2.1

Damping device detailed structure

The anti-buckling graded yield type metal damper consists of an hourglass-shaped shear energy dissipation plate and a K-shaped bending energy dissipation plate. The energy-dissipating portion of the damper is connected to the end plate by full penetration butt welding, while the anti-buckling plate is connected to the end plate by single-sided fillet welding. The anti-buckling plate is fixed on both sides of the shear energy dissipation plate, and the anti-buckling plates are connected by high-strength bolts. 0 shows the construction of the damper, where the outer side is the bending energy dissipation plate and the component in contact with it is the anti-buckling plate. There is only a contact relationship between the two. Anti-yield is arranged on both sides of the shear plates, and the anti-yield plates are connected by high-strength bolts. The construction diagrams of the shear energy dissipation and bending energy dissipation are shown in 0 and 0, respectively.

Figure1.

The construction diagram of a staged yielding damper

Figure2.

The construction diagram of a shear energy dissipation component

Figure3.

The construction diagram of the bending energy dissipation component

2.2

Design philosophy

This damper is composed of a shear energy dissipation plate with high initial stiffness and low displacement capacity, and a bending energy dissipation plate with low initial stiffness and high displacement capacity. Both energy dissipation plates are made of low yield point steel. Ordinary steel plates are added on both sides of the shear energy dissipation plate to restrain its premature buckling deformation. By utilizing the different mechanical properties of these two energy dissipation plates and designing them reasonably, the damper has the characteristic of staged yielding. When the earthquake intensity is low, only the shear energy dissipation plate works, and the bending energy dissipation plate remains in an elastic state without consuming energy. When the earthquake intensity is high, both the shear and bending energy dissipation plates work together, increasing the energy dissipation value and efficiency. The two-stage energy dissipation of this damper can improve the situation where traditional dampers, which can only respond to a relatively single type of earthquake, cannot dissipate energy when the stiffness is high and the earthquake intensity is low, or when the stiffness is low and the earthquake intensity is too high. This design ensures that the average power of energy dissipation is greater than that of the earthquake transmission energy.

0 shows the mechanical model of the damper, based on its construction form. Here, represents the stiffness of the shear energy dissipation plate under different displacement loads, where α₁ is the stiffness degradation coefficient of the shear energy dissipation plate, and h_e1 is the viscous damping coefficient of the shear energy dissipation plate. Similarly, α₂K₂ represents the stiffness of the bending energy dissipation plate under different displacement loads, where α₂ is the stiffness degradation coefficient of the bending energy dissipation plate, and h_e2 is the viscous damping coefficient of the bending energy dissipation plate.

Based on 0, the damper device works as follows:

Normal operation stage: the damper device remains inactive, and all dampers are in an elastic state with no viscous damping coefficient. At this stage, the overall stiffness is K₁ + K₂.

The first yield: During the first yield stage, the shear-type metal dampers provide initial stiffness to the structure before yielding and additional damping ratios after yielding. The designed yield displacement is δ₁, and the bending energy absorption plate provides the initial stiffness K₂ to the structure. At this stage, the overall stiffness is α₁K₁ + K₂, and the viscous damper coefficient is h_e1.

The second yield: Shear-type metal dampers provide additional damping ratios for structures. The designed yield displacement is δ₂. The bending energy absorption plate provides the initial stiffness for the structure after yielding, while the overall stiffness provides additional damping ratios for the structure after yielding. The overall stiffness is α₁K₁ + α₂K₂, and the viscous damper coefficient is h_e1 + h_e2.

By combining the working principle of the damper shown in Figure 4, we can derive the mathematical relationship between damper stiffness and displacement as follows:

Figure4.

Mechanical model of the damper device construction form

where K₁ is the initial stiffness of the shear energy dissipation plate, K₂ is the initial stiffness of the yielding energy dissipation plate, α₁ is the stiffness degradation coefficient when the shear energy dissipation plate yields, α₂ is the stiffness degradation coefficient when the bending energy dissipation plate yields, δ is the damper displacement, δ₁ is the displacement value when the damper yields at the first stage, and δ₂ is the displacement value when the damper yields at the second stage.

