Development and test of a self-centering fluidic viscous damper

Abstract

This research presents a novel self-centering fluidic viscous damper that incorporates preloaded ring springs to offer self-centering capability and a fluidic viscous damper for energy dissipation. A full-scale self-centering fluidic viscous damper was developed and subjected to low-cyclic reversed loading tests. The test results show the self-centering fluidic viscous damper has both displacement-dependent and velocity-dependent hysteric responses with self-centering capability. Fatigue tests further show that the self-centering fluidic viscous damper maintains a stable hysteretic response under reversed loading. An analytical model and a numerical model are developed for the proposed self-centering fluidic viscous damper and analyzed. Comparisons of test results and the numerical and analytical models show similar hysteric responses, thereby validating the accuracy of the numerical and analytical models to simulate the behavior of the proposed damper.

Keywords

energy dissipation fluidic viscous damper low-cyclic reversed loading test ring springs self-centering

Introduction

In traditional seismic design, earthquake-induced energy is dissipated by buildings through plastic deformation. Large plastic deformation will inevitably prevent the rapid restoration of structural function and result in difficult and costly post-earthquake repair. Reconstruction is more economical than restoration when the residual drift exceeds 0.5% (McCormick et al., 2008). To increase the seismic resilience, self-centering (SC) energy dissipation devices have been proposed and employed, which utilize energy dissipation units to reduce the earthquake response and SC units to eliminate residual deformation (Filiatrault et al., 2000; Tsopelas and Constantinou, 1994). Researchers in the last two decades have conducted investigations to find appropriate materials/devices that can achieve SC capability, which include the use of shape-memory alloys (SMAs) (Miller et al., 2012; Ozbulut and Hurlebaus, 2011; Zhang and Zhu, 2007), high-strength steel tendons (Chou and Chung, 2014; Chou et al., 2016b; Liu and Wu, 2012), composite fiber tendons (Christopoulos et al., 2008; Erochko et al., 2014; Zhou et al., 2015), disk springs (Fan et al., 2019), and ring springs (Filiatrault et al., 2000; Golzar et al., 2018). In these SC systems, seismic energy is dissipated through metallic yielding (Chou et al., 2016b; Liu and Wu, 2012; Miller et al., 2012; Zhou et al., 2015), friction (Chou and Chung, 2014; Christopoulos et al., 2008; Erochko et al., 2014; Fan et al., 2019),; (Filiatrault et al., 2000; Ozbulut and Hurlebaus, 2011), and viscous damping (Golzar et al., 2017; Tsopelas and Constantinou, 1994).

In the past decade, extensive investigations have been made on experimental, numerical, and probabilistic analyses on the SC systems (Chou et al., 2016c; Dong et al., 2019; Eatherton et al., 2014; Qiu and Zhu, 2016; Silwal and Ozbulut, 2018; Tremblay et al., 2008; Zhu and Zhang, 2008), and design methods have been proposed for the structures with SC elements (Qiu and Zhu, 2017; Tzimas et al., 2015). A few applications of SC structures further show the broad prospect of the novel structure (Chou et al., 2016a). The desirable SC systems should have stable and controllable SC and energy dissipation capacity, and their configuration should not be too complicated for the ease of repair and should be cost effective. In order to achieve these requirements, the SC viscous damper has been proposed and investigated (Golzar et al., 2017, 2018, 2019; Kordani et al., 2015), which consisted of two connected components, a viscous damper and a cylinder housing the ring springs which was screwed at the end of the fluid viscous damper.

The ring springs consist of a stack of inner and outer rings, and previous investigation (Ringfeder Power Transmission GmbH, 2018) indicated that the load bearing capacity of typical ring springs can range from 5 to 1800 kN. The friction between the inner and outer rings can dissipate energy during their relative sliding. Owing to the excellent energy dissipation and load-carrying capacities, ring springs have been adopted in mechanical elements used in the buffer, seismic damper, and SC connections (Filiatrault et al., 2000; Hill, 1995; Kar et al., 1996; Khoo et al., 2013; Ringfeder Power Transmission GmbH, 2018). More recently, SMAs were suggested to replace traditional steel in ring springs (Fang et al., 2015; Spaggiari et al., 2018; Wang et al., 2017), so that more energy could be dissipated through internal hysteresis of the material (Spaggiari et al., 2018). In general, the ease of installation and ability to achieve large deformation make ring springs capable for the SC system.

