Evaluation of Viscoelastic and Rotational Friction Dampers for Coupled Shear Wall System

Abstract

This research experimentally and numerically evaluates the effectiveness of viscoelastic (VE) and rotational friction (RF) dampers in enhancing the seismic performance of coupled shear wall (CSW) systems. This study consists of two phases: (1) element testing to characterize the hysteretic behavior and energy dissipation capacity of VE and RF dampers, and (2) shake table testing of a large-scale CSW structure equipped with these dampers under the white noise, sinusoidal and Kokuji waves. The experimental results are validated through numerical analysis using STERA 3D (version 11.5), a nonlinear finite element software, to simulate the dynamic response of the damped CSW system. Key performance indicators, including inter-story drift, base shear, and energy dissipation, are compared between experimental and numerical results, demonstrating strong correlation. The findings reveal that VE dampers effectively control high-frequency vibrations, while RF dampers provide stable energy dissipation across varying displacement amplitudes. The validated numerical model facilitates the optimization of damper configurations for performance-based seismic design. This study provides valuable insights into the selection and implementation of supplemental damping systems for CSW structures, contributing to improved seismic resilience in buildings.

1. Introduction

The coupled shear wall system has been introduced due to its superior lateral stiffness compared to other lateral force-resisting systems [1]. The incorporation of high-stiffness structural members enhances the control of lateral forces acting on buildings, effectively minimizing lateral deformations. This characteristic is particularly crucial for high-rise buildings, where structural design is predominantly influenced by dynamic lateral loads. Coupling beams facilitate shear force transfer between shear walls, thereby enhancing energy dissipation. Consequently, coupled shear walls are regarded as an optimal solution for achieving the desired strength, stiffness, and ductility in structures [2]. However, inadequate design capacity or excessive lateral loading may lead to structural deterioration, including flexural failure at coupling beam joints and the base of structural walls. The degradation of lateral stiffness due to excessive damage further complicates the control of structural vibrations, posing significant challenges in maintaining the building’s overall stability.

The VE damper represents a highly effective alternative for energy dissipation systems and has been widely utilized for wind and seismic protection of buildings for nearly five decades [3,4,5]. The implementation of VE dampers in coupled shear wall structures is particularly advantageous due to their dual function of enhancing stiffness and dissipating energy, thereby effectively mitigating drift and structural forces. In VE dampers, shear deformation is the primary mechanism for energy dissipation. When subjected to lateral forces, the viscoelastic material (typically a polymer) undergoes cyclic shear straining, causing internal friction and heat generation. The displacement-dependent force arises from the elastic component of the material, which stores energy as it deforms, while the velocity-dependent force comes from the viscous component, which resists rapid motion, converting kinetic energy into heat. Together, these forces create a hysteresis loop in the stress-strain curve, where the area enclosed represents energy dissipated per cycle. In practical terms, as the damper experiences seismic or wind-induced vibrations, the combined effect of elastic stiffness (resisting displacement) and viscous damping (resisting velocity) effectively absorbs and dissipates energy, reducing structural vibrations. Efficiency depends on the material properties, frequency of loading, and temperature, making VE dampers highly effective for mitigating dynamic responses in buildings and bridges. The implementation of dampers as substitutes for structural elements, such as coupling beams or outriggers, ensures that no usable architectural space is compromised. One effective approach involves embedding dampers within the coupling beams linking adjacent shear walls, utilizing the structural depth already allocated for beam reinforcement. For instance, compact viscous or viscoelastic dampers can be installed in staggered or diagonal arrangements within the beam midspan, where shear demands are highest, without encroaching on functional floor space. Under lateral or in-plane torsional deformation of the building, the relative displacement between walls induces differential vertical movement within the coupling elements, subjecting the VE material layers to shear deformation. This mechanism generates a force that is both displacement and velocity-dependent, thereby enhancing wall coupling and providing supplemental viscous damping to the overall structural system. Proper distribution of dampers along the building’s height enhances supplemental viscous damping across all lateral and torsional vibration modes, effectively mitigating dynamic responses to wind and seismic excitations. Montgomery’s research [6] confirms the efficacy of viscoelastic coupling dampers in improving the dynamic performance of high-rise buildings. Full-scale experimental evaluations demonstrate that the viscoelastic coupling damper (VCD), as implemented in the prototype structure, effectively contributed to both viscous damping and shear stiffness within the coupled wall system. However, further advancements in viscoelastic damper design are necessary to enhance flexibility and optimize performance. A newly developed VCD system has been introduced to enhance the dynamic performance of high-rise buildings under wind and seismic loads. This system consists of viscoelastic material layers bonded between steel plates, with alternating steel layers extending to opposite sides and securely anchored to the structural walls, thereby optimizing energy dissipation and structural stability. VE dampers offer distinct advantages over metallic yield dampers and buckling-based energy dissipation systems due to their stable hysteretic behavior, minimal residual deformation, and velocity-dependent energy dissipation. Unlike metallic yield dampers [7,8], which rely on plastic deformation and may suffer from low-cycle fatigue, VE dampers dissipate energy through viscoelastic shear deformation, ensuring consistent performance over repeated cycles without permanent damage. Additionally, systems like energy-early-dissipated braces [9] depend on steel web buckling, which can lead to unpredictable post-buckling behavior and require complex detailing. In contrast, VE dampers provide predictable stiffness and damping across a wide frequency range, making them ideal for both seismic and wind-induced vibrations. Their self-centering capability (near-zero residual displacement) further reduces post-event repairs compared to metallic systems, which often retain plastic deformations. While metallic dampers excel in high-force applications, VE dampers are superior in scenarios requiring smooth, fatigue-resistant, and maintenance-free operation, particularly in buildings where serviceability and long-term reliability are critical.