2.2.1

Theoretical calculation of mechanical properties of bending energy absorption plate

Assuming the thickness of the steel plate of the bending energy absorption plate is t, the height is h, the minimum width is a, and the maximum width is b, the mechanical performance calculation formula is [19]:

Yield Shear Force:

Ultimate Shear Force:

Initial Stiffness:

Where E is the elastic modulus of the yield-type damper, t is the thickness of the yield-type damper, h is the height of the yield-type damper, а is the minimum width of the yield-type damper, b is the maximum width of the yield-type damper, and f_y is the yield stress.

According to the formula, the height and thickness of the yield-type energy absorption plate have the most significant impact on the initial stiffness K₁ of the yield-type damper. Specifically, the thickness has a cubic effect on K₁, while the height has a negative cubic effect. This means that increasing the thickness of the energy absorption plate and decreasing the height will result in a smaller initial stiffness K₁.

2.2.2

Theoretical calculation of mechanical properties of shear energy dissipation plate

Assuming the thickness of the steel plate of the shear energy dissipation plate is t, the height is h, the minimum width is a, and the maximum width is b. Since the shear energy dissipation plate is originally a rectangular energy dissipation plate, the change to a hourglass shape is to avoid stress concentration at the edges of the rectangle. Therefore, the formula for calculating the mechanical properties of the shear energy dissipation plate can be the same as that of the rectangular shear energy dissipation plate [20].

Yield shear force:

Ultimate shear force:

Initial stiffness:

where G is the shear modulus of the shear energy dissipation plate, t is the thickness of the shear energy dissipation plate, h is the height of the shear energy dissipation plate, a is the minimum width of the shear energy dissipation plate, b is the maximum width of the shear energy dissipation plate, and f_y is the yield stress. From the formulas, it can be deduced that the shear modulus G, height h, and thickness t all have an impact on the initial stiffness K₂ of the shear energy dissipation plate.

3.1

Material properties

The yield bearing capacity and yield displacement are crucial indicators of the damper’s performance. To ensure optimal performance, high-quality materials should be selected for the damper. The mechanical properties of the damper material are presented in 0 below:

Table1.

Mechanical properties of experimental materials

3.2

Experimental results

The experimental specimen and loading device of the damper are connected using bolts, and a quasi-static loading system is employed. The loading level is controlled based on the shear displacement of the damper, and the relationship between the loading displacement and time is illustrated in 0. The experimental specimen is depicted in 0. At a displacement of 0.20mm, a portion of the damper has already yielded and started to function. At a displacement of 2.67mm, the bending energy plate and the shearing energy plate jointly yield and consume energy, causing the damper to enter a plastic state. The shearing energy plate undergoes uniform shearing deformation in the plane, while the bending energy plate exhibits an S-shape outside the plane, with the inflection point located in the middle of the damper height. The experimental results are presented in 0, which shows a spindle-shaped hysteresis curve with a full shape and excellent energy consumption effect. The skeleton curve reveals a staged yielding phenomenon, which can effectively absorb and dissipate energy under earthquake action, thereby enhancing the structure’s seismic performance.

The hysteresis curve of the damper reveals obvious staged energy consumption characteristics at different displacement amplitudes. Specifically, it exhibits a linear zone with high stiffness and low energy consumption in a small displacement range, and a nonlinear zone with low stiffness and high energy consumption in a large displacement range. Moreover, the area of the hysteresis curve indicates that the damper has a strong energy consumption ability, with the mechanical work consumed in a single cycle increasing with the displacement amplitude. The skeleton curve displays an obvious segmentation phenomenon, which confirms the damper’s good staged yielding characteristics. As a result, it can be regarded as an efficient, reliable, and adjustable passive control device.

Figure5.

Experiment with loading displacement plots

Figure6.

Experiment sample diagram

Figure7.

Experiment with hysteresis curves

4.1

Finite element model establishment

The various components of the damper are simulated using solid elements, taking into account the isotropy of the material. Constraints are applied to replicate the actual situation, with the fixed end of the damper being fixed and a displacement constraint being applied to the upper plate. LY225 steel is used as an ideal elastic-plastic material, and a bilinear kinematic hardening model is employed to simulate the constitutive relationship. The elastic modulus is 205GPa and Poisson’s ratio is 0.3, respectively, while the other properties of the steel are input based on 0

