Advances and challenges in friction pendulum bearings for seismic isolation systems

Abstract

Friction pendulum bearings (FPBs) have emerged as critical structural isolation devices in the field of earthquake engineering. Extensive research and development efforts have led to the exploration and refinement of these bearings, resulting in the creation of various models with unique structural configurations and superior mechanical properties. This paper offers an in-depth review of the friction materials employed in FPBs, alongside an analysis of the mechanical performance and advancements in research regarding single-pendulum, double-pendulum, multiple-pendulum, and other types of friction bearings. Characterized by their low sensitivity and high stability, these bearings are adept at resisting seismic forces, thus providing dependable isolation protection for structures. This review also includes a succinct examination of the seismic performance and engineering applications of these isolation structures. With robust self-centering capabilities, excellent isolation, and energy dissipation mechanisms, FPBs are capable of quickly resuming normal operations post-seismic events. This reduces structural damage and maintenance expenses, significantly improving the seismic resilience of structures. Moreover, the paper outlines the current challenges in the research and development of FPBs and suggests future research directions, including optimizing friction materials, enhancing the design and performance of isolation structures, and improving the seismic performance and engineering application efficiency of FPBs. By identifying underexplored areas and synthesizing findings differently, this review provides a comprehensive and novel perspective that advances the field of earthquake engineering.

Keywords

friction pendulum bearings energy dissipation seismic resilience isolation system engineering application

Introduction

Earthquakes, marked by their unpredictability, spontaneous occurrences, substantial short-term energy releases, and extensive impacts, represent a significant natural hazard. They pose considerable risks to societal assets, national economies, and the normal functioning of communities. Historically, earthquakes have consistently ranked among the most devastating natural disasters encountered by humankind (Xu et al., 2023, 2024), as shown in Figure 1. The 7.8 magnitude earthquake in Tangshan in 1976 resulted in the deaths of 240,000 people and left 160,000 seriously injured, reducing a century-old industrial city to rubble (Cheng and Wang, 2006). The 7.2 magnitude earthquake in Hanshin, Japan, in 1996 claimed over 5400 lives, left over 300,000 homeless, and caused economic losses exceeding $100 billion (Zhou, 1996). The 8.0 magnitude Wenchuan earthquake in China in 2008 led to nearly 70,000 deaths, around 20,000 people missing, approximately 370,000 injured, and affected over 40 million people, with direct economic losses exceeding 845.1 billion RMB and reconstruction costs estimated at around 1 trillion RMB (Wei, 2008; Zhao et al., 2009). In 2011, the 6.3 magnitude earthquake in Christchurch, New Zealand, resulted in nearly half of the buildings in the central business district becoming unusable due to severe damage, leading to the demolition of nearly 1000 structures. The estimated cost for recovery and reconstruction following the earthquake was projected to be around NZ$40 billion (ATC, 2005; New Zealand Treasury, 2013).

Figure 1.

Earthquake induced damage to buildings.

Given the current technological limitations in earthquake prediction, the primary strategy for mitigating earthquake risk focuses on enhancing the seismic performance of building structures (Xu et al., 2023a, 2023b; Xu and Li, 2020). Recent advancements in seismic isolation technology have been crucial in increasing the seismic resilience of buildings. Traditional seismic reinforcement methods typically involve enlarging member cross-sections and enhancing the load-bearing and deformation capacities of structures or components to improve inherent seismic resistance. Although these approaches have significantly improved structural durability against earthquakes, they face several challenges, including difficulties in ensuring seismic safety beyond the design basis, limited adaptability, suboptimal cost-effectiveness, and complexities in post-earthquake repairs.

Contrary to traditional methods that emphasize resistance, seismic isolation strategies involve situating the entire building or specific floors atop isolation layers. As seismic waves travel through the soil and reach the structure, the isolation bearings within these layers serve to filter out high-frequency vibrations, enabling the isolation layer to absorb most of the seismic energy transmitted. This approach significantly localizes the displacement response to the isolation layer itself, markedly reducing the impact on the structure above and minimizing damage to non-structural elements. By removing the rigid connection between the superstructure and the foundation, seismic isolation bearings cause an increase in the structure’s period due to a pronounced reduction in lateral stiffness at the base, and enhance the damping ratio of the entire structure. Thus, seismic isolation devices effectively mitigate the structural response to seismic activity by employing a strategy of “overcoming firmness with flexibility,” making them more adept at controlling structural acceleration and damage than traditional seismic resistance and damping methods. This technology not only preserves the primary integrity of the structure but also substantially limits seismic damage to non-structural components, offering both safety and functional protection. Remarkably, even in the event of seismic activity that exceeds design expectations, seismic isolation technology can effectively maintain the structural integrity of buildings.

