure and high reliability: each component is modularly designed and the connection is clear, which facilitates industrial production, on-site installation and subsequent inspection and maintenance. Attached Figure Description

[0066] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0067] Figure 1 This is an overall schematic diagram of an embodiment of the present invention.

[0068] Figure 2 for Figure 1 Front view.

[0069] Figure 3 This is a schematic diagram of the anti-sway unit in an embodiment of the present invention.

[0070] Figure 4 This is an exploded view of the structural components of the anti-sway unit according to an embodiment of the present invention.

[0071] Figure 5 This is a schematic diagram of the structure of the horizontal rubber support according to an embodiment of the present invention.

[0072] Figure 6 This is a schematic diagram of the spring support of the present invention.

[0073] The attached diagram is labeled as follows: 1. Top plate; 2. Bottom plate; 3. Horizontal rubber support; 4. Spring support; 5. Anti-sway unit; 6. Central mass block; 7. Limiting plate; 8. Friction plate; 9. Vertical rubber support; 10. Side of bottom plate; 11. Bolt; 12. Friction material. Detailed Implementation

[0074] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0075] Example 1: See Figures 1 to 6 The technical solution provided in this embodiment is: a three-dimensional vibration isolation device with variable stiffness friction sliding anti-sway, including an upper horizontal vibration isolation system, a middle vertical vibration isolation and reset system and a lower integrated vertical energy dissipation anti-sway system;

[0076] The horizontal seismic isolation system includes a top plate 1, a horizontal rubber bearing 3, and a central mass block 6. The upper end of the horizontal rubber bearing 3 is connected to the top plate 1 by bolts, and the lower end is connected to the central mass block 6, forming the first horizontal seismic isolation layer, which mainly filters horizontal seismic energy.

[0077] The vertical seismic isolation and resetting system includes multiple spring supports 4 and a base plate 2;

[0078] The upper end of the spring support 4 is connected to the central mass block 6, and the lower end is connected to the base plate 2, providing the structure with initial vertical stiffness, elastic restoring force, and main vertical seismic isolation function.

[0079] The anti-sway system includes one anti-sway unit 5 on each side of the central mass block 6;

[0080] The anti-sway unit 5 includes a limiting plate 7, a friction plate 8, a vertical rubber support 9, a base plate side 10, and friction material 12. In the anti-sway unit 5, one side of the limiting plate 7 is connected to the side of the central mass block 6, the lower end of the base plate side 10 is connected to the base plate 2, the friction plate 8 is connected to the base plate side 10 via the vertical rubber support 9, and friction material 12 is provided between the limiting plate 7 and the friction plate 8. By adjusting the preload of the connecting bolts, the friction force between the sliding surfaces can be changed. By selecting friction materials with different friction coefficients and designing vertical rubber supports with different stiffnesses, comprehensive control of the vertical friction slip threshold, post-slip stiffness, and energy dissipation capacity of the device can be achieved, forming a multi-stage adaptive working mechanism of "no slippage during small earthquakes, slippage during medium earthquakes, and large slippage and energy dissipation during large earthquakes."

[0081] The vertical rubber bearing 9 is connected to the side of the base plate 10 by bolts 11. By tightening or loosening the bolts 11, the preload acting on the friction material 12 can be adjusted, thereby changing the sliding friction threshold. The vertical rubber bearing 9 not only provides the lateral stiffness required for anti-swaying, but its vertical deformation is also coupled with frictional slippage, participating in energy dissipation.

[0082] By reasonably selecting the friction material, rubber hardness, spring parameters and pre-tightening force, the mechanical properties of the device can be flexibly "customized" to meet the different seismic requirements from ordinary buildings to important projects.

[0083] Multiple horizontal rubber bearings 3 can be set, and they are arranged evenly or at intervals along the circumferential direction to jointly form a horizontal isolation layer.

[0084] Multiple spring bearings 4 are set, and the multiple spring bearings 4 are evenly distributed at intervals in the vertical isolation and reset system, mainly providing initial vertical stiffness and elastic reset force.

[0085] Multiple vertical rubber bearings 9 are set, arranged around the side of the central mass block 6, and integrated with the anti-sway system to jointly provide anti-sway stiffness and additional vertical energy dissipation.

[0086] The limiting plate 7 is set in a U-shaped form, and a fixing groove is opened on the inner side of the limiting plate 7, and the fixing groove is matched with the friction material 12.

[0087] Working process:

[0088] During small earthquakes or frequent wind loads: The vertical force is less than the static friction force, and the device works as a whole with a relatively large stiffness K1 to limit the tiny vibration of the structure.