4.2

Model validity validation

The reliability of the numerical simulation is verified by comparing and analyzing the results with the experimental data. The displacement and force curves of the damper are selected for different states, and it can be observed that the numerical simulation results were in good agreement with the experimental results, indicating that the dynamic characteristics and working performance of the damper are accurately reflected by the simulation. However, there are some differences between the simulated hysteresis loop and the experimental results in the softening transition section of each cycle, which may be due to the simplified bilinear kinematic hardening model used for the material constitutive relationship being different from the real material constitutive relationship. During the simulation process, it was noted that the shear energy consumption plate entered the plastic state before the bending energy consumption plate in the initial stage of loading, with the stress level of the latter being relatively low. With the displacement increasing, the shear energy consumption plate continued to consume energy, and the bending energy consumption plate gradually became plastic, with the two types of steel sheets working together. At a loading displacement of 30 mm, the soft steel sheet was completely plasticized, while the upper and lower connecting steel plates remained elastic. The deformation stress cloud map of the damper when the displacement loading is 40 mm is shown in 0.

Figure8.

The stress contour of the damper when the displacement is 40mm

The hysteresis curve of the numerical simulation and experimental results is shown in 0, indicating good consistency between the two. The experimental skeleton curve was also extracted, and both the skeleton curve (0) and the hysteresis curve demonstrate the good fit between the experimental data and the numerical simulation. This proves that the results of the numerical simulation are similar to the experimental results, and can serve as a basis for further research on the damper using numerical simulation.

The stress cloud map of the bending energy-absorbing plate at a displacement of 40mm is shown in 0. It can be observed that at a loading displacement of 40mm, the maximum stress reaches 269.6MPa, which exceeds the tensile strength. However, the stress in the middle of the energy-absorbing plate is 122MPa, and no buckling phenomenon has occurred, indicating that the bending energy-absorbing plate will not fracture and can still function normally at a displacement of 40mm. During the simulation process, the bending energy-absorbing plate began to buckle when the displacement reached 13mm, indicating that its energy-absorbing displacement is between 13mm and 40mm. Therefore, the bending energyabsorbing plate can work normally within this range.

Figure9.

Numerical simulation and experimental hysteresis curve comparison

Figure10.

Skeleton curve comparison

4.3

Parametric analysis

4.3.1

Analysis of bending energy-dissipating plate parameters

The stress cloud map of the bending energy-absorbing plate at a displacement of 40mm is shown in 0. At a loading displacement of 40mm, the maximum stress exceeds the tensile strength at 269.6MPa. However, the stress in the middle of the energy-absorbing plate is 122MPa, and no buckling phenomenon has occurred. This indicates that the bending energy-absorbing plate will not fracture and can still function normally at a displacement of 40mm. The simulation process shows that the bending energy-absorbing plate began to buckle when the displacement reached 13mm, indicating that its energy-absorbing displacement is between 13mm and 40mm. Therefore, the bending energy-absorbing plate can work normally within this range.

Figure11.

Stress cloud at 40mm displacement of bending energy-dissipating plates

Since the conclusions obtained through equations (2), (3), and (4) are all related to the thickness of the bending energy-absorbing plate, a comparison and analysis were conducted by increasing or decreasing the thickness of the energy-absorbing plate by 2cm. The geometric dimensions of the structure with the bending energy-absorbing plate thickness shown in 0 and 0 are as follows:

Table2.

Detailed table of bending energy-dissipating plate geometry

Name	Thickness (mm)	Hight (mm)	Width (mm)	Minimum width(mm)
WQ-1	10	400	100	20
WQ-2	12	400	100	20
WQ-3	14	400	100	20

The thickness of the bending energy-dissipating plate affects the energy-dissipating capacity

The equivalent viscous damping coefficient [22] describes the energy-absorbing capacity of the bending energy-absorbing plate. As shown in 0, the bending energy-absorbing plate starts to work when the displacement load exceeds 10mm, and its equivalent viscous damping coefficient he1 steadily increases. The equivalent viscous damping coefficient of the energy-absorbing plate almost increases proportionally with the thickness under the same displacement, which is consistent with the theoretical formula derivation. The energy-absorbing performance of the bending energy-absorbing plate is stable and gradually increasing, as seen from the line of WQ-2. This can compensate for the insufficient energy-absorbing capacity of the shear energy-absorbing plate at larger displacements and maintain the overall energy-absorbing capacity of the damper unchanged.