Seismic isolation bearings are essential in reducing seismic forces on structures, with various types available, including rubber bearings, flat sliding bearings, roller sliding bearings, and friction pendulum bearings, as shown in Figure 2. Among these, laminated rubber bearings are the most used in practical engineering due to their effective combination of rubber and steel plates. This configuration significantly enhances the vertical stiffness of the bearing while maintaining adequate horizontal flexibility, effectively isolating the structure from ground motion. Lead-core rubber bearings, a specific type of rubber bearing, have gained widespread recognition for their seismic isolation capabilities over the past few decades. However, rubber bearings come with their set of challenges. Their fire resistance is poor, and they exhibit a reduced load-bearing capacity at high temperatures. Additionally, these bearings can experience changes in their periods of vibration and are susceptible to aging, compromising their long-term effectiveness. A notable drawback is their lack of self-centering capability, which can necessitate the integration of auxiliary systems to reposition the structure post-earthquake. This lack of inherent self-centering makes the management of excessive sliding difficult, potentially damaging the isolation layer and increasing seismic risk.

Figure 2.

Seismic isolation bearings. (a) Rubber bearing. (b) Flat sliding bearing. (c) Roller sliding bearing. (d) FPB.

Flat sliding bearings offer a simpler solution by using a low-friction material layer between two metal plates, allowing for energy dissipation and seismic force isolation through sliding friction. Due to their relatively low manufacturing costs, they are a popular choice in less affluent regions. Roller sliding bearings, developed to further decrease horizontal stiffness, replace sliding friction with rolling friction. Despite their advantages, the higher costs and lack of self-restoring features after an earthquake limit their application in engineering projects.

Classic FPBs, introduced by Zayas et al. (1987), feature a horizontal slider and upper and lower sliding surfaces with matching curvature radii, coated with low-friction materials like PTFE or nylon. Under seismic forces, the slider moves in a pendulum-like motion along the concave surface, extending the structural natural period and increasing the damping ratio to achieve isolation. The restoring force, a combination of gravity and friction, re-centers the FPB after displacement. Subsequent studies by Zayas et al. (1993, 1997) examined FPBs’ mechanical performance under various conditions, highlighting their self-centering feature, which ensures a smooth return to equilibrium.

FPBs allow the isolation structure’s period to depend on the bearings’ design parameters, enabling predictable seismic responses. The alignment of the FPBs’ stiffness center with the isolation structure’s centroid reduces torsional movements, enhancing seismic impact mitigation. These bearings can be customized for period, vertical load capacity, damping ratio, lateral displacement, and tensile strength, allowing designers to optimize the isolation system for specific projects. FPBs are durable, with lifespans exceeding 100 years, and they exhibit minimal environmental impact and sensitivity to temperature variations, making them reliable in diverse conditions.

Since the advent of FPBs, a substantial body of research has been dedicated to exploring and enhancing their mechanical performance. With ongoing experiments and refinements, FPBs have diversified into various configurations based on the number of sliding surfaces, including single-pendulum, double-pendulum, triple-pendulum, and multiple-pendulum designs (Gong and Zhou, 2010). Unlike the single-pendulum variant, which incorporates only one sliding surface, the double, triple, and multiple-pendulum configurations feature multiple sliding surfaces, enabling larger horizontal displacements. By employing sliding surfaces with distinct curvature radii and friction coefficients, these configurations can offer variable stiffness at different displacement stages, thus providing enhanced design flexibility.

FPBs are predominantly classified into surface-type, groove-type, and hybrid surface-groove configurations based on their geometric design. The surface-type category encompasses traditional friction pendulum isolation bearings, along with those featuring variable curvature and friction coefficients. In comparison to rubber bearings, FPBs deliver comparable isolation performance but boast a significantly greater vertical load capacity. Moreover, for the same specifications, FPBs facilitate larger horizontal displacements, with the possibility of extending displacement limits through the addition of additional pendulums. Research on the performance of FPBs, as well as structures outfitted with them, has been conducted through theoretical analyses, experiments, and numerical simulations, affirming their superior isolation capabilities. After decades of development, both the theoretical foundation and practical applications of FPBs have reached a mature stage, leading to their broad implementation in engineering projects.

To provide a comprehensive overview of the recent advancements and prevailing challenges associated with FPBs, this paper begins with a review of the distinct types of FPBs, their characteristics, and research progress. It then highlights the latest research findings concerning the seismic performance of isolation structural systems employing FPBs. Additionally, this paper presents exemplary cases of engineering applications featuring FPBs. Concluding with an analysis of current issues facing FPBs, this paper sets the stage for future research directions and engineering applications.

Mechanical behavior of FPBs

Frictional coefficient

The friction coefficient on the sliding surface is a paramount parameter influencing the efficacy of FPBs. Unlike other factors, such as the curvature radius of the sliding surface, determining an accurate friction coefficient poses greater challenges. Comprehensive experimental investigations into the friction contact surface have revealed that materials like PTFE and ethylene propylene can be utilized to secure a lower friction coefficient on the sliding surface (Pigouni et al., 2020).