[0089] During medium earthquakes: The vertical force exceeds the static friction force, and the friction interface starts to slip. The vertical stiffness of the device drops to K2, entering the isolation energy dissipation state. At the same time, the vertical rubber bearing deforms and dissipates energy.

[0090] During large earthquakes: The slip displacement increases, and the springs and vertical rubber bearings continue to provide restoring force and energy dissipation, effectively extending the structural period, significantly reducing the transmission of seismic forces, and suppressing the overall sway of the structure.

[0091] After the earthquake: Under the elastic restoring force of the spring bearing and the vertical rubber bearing, the central mass block drives the upper structure to automatically reset.

[0092] The seismic reduction method based on the variable stiffness friction-sliding anti-sway three-dimensional isolation device includes the following steps:

[0093] S1. Design in the small earthquake stage, that is, the non-slip state

[0094] At this time, the device is in an elastic working state as a whole, and the friction interface does not slip; the total vertical stiffness K1 is provided in parallel by the stiffness of all spring bearings and vertical rubber bearings:

[0095] (1)

[0096] In the formula is the number of vertical rubber bearings and spring bearings (assuming they are equal); and The vertical stiffness of a single vertical rubber bearing and a single spring bearing are respectively.

[0097] (2)

[0098] In the formula , , These are the shear modulus, cross-sectional area, and thickness of the rubber body, respectively.

[0099] (3)

[0100] In the formula , , , These are the shear modulus of the spring, the diameter of the spring wire, the mean diameter of the spring, and the number of effective coils, respectively.

[0101] At this point, the maximum vertical yield force is also known as the slip initiation force.

[0102] (4)

[0103] In the formula The yield displacement of the device is derived from geometric relationships and material properties, and is mainly related to the initial gap between the vertical rubber support and the limiting plate, as well as the compressive deformation caused by the bolt preload.

[0104] (5)

[0105] In the formula 静 Let be the static friction coefficient between the friction plate and the limiting plate. In order to apply preload, The distance between the vertical rubber support and the limiting plate baffle;

[0106] (6)

[0107] In the formula For pressure, The area under stress;

[0108] Solve equations (1)-(6) simultaneously to obtain the maximum vertical yield force Q of the support. d K1:

[0109] (7)

[0110] (8)

[0111] S2, moderate and major earthquake stages, i.e., slip state design

[0112] When the vertical force exceeds Q dAfterwards, the friction interface begins to slip, and the device enters the second working stage; at this time, the vertical stiffness K2 is mainly provided by the spring support:

[0113] (9)

[0114] Vertical force is

[0115] (10)

[0116] In the formula, Fp is the restoring force of the rubber bearing. The dynamic friction force between the friction plate and the limiting plate;

[0117]

[0118] In the formula This represents the vertical displacement of the device;

[0119] (11)

[0120] In the formula 动 The coefficient of dynamic friction between the friction plate and the limiting plate of the device;

[0121] By combining equations (3), (9)-(11), the vertical forces Q and K2 of the support are obtained, and then it is verified whether the bearing capacity and stiffness of the device under large displacement meet the safety requirements and the seismic isolation target:

[0122] (12)

[0123] (13)

[0124] In summary, the vertical second-order stiffness and maximum vertical yield force of the device are:

[0125] (14)

[0126] (15)

[0127] S3, Parameter Optimization and Iteration

[0128] During the design process, it is necessary to consider the static friction coefficient, dynamic friction coefficient, and preload P. h Vertical rubber bearing stiffness k r and spring stiffness k s Comprehensive adjustments and iterative calculations are performed until the stiffness K1, K2 and yield force Q of the device at each level are reached. dIt fully meets the seismic design requirements of the installation structure; the final design ensures that the structure remains basically elastic under common earthquakes, enters the friction slip energy dissipation stage under the design earthquake, has sufficient deformation and energy dissipation capacity under rare earthquakes, and guarantees post-earthquake recovery.

[0129] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A variable stiffness friction sliding anti-sway three-dimensional vibration isolation device, characterized in that: It includes a horizontal seismic isolation system at the upper part, a vertical seismic isolation and reset system in the middle, and an anti-sway system with integrated vertical energy dissipation at the lower part; The horizontal seismic isolation system includes a top plate (1), horizontal rubber bearings (3), and a central mass block (6); the upper end of the horizontal rubber bearing (3) is connected to the top plate (1) by bolts, and the lower end is connected to the central mass block (6), forming the first horizontal seismic isolation layer, mainly filtering horizontal seismic ground motion energy; The vertical seismic isolation and reset system includes a plurality of spring bearings (4) and a bottom plate (2); The upper end of the spring bearing (4) is connected to the central mass block (6), and the lower end is connected to the bottom plate (2), providing the initial vertical stiffness, elastic restoring force, and the main vertical seismic isolation function for the structure; The anti-sway system includes an anti-sway unit (5) arranged on each side of the central mass block (6); The anti-sway unit (5) includes a limit plate (7), a friction plate (8), a vertical rubber bearing (9), a side of the bottom plate (10), and a friction material (12); in the anti-sway unit (5), one side of the limit plate (7) is connected to the side of the central mass block (6), the lower end of the side of the bottom plate (10) is connected to the bottom plate (2), the friction plate (8) is connected to the side of the bottom plate (10) through the vertical rubber bearing (9), and a friction material (12) is arranged between the limit plate (7) and the friction plate (8).