Figure12.

Equivalent viscous damping coefficient when the thickness of curved energy-dissipating plate changes

Based on the analysis above, the following conclusions can be made:

• 1. The bending energy dissipation plate works by using the plastic deformation generated by the bending stress to absorb the vibration energy of the structure, achieving shock absorption and isolation.

• 2. The equivalent viscous damping coefficient of the bending energy dissipation plate increases with displacement and thickness, indicating good energy dissipation characteristics.

• 3. The bending energy dissipation plate can be combined with the shear energy dissipation plate to form a composite damper. This allows the damper to take advantage of the shear energy dissipation plate under small displacement and the supplementary effect of the bending energy dissipation plate under large displacement, resulting in efficient and stable operation.

Effect of bending energy-dissipating plate thickness on stiffness degradation curve

0 shows a comparison of the stiffness degradation curves for three different thicknesses of the bending energy-absorbing plate through numerical simulation and integration. The general shape of the stiffness degradation curve remains unchanged regardless of the thickness, but the stiffness values at the same displacement increase with increasing thickness. However, the stiffness is less than 1 kN/mm for all thicknesses. While the stiffness of the bending energy-absorbing plate has improved, for a damper with a large stiffness, the increase in thickness of the bending energy-absorbing plate is negligible in terms of stiffness improvement.

Based on the analysis above, the following conclusions can be made:

• 1. The thickness of the bending energy-absorbing plate has a linear relationship with the stiffness, with the stiffness increasing first and then decreasing.

• 2. Changing the thickness of the bending energy-absorbing plate will hardly improve the overall stiffness of the damper, and the stiffness of the bending energy-absorbing plate can be disregarded in the design.

Figure13

Stiffness degradation curves of bending dampers of different thicknesses

4.3.2

Parameter Analysis of Shear Energy Dissipating Panel

During numerical simulation, the shear energy-absorbing plate underwent buckling and entered the energy-absorbing stage when the displacement reached 0.4mm. As displacement increased, buckling deformation occurred, causing the anti-yield plate to enter the working state. Without an anti-yield plate, the shear energy-absorbing plate would buckle prematurely, reducing its bearing capacity. 0 shows that without an anti-yield plate, the shear energy-absorbing plate undergoes large displacement deformation. Therefore, adding an anti-yield plate can increase the bearing and energy absorption capacity of the shear energy-absorbing plate by constraining deformation caused by buckling.

The simulation results indicate that the hysteresis curve (see 0) is rich, with the steel sheet remaining elastic at small displacements, followed by softening and finally stabilizing the damper’s stiffness. At large displacements, the hysteresis curve is approximately rectangular, conforming to the typical ideal elastic-plastic model, and the steel sheet exhibits strong energy absorption capacity. The theoretical formulas obtained from equations (5), (6), and (7) are related to the thickness and width of the shear energy-absorbing plate. Therefore, comparative analysis was conducted by increasing or decreasing the thickness and width of the shear energy-absorbing plate by 2cm, and the detailed geometric structure of the shear energy-absorbing plate is shown in 0

Table 3.

Detailed table of shear energy plate geometry

Name	Thickness (mm)	Hight (mm)	Width (mm)	Minimum width(mm)
JQT-1	4	400	360	180.24
JQT-2	6	400	360	180.24
JQT-3	8	400	360	180.24
JQK-1	6	400	364	180.24
JQK-2	6	400	360	180.24
JQK-3	6	400	380	180.24

Figure14.

No anti-buckling plate deformation cloud at 40mm

Figure15.

Shear the hysteresis curve of the energy-dissipating plate

The thickness of the shear plate affects the energy dissipation capacity

Specimens JQT-1, JQT-2, and JQT-3 were analyzed using finite element analysis, and the results are shown in 0. The equivalent viscous damping coefficient of the shear energy-absorbing plate continuously increases before the displacement reaches 15mm, followed by buckling and stiffness degradation, causing the equivalent viscous damping coefficient to drop sharply and decrease with increasing displacement. The thickness of the shear energy-absorbing plate has little effect on its energy absorption capacity. However, increasing the thickness of the energy-absorbing plate requires an increase in the thickness of the anti-yield plate, making the overall part of the energy-absorbing plate bulky.

Figure 16.