The configuration of the self-centering fluidic viscous damper (SC-FVD) in this article is such that the FVD has been installed inside the ring springs rather than being connected in series, thereby reducing the overall length and size of the device. Accordingly, the working mechanism and analytical model of the SC-FVD are presented. Cyclic tests of a set of ring springs were conducted, and a full-scale SC-FVD with the capacity of 190 kN, comprising a FVD with ±75 mm stroke and 26 ring spring segments, was tested to verify the proposed mechanical model. Note that in previous tests, only scaled specimens with the capacity of 30 kN and the available stroke of ±30 mm were tested (Golzar et al., 2018). Finally, a numerical model for SC-FVD is developed based on the finite element software OpenSees (McKenna et al., 2000).

Self-centering fluidic viscous damper

Structural configuration

The SC-FVD consists of two main units, that is, the viscous energy dissipation unit and the SC unit, as illustrated in Figure 1. The viscous energy dissipation unit is a FVD, consisting of the cylinder, silicone oil, piston, piston rod, and seal covers. The two ends of the viscous damper are threaded with end tubes, while the other ends of end tubes are connected with end covers through bolts. Both of the ends of the outer tube are also connected with end covers. Therefore, the positions of the viscous damper and the outer tube are relatively fixed, and the viscous force generated by the viscous damper can transfer to the outer tube through the end tube and end cover. The end tube has slots, which enable the connector to slide freely along those slots in the end tube.

Figure 1.

Schematic drawing of SC-FVD: (a) exploded view, (b) assembly view 1, (c) assembly view 2, and (d) assembly view 3.

The SC unit consists of the ring springs, outer tube, end covers, platens, piston rod, and connectors. The preloaded ring springs are located between the outer tube and the cylinder. Platens are placed on both the ends of the ring springs, which can slide freely in the end tube. The piston rod passes through the platens, and the connectors located in the platens are fixed on both the ends of the piston rod. When the piston rod moves, the connector on the piston rod will drive the platen movement which will compress the ring spring.

Working mechanism

The working mechanism of the SC-FVD is depicted in Figure 2. When in compression, the piston rod moves to the left, thereby driving the piston and the right platen to move to the left. When in tension, the piston rod moves to the right, thereby the piston and the left platen moving to the right. The platen movement will compress the ring springs, generating the SC force to drive the damper back to the initial equilibrium position and dissipating energy due to friction. Meanwhile, the piston rod also drives the piston to move in silicon oil to dissipate energy.

Figure 2.

Working mechanism of the SC-FVD.

The hysteresis model of the SC-FVD

According to the working mechanism, the SC-FVD is equivalent to a viscous damper with ring springs in parallel, as illustrated in Figure 3. Therefore, its analytical model can be obtained by superimposing the mechanical models of a viscous damper with ring springs.

Figure 3.

Behaviors of the SC-FVD: (a) at neutral position, (b) in tension, and (c) in compression.

The ring springs consist of a series of inner rings, outer rings, and two end rings (i.e. half inner ring), as shown in Figure 4. Under compressive loading, the wedging action of the tapered rings expands the outer ring and contracts the inner ring allowing for axial deflection. Friction exists on the contact surfaces, and the relative slip between the outer ring and inner ring can dissipate energy. Therefore, ring springs can be modeled by a spring and a friction mechanism that are connected in parallel, as shown in Figure 5, and the friction force is proportional to the spring force, which will cause enlarged spring stiffness (denoted as k₂) when loading and reduced stiffness (denoted as k₃) when unloading. The stiffness k₁ is mainly caused by the elastic deformation without relative sliding between the inner and outer rings. When the ring spring is preloaded, there will be an initial displacement Δ.

Figure 4.

Behavior of ring springs.

Figure 5.

The model of ring springs: (a) mechanical mechanism, (b) mechanical model without preload, and (c) mechanical model with preload.

When the ring springs are installed in the damper, the preload force P_a causes deformations of the ring springs, outer tube, and piston rod. The stiffness of the outer cylinder and piston rod is much larger than that of the ring spring; therefore, the effect of stiffness on the outer cylinder and piston rod can be neglected. Therefore, the force–displacement relationship of ring springs can be expressed as shown in Figure 6 and equation (1) when the ring springs are installed in SC-FVD.

F_{r} = {\begin{array}{l} P_{r} + k_{1} u & No load \\ P_{a} sgn (u) + k_{2} (u - u_{a} sgn (u)) & Loading \\ P_{r} sgn (u) + k_{3} & Unloading \end{array}

(1)

where k₁, k₂, and k₃ are the initial, loading, and unloading axial stiffness of the ring springs, respectively; P_a and P_r are the preload and residual force, respectively; u_a is the activation displacement given by (P_a–P_r)/k₁.