Friction dampers are among the most effective and widely utilized solutions for vibration control. These devices operate by dissipating vibration energy through frictional sliding between contact surfaces. In 1989, Fitzgerald et al. introduced a classical friction-based energy dissipation mechanism known as the slotted bolted connection to improve the seismic response of ordinary brace frame and braced moment resistance frame [10]. Friction-based energy dissipation systems have been implemented in various structural components to mitigate seismic-induced plastic damage and enhance earthquake resilience. Their widespread adoption is attributed to their high energy dissipation efficiency, ease of maintenance, and rapid post-earthquake repairability. Applications include damage-free beam-column connections [11,12,13,14,15], rocking timber walls with slip-friction connectors [16], and steel column bases incorporating friction devices [17,18]. More recently, in 2022, Javidan et al. [19] proposed a ductile bracing system incorporating a rotational friction damper joint, characterized by an eccentric placement relative to the bay diagonal. A ductility-based design methodology was developed for structures utilizing this system, and a three-dimensional structural model was designed and analyzed through various analytical approaches. The findings demonstrated that the proposed damper-brace system and associated design methodology are effective for practical implementation. Additionally, Monir et al. [20] modified the rotational friction damper for bracing applications by introducing a square-shaped configuration, designed specifically for installation within square spans. The results indicated a significant reduction in lateral displacements and base shear in multi-story buildings equipped with this modified energy dissipation device, highlighting its efficiency in dissipating seismic energy.

The ultimate goal of this research is to develop a hybrid damper that combines a VE damper and a RF damper. The hybrid damper’s mechanism begins with the shear deformation of the VE component, which dissipates energy through viscous hysteresis under small to moderate displacements. As the applied load increases, the resulting moment at the damper’s joints reaches a critical threshold, triggering the activation of the RF dampers. This sequential engagement ensures efficient energy dissipation: the VE damper handles low-amplitude vibrations, while the RF damper provides supplemental resistance under extreme displacements, creating a two-stage energy dissipation system that optimizes performance across varying demand levels. In this paper, as a first step, experiments and analyses are conducted separately for the VE damper and the RF damper to verify their effectiveness. First, the hysteretic behavior and damping effectiveness of each damper are examined through element tests and their numerical modes are constructed. Then, large-scale shake table tests of the frame with coupled shear walls and the damper are conducted to evaluate the effectiveness of the damper under the white noise, sinusoidal, and Kokuji wave excitations. Finally, the accuracy of the numerical model is verified by comparing the experimental results with the numerical results.