Equivalent viscous damping coefficient when the thickness of the shear plate changes

Stress distribution diagrams of JQT-1, JQT-2, and JQT-3 at different displacements were analyzed to study the influence of the thickness of the shear energy-absorbing plate on its energy absorption characteristics, as shown in 0. As the displacement increases, the stress concentration area of the shear energy-absorbing plate gradually moves towards the center, and the stress value also gradually increases. Comparing the images when the displacement reaches 5mm and 15mm, it can be seen from the stress of the anti-yield plate that the stress concentration area becomes more obvious, and the stress also reaches the maximum value. The stress distribution of shear energy-absorbing plates with different thicknesses is basically the same under the same displacement, indicating that the thickness of the shear energy-absorbing plate has little effect on its stress state.

Figure17.

Stress distribution plot at different thicknesses and displacements

Based on the analysis, the following conclusions can be drawn:

• 1. The equivalent viscous damping coefficient of the shear energy-absorbing plate continuously increases before the displacement reaches 15mm, followed by buckling and stiffness degradation.

• 2. The thickness of the shear energy-absorbing plate has little effect on its energy absorption capacity.

• 3. Increasing the thickness of the energy-absorbing plate requires an increase in the thickness of the anti-yield plate, making the overall part of the energy-absorbing plate bulky.

• 4. As the displacement increases, the stress concentration area of the shear energy-absorbing plate gradually moves towards the center, and the stress value also gradually increases.

• 5. The stress distribution of shear energy-absorbing plates with different thicknesses is basically the same under the same displacement, indicating that the thickness of the shear energy-absorbing plate has little effect on its stress state.

The maximum width of shear energy dissipation affects the energy dissipation capacity

JQK-1, JQK-2, and JQK-3 were comparatively analyzed, and the results are shown in 0. The maximum width of the shear energy-absorbing plate affects its energy absorption capacity, and the wider the width, the larger the equivalent viscous damping coefficient. When the displacement reaches 40mm, the contribution of the width of the shear energy-absorbing plate to the energy absorption capacity of the damper is almost the same. However, at small displacements, the influence of the width on the equivalent viscous damping coefficient changes.

Figure18.

The maximum width of the shear energy dissipation plate is not equivalent to the viscous damping coefficient when it is not the same

Based on the above analysis, the following conclusions can be drawn:

• 1. The maximum width of the shear energy-absorbing plate affects its energy absorption capacity, and the energy absorption capacity increases with an increase in the maximum width.

• 2. At a displacement load of 40mm, the energy absorption capacity is almost independent of the maximum width. Increasing the maximum width only effectively improves the energy absorption capacity under conditions of small displacement.

• 3. At small displacements, the influence of the width on the equivalent viscous damping coefficient changes.

Therefore, it is recommended to choose a wider maximum width of the shear energy-absorbing plate to improve the energy absorption capacity of the damper, especially under conditions of small displacement.

Effect of the maximum width of the shear plate on stiffness

The numerical simulation results of JQT-1, JQT-2, and JQT-3 were analyzed, and the stiffness degradation curves were integrated under different shear energy-absorbing plate thicknesses, as shown in 0. It can be observed that the change in shear energy-absorbing plate thickness has a significant impact on the initial stiffness. Each curve can be fitted, and the curves almost show a power function growth trend. The initial stiffness values are presented in 0.

Table4.

Shear the initial stiffness of the energy-dissipating plate

Name	JQT-1	JQT-2	JQT-3
Initial stiffness(kN/mm)	130	180	900

It can be seen that the initial stiffness increases sharply with an increase in thickness, showing a nonlinear relationship, which is consistent with the theoretical formula. The shape of the stiffness degradation curve did not change, and the stiffness of the shear energy-absorbing plate also rapidly decreased with an increase in displacement. Finally, at a displacement of 40mm, its stiffness degraded to 5% of the original value.

Figure19.

Stiffness degradation curves of shear energy-dissipating plates of different thicknesses

Based on the analysis, the following conclusions can be drawn:

• 1. The thickness of the shear energy-absorbing plate has a significant impact on the initial stiffness of the damper, and the relationship between thickness and initial stiffness can be fitted by a power function.

• 2. As the displacement increases, the stiffness of the damper rapidly degrades and eventually stabilizes at larger displacements, with a stiffness change of approximately 5% of the initial stiffness.