Figure 6.

Force–displacement relationship of ring springs in the SC-FVD.

The restoring force of a viscous damper obtained using the Maxwell model is as follows:

F_{v} = C {\overset{\cdot}{u}}^{α}

(2)

where C and α are the damping coefficient and velocity exponent of the viscous damper part, respectively.

Since the SC-FVD is equivalent to a viscous damper and ring springs in parallel, the analytical model can be expressed by Figure 7 and equation (3).

\begin{matrix} F_{r} = F_{r} + F_{v} = \\ {\begin{matrix} P_{r} + k_{1} u + C {\overset{\cdot}{u}}^{α} & No load \\ P_{a} sgn (u) + k_{2} (u - u_{a} sgn (u)) + C {\overset{\cdot}{u}}^{α} & Loading \\ P_{r} sgn (u) + k_{3} + C {\overset{\cdot}{u}}^{α} & Unloading \end{matrix} \end{matrix}

(3)

Figure 7.

The analytical model of the SC-FVD.

Testing of ring springs

In order to obtain the mechanical parameters of the ring springs used in the SC-FVD and verify their SC ability, four sets of ring springs, numbered H-1, H-2, H-3, and H-4, were tested as shown in Figure 8. Each set of specimen contains one outer ring and two end rings (i.e. half of the inner ring), as illustrated in Figure 9. The loading protocols adopted the force-control scheme, as shown in Figure 10, where the corresponding force and displacement responses of the specimens were measured through the in-built force and displacement transducers of the test equipment. Figure 10(a) shows the protocol with varied force amplitudes, and constant force amplitude with a pre-compression of 3 mm (corresponding to a preload of about 10 kN) was used in Figure 10(b).

Figure 8.

Testing of ring springs.

Figure 9.

Schematic drawing of ring springs.

Figure 10.

Loading protocols of ring springs: (a) varied force amplitudes and (b) constant force amplitude with preload.

Representative force–displacement hysteretic curves of the ring springs are shown in Figure 11, where the ring springs have stable, repeatable, and identical hysteretic responses. In Figure 11(a), it can be seen that the force is almost constant at zero because of the gap caused by manufacturing errors between the inner and outer rings in the initial stage. After the displacement reaches 2 mm, the force begins to load linearly from zero to the maximum force P_m and then unload down to the residual force P_r. Finally, the force is unloaded from P_r to zero. Calculations based on experimental data show that the initial stiffness k₁,’ loading stiffness k₂’, and unloading stiffness k₃’ are approximately 286, 37.5, and 6.7 kN/mm, respectively. As per the hysteretic loops, the springs can dissipate 70% of the input energy (with the rest mainly being kinetic energy). In Figure 11(b) where the preload (i.e. pre-compression of 3 mm) was applied, flag-shaped hysteretic responses without initial slackness and residual deformation are observed, demonstrating that the preloaded ring springs can achieve desirable SC performance under reversed loading.

Figure 11.

Force–displacement hysteresis curves of spring rings:(a) using the load protocol in Figure 10(a) and (b) using the load protocol in Figure 10(b).

Testing of the viscous damper

A viscous damper with design parameters described in Table 1 was fabricated and tested as shown in Figure 12. Displacement-control loading scheme with a sinusoidal waveform u =Asin(2πft) was used in the test, where A is the displacement amplitude, f is the excitation frequency, and t is the loading time. The selected series of displacement amplitudes and frequencies are listed in Table 2. Each test under a given loading condition was conducted for 5 cycles; only the third circle is selected for analysis. The force and displacement responses of the damper were measured by the built-in force and displacement transducers of the test equipment.

Table 1.

Design parameters of the viscous damper.

Cylinder		Piston		Diameter of the piston rod	Viscosity of silicone oil	Stroke	Design velocity
Outer diameter	Inter diameter	Length	Holes	Diameter of the piston rod	Viscosity of silicone oil	Stroke	Design velocity
166 mm	110 mm	30 mm	4Ø2	60 mm	300000cst	±75 mm	200 mm/s

Figure 12.

A test photograph of the viscous damper.

Table 2.

Loading cases of the tests on the viscous damper.