2. Element Test of Viscoelastic and Rotational Friction Damper

2.1. Configuration of VE with RF Damper

Figure 1 illustrates the energy dissipation device developed in this study, which integrates a VE damper at its center and RF dampers on both the left and right sides. This damper is designed to absorb energy during small to medium earthquakes with the VE damper, and to further increase energy absorption by sliding the RF damper during large earthquakes. As the first stage of this research, we examine the characteristics of each damper when they act independently. Figure 1a provides a detailed front view of the damper attached to a frame, while Figure 1b presents a top view, revealing two layers of VE material and four friction pads. Additionally, M10 bolt gauges were installed at the center of the RF dampers to apply the necessary clamping force.

2.2. Damper Design and Material

Figure 2a presents a model representing the behavior of the Kelvin solid model, while Figure 2b depicts the shear deformation of viscoelastic material. Parameters of the VE damper are obtained as below in Equations (1)–(4) [5].

Figure 2. VE damper schematic diagram: (a) Kelvin solid model, (b) VE material deformation.

Figure 2. VE damper schematic diagram: (a) Kelvin solid model, (b) VE material deformation.

$$k={\displaystyle \frac{G_{E}A}{h}}$$

(1)

$$G_C={\displaystyle \frac{G_E\mathsf{\eta }}{Ꞷ}}$$

(2)

$$c={\displaystyle \frac{G_{C}A}{h}}$$

(3)

$${F\left(t\right)=kX}_0(t)+c\dot{X_0}(t)$$

(4)

where

• $k$ is elastic stiffness;
• $c$ is damping coefficient;
• $G_E$ is elastic shear modulus;
• $G_c$ is shear viscous damping constant;
• $A$ is VE surface area;
• $\eta$ is loss factor;
• h is VE thickness;
• ${\tau }_s$ is shear stress;
• ${\gamma }_s$ is shear strain;
• $Ꞷ$ is angular frequency;
• $X_0$ is displacement.

Figure 3 shows the schematic diagram of RF damper which represents the activation moment. Equation (5) defines the moment capacity of the rotational friction damper, with the following parameters: number of friction surfaces (N = 2), internal radius ($r_i=5 \mathrm{m}\mathrm{m}$), and outer radius ($r_o=75 \mathrm{m}\mathrm{m}$).

Figure 3. Schematic diagram for calculating the activation moment of RF damper.

Figure 3. Schematic diagram for calculating the activation moment of RF damper.

$$M_y={\displaystyle \frac{2NQ\mu ({r_o}^3-{r_i}^3)}{3({r_o}^2-{r_i}^2)}}$$

(5)

where

• $M_y$ is moment capacity;
• $N$ is number of layers;
• $r_i$ is internal radius;
• $r_o$ is outer radius;
• $\mu$ is friction coefficient;
• $Q$ is clamping force.

Figure 4a illustrates the front view of the disassembled section, while Figure 4b presents the cross-section view of the damper assembly. The viscoelastic damper was designed with a capacity of 3 kN, which is sufficient for a six-story frame. The selected VE polymer material exhibits a storage shear modulus ($G_E$) of 0.174 N/mm² and a loss factor ($\eta$) of 0.19, ensuring optimal energy dissipation performance. The VE damper comprises two VE layers, each measuring 40 mm in width, 70 mm in length, and 5 mm in thickness. The RF damper consists of four friction disks, each with a 75 mm radius and 12 mm thickness, paired with four SUS plates (156 mm × 156 mm × 2 mm) serving as sliding surfaces. The sliding interface between the friction disk and SUS plate provides a friction coefficient of $\mu$ = 0.2 for the damper.

Table 1. Damper material list.

Type of Material	Width (mm)	Length (mm)	Radius (mm)	Thickness (mm)	No. of Layer
VE layer	40	70	-	5	2
SUS plate	156	156	-	2	4
Friction disk	-	-	75	12	4

summarizes the material specifications of the dampers.