2. The variable stiffness friction sliding anti-sway three-dimensional vibration isolation device according to claim 1, characterized in that: The vertical rubber bearing (9) is connected to the side of the bottom plate (10) by bolts (11).

3. The variable stiffness friction sliding anti-sway three-dimensional vibration isolation device according to claim 2, characterized in that: Multiple horizontal rubber bearings (3) can be provided, which are evenly or spaced along the circumference and jointly form the horizontal seismic isolation layer.

4. The variable stiffness friction sliding anti-sway three-dimensional vibration isolation device according to claim 3, characterized in that: Multiple spring bearings (4) are provided, and the multiple spring bearings (4) are evenly distributed at intervals in the vertical seismic isolation and reset system, providing the initial vertical stiffness and elastic restoring force.

5. The variable stiffness friction sliding anti-sway three-dimensional vibration isolation device according to claim 4, characterized in that: Multiple vertical rubber bearings (9) are provided, arranged around the side of the central mass block (6), integrated with the anti-sway system, and jointly providing the anti-sway stiffness and additional vertical energy dissipation.

6. The variable stiffness friction sliding anti-sway three-dimensional vibration isolation device according to claim 5, characterized in that: The limit plate (7) is set in a U-shaped, and a fixing groove is opened on the inner side of the limit plate (7), and the fixing groove is matched with the friction material (12).

7. A vibration reduction method based on the variable stiffness friction sliding anti-sway three-dimensional vibration isolation device according to any one of claims 1-6, characterized in that, It includes the following steps: S1. Design in the small earthquake stage, i.e., the non-slip state At this time, the whole device is in the elastic working state, and no slip occurs at the friction interface; the total vertical stiffness K1 is provided by the parallel connection of the stiffness of all spring bearings and vertical rubber bearings: (1)； In the formula This represents the number of vertical rubber supports and spring supports; and The vertical stiffness of a single vertical rubber bearing and a single spring bearing are respectively. (2)； In the formula , , These are the shear modulus, cross-sectional area, and thickness of the rubber body, respectively. (3)； In the formula , , , These are the shear modulus of the spring, the diameter of the spring wire, the mean diameter of the spring, and the number of effective coils, respectively. At this time, the maximum vertical yield force is the slip starting force: (4)； In the formula , , , , These are the maximum vertical yield force, yield displacement, first-order stiffness, static friction coefficient, and preload of the device, respectively. (5)； In the formula 静 Let be the static friction coefficient between the friction plate and the limiting plate. In order to apply preload, The distance between the vertical rubber support and the limiting plate baffle; (6)； In the formula For pressure, The area under stress; Solve equations (1)-(6) simultaneously to obtain the maximum vertical yield force Q of the support. d K1: (7)； (8)； S2. Design in the medium and large earthquake stages, i.e., the slip state When the vertical force exceeds Q d Afterwards, the friction interface begins to slip, and the device enters the second working stage; at this time, the vertical stiffness K2 is mainly provided by the spring support: (9)； The vertical force is (10)； In the formula F p f is the restoring force of the rubber bearing. 动 The dynamic friction force between the friction plate and the limiting plate; In the formula This represents the vertical displacement of the device; (11)； In the formula 动 The coefficient of dynamic friction between the friction plate and the limiting plate of the device; By联立 equations (3), (9)-(11), the vertical force Q and K2 of the bearing are obtained, and it is verified whether the bearing capacity and stiffness of the device under large displacements meet the safety requirements and seismic isolation objectives: (12)； (13)； The vertical second-order stiffness and the maximum vertical yield force of the device are: (14)； (15)； S3. Parameter optimization and iteration During the design process, the static friction coefficient, dynamic friction coefficient, and preload P were considered. h Vertical rubber bearing stiffness k r and spring stiffness k s Comprehensive adjustments and iterative calculations are performed until the stiffness K1, K2 and yield force Q of the device at each level are reached. d It meets the seismic design requirements of the installation structure.

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