Displacement amplitude (mm)	Frequency (Hz)	Cycles
50, 40, 35, 30, 25, 20, 10	0.6, 0.4, 0.2, 0.1	5

On the basis of the test results, the representative force–displacement curves of the viscous damper are plotted in Figure 13, where Figure 13(a) shows the results at a constant frequency of 0.6 Hz and varied displacement amplitudes of 20, 25, 30, 35, 40, and 50 mm. In Figure 13(b), the tests were conducted under the constant displacement amplitude of 50 mm and varied frequencies of 0.1, 0.2, 0.4, and 0.6 Hz. It can be observed that the damping force increased with the increase of loading frequency and displacements (corresponding to the increased velocity), indicating that the viscous damper is a typical velocity-dependent damper. Moreover, the influence of dynamic stiffness on the damper is insignificant. Therefore, the restoring force model of the viscous damper can be expressed by the force–velocity relationship based on the Maxwell model, which can be expressed by equation (2).

Figure 13.

Force–displacement hysteresis curves of the viscous damper: (a) with varied displacement amplitudes and (b) at varied frequencies.

Fitting the test results with equation (2), the damping coefficient and velocity exponent are 44.034 kN/(mm/s) and 0.2151, respectively, which is plotted in Figure 14. It can be seen that the fitting curve coincides with the test result prior to the loading speed of 150 mm/s. After the loading speed reached 170 mm/s, the pressure in the cylinder became very high (i.e. 25 MPa); therefore, the performance of the damper became unstable. In general, the restoring force model of a viscous damper can be expressed by F_v = C ${\overset{\cdot}{u}}^{α}$ when loading speed is below 150 mm/s.

Figure 14.

Fitting of force–displacement curve of the viscous damper.

Experimental study on the SC-FVD

Test setup

An SC-FVD with the length of 1912 mm and a stroke of 75 mm was fabricated and tested to study its hysteretic behavior and fatigue performance. The outer tube is a circular steel tube with a 268-mm outer diameter, 215-mm inner diameter, and 1147-mm length. A circular steel tube with a 166-mm outer diameter, 126-mm inner diameter, and 423-mm length was used as the end tube, which is connected with the viscous damper and has four slots with 260 mm in length and 30 mm in width. The piston rod is a steel rod of 1023 mm in length and 60 mm in diameter. Twenty-six ring spring segments made up of a total of 26 outer rings, 25 inner rings, and 2 end rings were used in the SC system, which was preloaded with 10 kN.

The tests were conducted on a 1000-kN servo-hydraulic test system, as is illustrated in Figure 15. The test scheme also adopted the displacement-control loading scheme with sinusoidal input, as shown in Table 3. Note that the loading system has the maximum velocity of 200 mm/s; for the maximum displacement amplitude of 50 mm, the corresponding frequency is 0.637 Hz. In addition, to test the damper at low velocity, a frequency of 0.05 Hz was also adopted. Therefore, the range of loading frequency was taken from 0.05 to 0.6 Hz, which basically covers the range of application since the damper is developed for high-rise buildings where low-frequency vibrations are the major concern. The performance of the damper at higher frequencies could be further tested when larger test facility is available or with smaller amplitudes.

Table 3.

Loading cases of the tests on the SC-FVD.

Displacement amplitude (mm)	Frequency (Hz)	Cycles
50, 40, 35, 30, 25, 20, 10	0.6, 0.4, 0.2, 0.1, 0.05	5
50	0.6	30

Figure 15.

A test photograph of the SC-FVD.

Hysteretic behaviors

On the basis of the test data, the hysteresis curves of SC-FVD are obtained as shown in Figure 16, where Figure 16(a) shows the results under constant frequency of 0.05 Hz and varied displacement amplitudes of 20 mm, 25 mm, 30 mm, 35 mm, 40 mm, and 50 mm. In Figure 16(b), the tests were conducted at a constant displacement amplitude of 50 mm and varied frequencies of 0.1, 0.2, 0.4, and 0.6 Hz. It can be observed that the hysteretic curve of the SC-FVD is inclined because of the influence of the additional stiffness of the ring springs, as compared with that in Figure 13. Moreover, there is a steep increase in the force at zero displacement owing to the influence of the preloading of the ring springs. With the increase of loading displacement and frequency, the envelope of the hysteretic curve increases gradually. The peak force of the SC-FVD is less than the sum of the peak forces of the ring springs and viscous damper. This is mainly because the maximum force of the ring spring appears at the maximum displacement and the maximum force of viscous damper appears approximately at zero displacement.

Figure 16.

Force–displacement curves of the SC-FVD: (a) with varied displacement amplitudes and (b) at varied frequencies.