2.3. Specimen Setup

Figure 5 illustrates the 3D configuration of the experimental test setup, with numbered components representing key elements of the shake table test assembly. Component (1) denotes the shake table actuator that provides the output force excitation. The damper frame is mounted on the shake table platform (2), which transmits the dynamic loading. A rigid reaction frame (3) is fixed to the laboratory floor to provide structural stability. The test specimen consisting of integrated VE and RF dampers is housed within the damper frame (4). Figure 6 presents the elevation view of the test configuration. The elevation view demonstrates the deformation behavior of the RF damper during cyclic testing, providing insight into its energy dissipation mechanism. In friction dampers, both sides undergo identical angular rotation, whereas VE dampers exhibit primarily vertical displacement. Conducting element tests is crucial for evaluating the performance of individual damper units. For VE dampers, the tests assess energy dissipation, stiffness, and damping characteristics under cyclic loading, varying frequencies, temperatures, and strain levels, ensuring mechanical integrity and quantifying hysteresis behavior. For friction dampers, the tests determine frictional resistance, sliding force, and energy dissipation capacity, evaluate wear and tear, confirm long-term durability, and analyze the sliding mechanism under diverse load and pressure conditions to ensure consistent performance. Element tests for both VE and RF dampers are indispensable for validating their performance, enhancing the safety and reliability of the structure during shake table tests, and providing critical data for numerical modeling and system optimization.

2.3.1. Viscoelastic Damper Test

Figure 7 illustrates the configuration of the VE damper, wherein the RF damper sections are secured between the top and bottom plates (highlighted in blue) to ensure that only the VE damper undergoes movement during excitation.

2.3.2. Rotational Friction Damper Test

Figure 8 illustrates the configuration of the RF damper, wherein the VE damper sections are secured between the top and bottom plates (highlighted in blue), ensuring that only the RF damper is permitted to rotate during excitation.

2.4. Loading Protocol

Table 2. Loading protocol for each damper.

Element Test	Viscoelastic Damper	Friction Damper
Frequency (Hz)	0.5, 1.0	0.5
Clamping force (kN)	0	0, 2, 5, 6, 8, 10

presents a loading protocol of the test parameters for VE and RF dampers. Viscoelastic dampers were evaluated under cyclic loading conditions at a consistent frequency of 0.5 Hz and 1.0 Hz, while the rotational friction damper’s cyclic loading frequency was set at 0.5 Hz. The RF damper clamping forces varied at 0, 2, 5, 6, 8, and 10 kN. The VE damper’s behavior is primarily governed by its intrinsic material properties, while the performance of the friction damper is influenced by the applied clamping forces, which regulate the sliding resistance.

2.5. Damper Hysteresis

2.5.1. Viscoelastic Damper

Figure 9 shows VE hysteresis under 0.22 volt. The damper designed with a maximum load capacity of 3 kN and an allowable displacement of 5 mm (equivalent to 100% of the VE material’s thickness) was tested under cyclic loading at a frequency of 0.5 Hz and 1.0 Hz.

2.5.2. Rotational Friction Damper

Figure 10a shows the hysteresis of the west side RF dampers while Figure 10b is for east side under different clamping forces. The damper hysteresis was used to evaluate the relationship between torque force and angular rotation under cyclic loading conditions.

Table 3. Rotational friction clamping force.

Test	1	2	3	4	5	6
Clamping Force (kN)	0	2	5	6	8	10

represents the clamping force applied to RV. The RF damper testing protocol initiated with 0 kN initial clamping force, followed by progressive increments up to 10 kN. The experimental data demonstrates a direct correlation between clamping force magnitude and resulting torque output, with measured torque values increased corresponding to the applied normal force.

3. Shake Table Test of Six-Story Coupled Wall System with Damper

3.1. Shake Table Test Procedure

Next, the damper is incorporated into a six-story frame from the previous study [21] with coupled shear walls to evaluate its effectiveness by the shake table test. Figure 11 shows a comprehensive shake table test procedure to investigate the dynamic behavior of four distinct structural configurations: a bare frame (case 0), a frame with coupled shear wall (case 1), a frame with coupled shear walls and a friction damper (case 2), and a frame with coupled shear walls and a VE damper (case 3). The experimental protocol in Step 1 begins with a free vibration test to determine the natural frequency and damping characteristics of each specimen. In Step 2, white noise excitation is applied at progressively increasing intensity levels. In Step 3, sinusoidal excitation is set at a frequency of 1.1 Hz to examine resonance behavior. Finally in Step 4, earthquake simulations utilizing the Kokuji waves are conducted at incrementally scaled intensities to assess the seismic performance of each configuration.

3.2. Test Setup

Figure 12 depicts the test specimen assembly, including the rigid frame (blue) mounted at the center of the shake table. Figure 13 illustrates the test specimen for the six-story frame (brown), the coupled shear walls (blue), and the damper attached to the coupled shear walls. Figure 14a shows the elevation view and Figure 14b shows the top view of the damper.

Each story of the frame consists of a main steel plate, a Natural Rubber Bearing (NRB) with a diameter of 200 mm and height of 132 mm placed on the floor center, and four linear motion (LM) guides. The steel floor size is 1500 mm by 300 mm, with a thickness of 25 mm. The story stiffness and restoring force are provided by the NRBs. NRBs contribute to the restoring force through their inherent elasticity, where the rubber layers deform under lateral loads and then rebound, recentering the structure after shaking. The LM guides are installed to restrain the bending deformation of the specimen during excitation.

Table 4. Properties of the 6-story frame.

Story	Stiffness (N/mm)	Weight (N)	Height (mm)
6	245.5	4021.6	300
5	237.6	2594.0	300
4	194.2	2545.2	300
3	226.7	2839.6	300
2	188.1	2545.2	300
1	186.4	2173.2	300
0	-	-	-
Total	-	16,718.8	1800

presents a summary of the structural properties of the six-story frame. A damper installed between the fifth and sixth stories introduces an additional mass of approximately 2510 N.

3.3. Input Waves

As illustrated in Figure 15, the input waves utilized in the experiments include the white noise, sinusoidal, and Kokuji waves. The white noise, characterized by a broad frequency spectrum, was applied to identify the structure’s natural frequencies and damping properties. The sinusoidal wave, with its incremental amplitude and frequency, was used to assess resonance effects, enabling the observation of amplified vibrations at critical frequencies. Additionally, the Kokuji wave, which simulates actual earthquake ground shaking, was implemented to evaluate structural performance under seismic loading conditions.

3.4. Measurement Scheme

The experimental setup was designed to monitor the structural response of the six-story frame specimen under various loading conditions, as illustrated in Figure 16. Accelerometers (A0 to A18) were positioned across multiple stories to capture acceleration data, enabling a detailed analysis of dynamic responses at each level. Laser displacement sensors (D0 to D6) were employed to measure inter-story displacements. High-precision small laser displacement sensors (VE01 to VE04) were utilized to obtain detailed displacement measurements for the VE damper, while gyro sensors (R01, R02) were incorporated to detect rotational movements. Additionally, bolt gauges (F01, F02) were installed to determine the clamping force applied, and wire sensors (W01, W02) were used to record circumferential displacements of the RF damper.

3.5. Experimental Test Results of the Six-Story Frame

3.5.1. Natural Frequency Under White Noise

Table 5. Natural frequency of the 6-story frame under the white noise waves.

White Noise Intensity (gal)	Shear Wall Natural Frequency (Hz)	Shear Wall + RF Natural Frequency (Hz)	Shear Wall + VE Natural Frequency (Hz)
40	1.48	2.43	2.32
80	1.07	1.98	1.71
120	1.07	1.77	1.48
160	1.07	1.77	1.48
200	-	1.48	1.48

presents the natural frequencies of a six-story frame structure subjected to varying intensities of white noise seismic waves, comparing three different structural systems: the frame with the coupled shear walls without damper (Shear Wall), with rotational friction damper (Shear Wall + RF), and with a viscoelastic damper (Shear Wall + VE). The results indicate that as the white noise intensity increases from 40 to 200 gal, the natural frequencies of all systems generally decrease, reflecting a reduction in structural stiffness due to higher excitation levels. The RF dampers excel in high-intensity scenarios due to their predictable force-limiting behavior but offer no adaptability to varying frequencies. The VE damper performs well across moderate intensities but may lose efficiency under extreme loads due to material limits. The Shear Wall system exhibits the lowest natural frequencies across all intensities, starting at 1.48 Hz at 40 gal and dropping to 1.07 Hz at higher intensities. In contrast, the Shear Wall + RF and Shear Wall + VE systems show higher initial frequencies (2.43 Hz and 2.32 Hz, respectively, at 40 gal) but experience more pronounced declines as intensity rises, eventually converging to 1.48 Hz at 200 gal. The analysis for three different models reveals a systematic reduction in natural frequency under higher excitation levels. The frequency stabilizes when the LM guides slide, because during small intensity, LM guides do not move due to friction, and then start to slide under higher intensity.