Peak force analysis

Figure 17 shows the force changing with displacement amplitude and loading frequency. The peak force in Figure 17 is taken as the average of the maximum positive and negative forces under various loading conditions. Figure 17(a) shows the changes in peak force with loading frequency, in which the frequencies are 0.05, 0.1, 0.2, 0.4, and 0.6 Hz. It can be seen that there is a positive correlation between peak force and frequency, which is consistent with the behavior of the viscous damper, and the relationship is exponential. Figure 17(b) shows changes of the peak force with displacement, in which the displacements are 20, 25, 30, 35, 40, and 50 mm. It can be seen that force and displacement relationships at a certain frequency are also positively correlated, being almost linear, similar to the behavior of ring springs.

Figure 17.

Variation of peak force with (a) loading frequency and (b) displacement amplitude.

Residual displacement analysis

As mentioned previously, the displacement-control loading scheme was used and the displacements were recorded through the built-in transducer of the loading system. However, at the end of each test, the load was automatically stopped by the control system as the displacements were close to zero; at the same time, the built-in transducer ceased working. To obtain the final displacements after loading, two external transducers were used, as shown in Figure 18. Figure 19 shows the displacements at the end of loading and at the end of tests (measured by using the external transducers). As per Figure 19, after the loading was stopped, the damper with the actuator was pushed back to its original position because of the ring springs, and the residual displacements at the end of tests were almost zero, showing the desirable SC capacity of the damper.

Figure 18.

Displacement measurement (displacement amplitude: 40 mm, frequency: 0.6 Hz).

Figure 19.

Displacements at the end of loading and residual displacements after tests: (a) displacement amplitude of 40 mm and (b) displacement amplitude of 50 mm.

Fatigue performance

In the fatigue test, the loading frequency, displacement amplitude, and loading cycles were 0.6 Hz, 50 mm, and 30 mm, respectively. The force–displacement hysteresis curves of fatigue test are shown in Figure 20. In order to further quantitatively understand the performance changes of the SC-FVD in the fatigue test, Figure 21 presents the ratios of the energy dissipation and peak force per cycle of loading to that in the first cycle of the fatigue test. It is clearly observed that there is slight performance deterioration at first, then the deterioration recovers, and finally tends to be stable. Peak force and energy dissipation in the final steady state were reduced by about 7% and 4% respectively, as compared with the initial state, indicating that the performance of the SC-FVD is relatively stable.

Figure 20.

Hysteresis curves of the fatigue test.

Figure 21.

Variation of peak force and energy dissipation.

Validation of the analytical model

For the SC-FVD used in this article, the mechanical parameters were obtained from the tests of the ring springs and viscous damper, which are listed in Table 4. In order to verify the analytical model, the hysteretic curves obtained from the test of the SC-FVD and results calculated from the mechanical model in different loading conditions are compared in Figure 22. It can be seen that the calculated data are consistent with the test data. Table 5 further compares the peak forces, where the maximum difference is less than 7%. In general, the proposed analytical model can accurately describe the mechanical properties of the SC-FVD.

Table 4.

Mechanical parameters of the SC-FVD.

Parameters	Values
Initial stiffness k₁	k₁ = k₁’/26 = 11 kN/mm
Loading stiffness k₂	k₂ = k₂’/26 = 1.442 kN/mm
Unloading stiffness k₃	k₃ = k₃’/26 = 0.256 kN/mm
Damping coefficient C	C = 44.034 kN/(mm/s) ^0.2151
Velocity exponent α	α = 0.2151
Activation force P_a	P_a = 10 kN
Residual force P_r	P_r = 1.6 kN

Figure 22.

Comparison of analytical and measured hysteretic responses: (a) 0.05 Hz; 50 mm, (b) 0.05 Hz; 30 mm, (c) 0.1 Hz; 50 mm, and (d) 0.6 Hz; 50 mm.

Table 5.

Comparison of analytical and measured peak forces.