3.5.2. Results Under Sinusoidal Waves

Figure 17 shows the maximum displacement response under sinusoidal wave excitations of 50 gal and 100 gal, comparing the performance of three configurations: the frame with shear wall (Shear Wall), the frame with shear wall and an RF damper (Shear Wall + RF), and the frame and shear wall and a VE damper (Shear Wall + VE). As shown in Figure 17, the story displacement under sinusoidal waves indicates that both the RF and VE dampers significantly reduce displacement compared to the shear wall. Under the 50 gal sinusoidal wave, the RF damper reduces displacement by approximately 42%, while the VE damper achieves a 62% reduction. Under the 100 gal excitation, the VE damper reduces displacement by 37%, whereas the RF damper achieves a 25% reduction.

Figure 18 presents the maximum acceleration response, demonstrating that the damped configurations substantially reduce peak accelerations. Under the 50 gal excitation, the RF damper reduces acceleration by 35%, whereas the VE damper provides a reduction of about 41%. Under the 100 gal excitation, the VE damper reduces acceleration by 18%, whereas the RF damper achieves a reduction of 26%. These results highlight the efficacy of friction and VE dampers in enhancing structural performance by reducing both displacement and acceleration under dynamic loading conditions.

3.5.3. Results Under Kokuji Waves

Figure 19 shows the maximum displacement response under Kokuji wave excitations at varying intensity levels (ranging from 20% to 100%, corresponding to 70 gal to 350 gal) for three configurations: the frame and shear wall, the frame and shear wall equipped with an RF damper, and the frame and shear wall with a VE damper. The results demonstrate that the RF damper consistently reduces story displacement by approximately 40% across all intensity levels, highlighting its robust energy dissipation capabilities, particularly under higher excitation intensities. In contrast, the VE damper exhibits a progressive improvement in displacement reduction, achieving a 22% reduction at Kokuji 20% and increasing to 35% at Kokuji 80% intensity, indicating its enhanced effectiveness in mitigating displacement as excitation levels increase.

Figure 20 shows the maximum acceleration response under Kokuji wave excitations at progressively increasing intensities. The RF damper demonstrates consistent acceleration control, reducing peak acceleration responses by approximately 12% to 18% across all intensity levels. In comparison, the VE damper exhibits an intensity-dependent performance, showing moderate acceleration reduction of up to 18%. These findings under-score the superior performance of the RF damper in high-intensity scenarios, while the VE damper demonstrates reliable and adaptive performance across varying load conditions. At higher seismic intensities, the performance differences between RF and VE dampers become more pronounced due to their distinct energy dissipation mechanisms. RF dampers rely on sliding friction, where the resisting shear force is capped by the friction force, preventing excessive load transfer to the structure. The RF dampers dissipated energy by sliding deformation with constant friction force. This makes them particularly effective in high-intensity scenarios, as their limiting force prevents structural overloading while maintaining consistent energy dissipation. In contrast, VE dampers generate shear forces that are velocity and displacement-dependent, as written in Equation (4), meaning that their resistance increases with higher deformation rates. While this adaptive behavior allows VE dampers to efficiently dissipate energy across varying load conditions, their force output can rise significantly under extreme shaking, potentially leading to higher structural demands.

4. Numerical Analysis Using STERA 3D

4.1. Objectives

In the following, numerical models of the VE damper and RF damper are constructed based on the results of the elemental test. The accuracy of the models was then verified by comparing the analytical results with shake table tests on a frame with coupled shear wall and dampers.