Displacement amplitude (mm)		Frequency
		0.1 Hz		0.2 Hz		0.4 Hz		0.6 Hz
		Peak force	Deviation	Peak force	Deviation	Peak force	Deviation	Peak force	Deviation
20	Test	104.53	4.53%	113.41	2.20%	125.69	1.36%	130.38	–1.74%
20	Analytical	99.80	4.53%	110.92	2.20%	123.98	1.36%	132.65	–1.74%
25	Test	108.62	–0.23%	118.25	–1.79%	130.46	–2.61%	136.33	–4.76%
25	Analytical	108.87	–0.23%	120.36	–1.79%	133.87	–2.61%	142.83	–4.76%
30	Test	113.31	–3.81%	122.61	–5.55%	138.82	–3.22%	143.27	–6.44%
30	Analytical	117.63	–3.81%	129.42	–5.55%	143.29	–3.22%	152.49	–6.44%
35	Test	119.51	–5.56%	131.72	–4.93%	143.08	–6.50%	155.24	–4.23%
35	Analytical	126.16	–5.56%	138.21	–4.93%	152.38	–6.50%	161.81	–4.23%
40	Test	127.49	–5.53%	142.91	–2.72%	165.03	2.30%	170.03	–0.46%
40	Analytical	134.53	–5.53%	146.80	–2.72%	161.24	2.30%	170.82	–0.46%
50	Test	152.16	0.82%	161.12	–1.51%	174.32	–2.37%	190.46	1.11%
50	Analytical	150.91	0.82%	163.56	–1.51%	178.45	–2.37%	188.35	1.11%

Numerical simulation of the SC-FVD

To provide a tool for analysis of structures with the SC-FVD, a numerical model using the finite element (FE) analysis software OpenSees was developed. The SC-FVD was modeled using the Two-node Link Element, and the uniaxial Viscous Material (available in the OpenSees) and ring spring material were used in parallel. However, there is no material model available for the ring spring in the material library of OpenSees. Therefore, a uniaxial ring spring material is developed, which can potentially be used for any SC system that exhibits a flag-shaped hysteretic response with different loading stiffness and unloading stiffness, as shown in Figure 23, where only the response in the positive direction is shown, for example, because of the symmetry. In Figure 23, the values of activation stress/force and residual stress/force are already determined, and when the strain is zero (line AB), the springs do not have any influence on the structure. The lines BC and DE have the same slope; therefore, the status of the springs can be simplified into three stages, that is, the loading, unloading, and middle stages, with the slopes of k₂, k₃. and k₁, respectively. The middle stage is the transition stage between the loading and unloading stages, which can be expressed by a series of lines parallel to line BC (or DE) in Figure 23, with the upper and lower points of ε_up(n) and ε_lp(n), respectively. The stage of ring springs in each load step is thus determined according to the judgment law, as shown in Figure 24, where the stage of ε(n) in the current step n is judged by the ε_up(n–1) and ε_lp(n–1) in the previous step, and then the stress is calculated accordingly. The initial values ε_up(0) and ε_lp(0) are activation strain and zero, respectively.

Figure 23.

The uniaxial ring spring material model.

Figure 24.

Stage judgment law of the ring springs.

Figure 25 shows the comparison of experimental and simulated hysteretic responses under the frequency of 0.05 Hz, 0.1 Hz, 0.2 Hz, and 0.4 Hz when the loading displacement amplitude is 50 mm. It can be seen that the simulated curves precisely coincide with the experimental curves, showing that the developed material model can accurately simulate hysteretic response of the SC-FVD.

Figure 25.

Comparison of simulated and measured hysteretic responses at the frequencies of (a) 0.05 Hz, (b) 0.1 Hz, (c) 0.2 Hz, and (d) 0.4 Hz.

Conclusion

A novel SC-FVD is proposed, and the analytical model is developed as per its working mechanism. A full-scale SC-FVD was further tested to investigate its hysteretic behaviors, fatigue performance, and SC capacity. In accordance with the presented work, the main conclusions are as follows:

The proposed SC-FVD consists of ring springs and fluidic viscous units, to achieve desirable energy dissipation and re-centering behavior. The combination of velocity-dependent and displacement-dependent system allows the SC-FVD to work at a wide range of frequencies.

The hysteretic curve of SC-FVD is inclined and has a steep increase at zero displacement owing to the influence of the ring springs with a preload, and the loops are stable and plump. Moreover, the residual displacements of the damper at the end of tests were almost zero, showing the desirable SC capacity of the damper.

The degradation rates of energy consumption capacity and peak force are only 7% and 5%, respectively, after 30 cycles of loading, showing that the fatigue performance of the SC-FVD is acceptable.

The proposed analytical model can accurately predict the hysteretic response of SC-FVD under various loading displacement amplitudes and frequencies, and the deviation between theoretical and test peak forces is less than 7%. A numerical model of the SC-FVD is also developed based on the OpenSees, which can accurately simulate the damper behavior.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The financial support for this study was provided by the Natural Science Foundation of China under Grant No. 51678147 and the Postgraduate Research & Practice Innovation Program of Jiangsu Province under Grant No. KYCX19_0097.

ORCID iD

Tong Guo

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