4.2. Numerical Model of VE Damper

Figure 21 illustrates the numerical model of the VE damper, represented by a four-element system consisting of a spring $K_1$, a parallel damper $C_1$, a second damper $C_2$, and an additional spring $K_2$ [22]. The components are labeled as follows: (1) elastic-plastic spring, (2) nonlinear Maxwell body, and (3) nonlinear viscous element. The parameters $K_1,C_1,$ and $C_2$ are derived from empirical formulas dependent on the shear strain γ as indicated by Equations (6)–(8). These parameters exhibit power-law scaling with respect to γ, while an exponential decay term introduces a time-dependent component. The bilinear stiffness behavior of the damper is captured by the spring $K_2$ in Equation (9). Where $A_s$ $d$, and $\theta$ indicate the area, the thickness of the VE material, and the room temperature, respectively.

Table 6. Parameters for adjusting the original coefficients.

Parameter	${\mathit{x}}_1$	${\mathit{x}}_2$	${\mathit{x}}_3$	${\mathit{x}}_4$	${\mathit{x}}_5$	${\mathit{x}}_6$	${\mathit{y}}_1$
Value	1	2	10	10	3	2	1

shows the parameters for adjusting the original coefficients in Ref. [22] determined from the comparison of the hysteresis of the VE damper between the element test and the numerical analysis, as shown in Figure 22. A parametric study was conducted to determine the optimal parameters for Equations (6)–(9), calibrated using element test data. For the VE damper, the 1.0 Hz hysteresis response was selected as the reference case, as it closely matches the fundamental frequency of the six-story frame structure.

$$K_1=2.83(x_1)\times {10}^{-1}{\gamma }^{-0.715(x_2)}\left(A_s/d\right)\mathrm{e}\mathrm{x}\mathrm{p} [-0.017\left(\theta -20\right)]$$

(6)

$$C_1=4.76(x_3)\times {10}^{-1}{\gamma }^{-0.640(x_4)}\left(A_s/d\right)\mathrm{e}\mathrm{x}\mathrm{p} [-0.017\left(\theta -20\right)]$$

(7)

$$C_2=1.59(x_5)\times {10}^{-1}{\gamma }^{-0.395\left(x_6\right)}\left(A_s/d\right)\mathrm{e}\mathrm{x}\mathrm{p} [-0.017\left(\theta -20\right)]$$

(8)

$$K_2=1.57(y_1)\times \left(A_s/d\right)\mathrm{e}\mathrm{x}\mathrm{p} [-0.017\left(\theta -20\right)]$$

(9)

4.3. Numerical Model of RF Damper

Figure 23 presents a bilinear hysteresis depicting the moment rotation relationship of the RF damper. The graph exhibits two distinct phases: an initial elastic phase where the damper resists rotation with minimal slip, followed by a sliding phase where the moment reaches a plateau ($M_y$), indicating full engagement of frictional resistance. Activation moment ($M_y$) is calculated by Equation (5). The parameters of the RF damper used in the shake table tests are given in

Table 7. Parameters to calculate the activation moment of the RF damper.

Number of Friction Surfaces (N)	Clamping Force (Q)	$\mathbf{Outer} \mathbf{Radius} \left({\mathit{r}}_{\mathit{o}}\right)$	$\mathbf{Inner} \mathbf{Radius} \left({\mathit{r}}_{\mathit{i}}\right)$	Fric. Coefficient (μ)
2	10 kN	75 mm	5 mm	0.2

, and the parameters of the hysteresis of the RF damper are given in

Table 8. Parameter of the hysteresis of the RF damper.

$\mathbf{Moment} ({\mathit{M}}_{\mathit{y}}$)	$\mathbf{Stiffness} \left({\mathit{K}}_1\right)$	$\mathbf{Stiffness} \mathbf{Ratio} ({\mathit{K}}_2/{\mathit{K}}_1)$
150 kNmm	84.23 kN/mm	0.001

.

4.4. Verification with Numerical Analysis (STERA 3D)

Numerical Model of Six-Story Coupled Wall System with Dampers

The numerical model of the six-story coupled wall system with dampers is built using STERA 3D (version 11.5), a nonlinear finite element software developed by one of the authors [23]. Figure 24 shows the interface of STERA 3D for the test specimen. The coupling beam element is modeled as a line element with two nonlinear flexural springs for the RF dampers at both ends and one nonlinear shear spring for the VE damper in the middle, as shown in Figure 25. The end displacement vector is obtained from Equation (10) as the sum of the displacement vector of each component.

$$\left\{\begin{array}{c}{\theta }_A\\ {\theta }_B\\ {\delta }_x\end{array}\right\}=\left\{\begin{array}{c}{\tau }_A\\ {\tau }_B\\ {\delta }_x\end{array}\right\}+\left\{\begin{array}{c}{\phi }_A\\ {\phi }_B\\ 0\end{array}\right\}+\left\{\begin{array}{c}{\eta }_A\\ {\eta }_B\\ 0\end{array}\right\}$$

(10)

where

• $\theta$ is the total rotation at the element joint;
• ${\delta }_x$ is the element deformation at direction x;
• $\tau$ is the elastic element rotation;
• $\varnothing$ is the nonlinear element rotation due to the RF damper;
• $\eta$ is the nonlinear element rotation due to the shear deformation of the VE damper.

Figure 24. Analytical model of the 6-story frame in STERA 3D.

Figure 24. Analytical model of the 6-story frame in STERA 3D.

Figure 25. Elastic, nonlinear bending (RF damper), and nonlinear shear springs (VE damper) for the coupling beam modeled by STERA 3D [23].

Figure 25. Elastic, nonlinear bending (RF damper), and nonlinear shear springs (VE damper) for the coupling beam modeled by STERA 3D [23].

4.5. Results and Discussion

Figure 26 presents the maximum displacement of the structure equipped with VE dampers under five intensity levels (100%, 80%, 60%, 40%, and 20%) of Kokuji waves. From the comparison of the shear wall with VE damper (Shear Wall + VE) and the STERA 3D simulation (STERA 3D), the analytical and experimental results are in good agreement for all intensity levels. Since only a single damper is installed at the top of the coupled shear wall system, the seismic performance of the structure is governed by the mechanical characteristics of this individual damper. This may be the reason for the high consistency between analysis and experiment.

Figure 27 shows the hysteresis of a VE damper under Kokuji wave excitations obtained by STERA 3D under five intensity levels (100%, 80%, 60%, 40%, and 20%). The viscoelastic (VE) damper’s performance varies with earthquake intensity. Under weak shaking (20–40%), it shows nearly linear behavior with small movements (0.5–1 mm) and modest energy absorption. As shaking intensifies (60–80%), the damper’s movements increase (up to 2 mm) and it absorbs significantly more energy, shown by wider hysteresis loops. During extreme shaking (100%), the damper maintains stable performance while handling large displacements, proving its ability to protect structures during severe earthquakes.

Figure 28 presents the maximum displacement of the structure with RF dampers under five intensity levels (100%, 80%, 60%, 40%, and 20%) of Kokuji waves. From the comparison of the shear wall with RF damper (Shear Wall + RF) and the STERA 3D simulation (STERA 3D), the larger the input, the closer the alignment between the analytical and test results.

Figure 29 depicts the hysteresis of a RF damper under Kokuji wave excitations obtained by STERA 3D under five intensity levels (100%, 80%, 60%, 40%, and 20%). The RF damper shows consistent frictional resistance across all shaking levels, which is its key advantage.

5. Conclusions

The ultimate goal of this study is to develop a hybrid damper that combines VE dampers and RF dampers for use in boundary beams between coupled shear walls. As the first step, the hysteresis models for the VE damper and RF damper were constructed through element tests. Subsequently, the dampers were installed in a six-story frame with coupled shear walls, and their effectiveness was verified through shake table tests.

The element tests successfully demonstrate the mechanical behavior and hysteretic response of both dampers. The damper characteristics obtained from these experimental tests provide reliable input parameters for subsequent analytical modeling.

The shake table tests were conducted using both sinusoidal and Kokuji wave excitations. Results demonstrated that structural walls with VE dampers achieved greater story displacement reduction under sinusoidal loading, whereas RF dampers exhibited superior performance under Kokuji wave excitation.

The analytical models of both dampers were constructed based on the element tests and installed to the STERA 3D software to simulate the shake table test of the six-story specimen. The analytical results demonstrated strong agreement with tests for both VE and RF dampers, confirming the accuracy and reliability of the STERA 3D models.

Future research will focus on determining the optimal combination of damper quantities when both VE and RF dampers interact, analyzing the behavior of buildings with coupled shear walls equipped with the hybrid dampers, and developing corresponding design methods.