PTFE is known for its excellent wear resistance, low friction, and thermal stability, making it suitable for FPBs. It can withstand high pressures and temperatures without significant degradation, ensuring long-term durability. High-density polyethylene (HDPE), on the other hand, offers high impact resistance and good wear properties but may not perform as well as PTFE under elevated temperatures and prolonged loading conditions.

Mechanical testing of FPBs under varying pressures, sliding velocities, and temperatures has demonstrated that the static friction coefficient on the sliding surface significantly exceeds the dynamic coefficient, approximately doubling it. The dynamic friction coefficient escalates with the bearing’s sliding speed and vertical load until it stabilizes at a constant value. This stability under prolonged load conditions renders it ideal for seismic isolation layers in construction (Mokha et al., 1991; Ryuichi et al., 2008). It is noteworthy that the vertical load’s impact on the friction coefficient becomes markedly significant only at elevated sliding speeds. The friction coefficient decreases swiftly with an increase in the temperature of the contact surface, particularly when temperatures are below 20°C. Frictional heating most prominently affects the friction coefficient under heavy vertical loads. In essence, the vertical load and sliding velocity’s effect on the structural response is minor, aligning closely with findings derived from Coulomb’s friction criterion (Kumar et al., 2015; Tsepelas and Constantinou, 1994), as shown in Figure 3.

Figure 3.

Friction coefficient on the sliding surface of the FPBs (Kumar et al., 2015). (a) Variation in the friction coefficient with sliding velocity, axial pressure and temperature. (b) Experimental and simulated normalized force-displacement histories of the FPB.

Constantinou et al. (1990) and Mokha et al. (1990, 1993) have performed extensive experimental and theoretical investigations into the reliability and durability of PTFE lining materials used on sliding surfaces in FPBs. These studies highlight that the friction coefficient in FPBs is influenced not only by the properties of the friction materials but also by the sliding speed, pressure, and temperature on the contact surface. Experimental findings demonstrate that the dynamic coefficient of friction is lower than the initial static coefficient, which remains stable even under prolonged external loading. The sliding friction coefficient consistently remains low, underscoring its suitability for base isolation applications. Dolce et al. provided comprehensive summaries of large-scale experimental studies on the steel-PTFE interface, offering expressions for modeling parameters of both lubricated and non-lubricated sliding surfaces as functions of bearing pressure and changes in air temperature. The findings show that the friction coefficient on the contact surface spikes with an increase in speed, then reaches a steady state. With an increase in contact pressure, the friction coefficient declines, and it similarly decreases as the air temperature rises (Bondonet and Filiatrault, 1997; Dolce et al., 2005).

Single-pendulum bearings

After decades of advancement, FPBs have diversified into various configurations. Among these, the classic friction single-pendulum bearings, depicted in Figure 4, feature a singular sliding surface. These bearings are differentiated into upper and lower bearings, with their sliding surfaces oriented upwards and downwards, respectively. Lower bearings, whose sliding surfaces face downwards, are predominantly utilized for inter-story isolation. Conversely, upper bearings, with sliding surfaces facing upwards, are primarily employed for base isolation. Within the isolation device, the contact surface radius between the sliding surface and the slider is uniform, resulting in surface contact between the slider and the sliding surface throughout the sliding motion. Despite a minor increase in contact surface amplitude during this process, the upper bearing plate of the FPB maintains a horizontal orientation, thanks to the convex sliding block. The sliding surface comprises a concave stainless steel arc, while the slider is a protruded sliding block. The horizontal restoring force generated by the concave arc surface enables the building’s upper structure to automatically revert to its original position, leveraging its self-weight (Zhu, 2018).

Figure 4.

Classic friction single-pendulum bearings (Zhu, 2018). (a) Sliding surface facing upwards. (b) Sliding surface facing downwards.

The bearing structure endures vertical loads alongside varying horizontal loads. When the actual horizontal force is below the frictional force threshold, the bearing remains stationary, exhibiting stiffness comparable to that of a fixed support. In contrast, significant seismic activities that induce horizontal forces surpassing the frictional force lead to relative sliding between the sliding surfaces, causing a minor uplift of the upper structure. This uplift triggers a restorative motion due to the structure’s weight, as depicted in Figure 5(a). Figure 5(b) illustrates the operational principle of the friction pendulum isolation system, where the bearings facilitate pendulum motion for the upper structure across the arc sliding surface, simultaneously ensuring horizontal stability via the sliding joint. The vertical force exerted on the bearings supplies the requisite restoring force, while frictional sliding between the surfaces provides initial stiffness and dissipates kinetic energy (Gong et al., 2011). The curvature radius between the sliding surfaces dictates the system’s overall stiffness and period, with damping efficiency governed by the friction coefficient between these surfaces (Gong and Zhou, 2010). Minimizing the friction coefficient between the sliding surfaces is crucial to effectively limiting shear forces transmitted to the upper structure. Yet, exceedingly low friction coefficients could undermine the bearings’ capacity to counter seismic forces during major earthquakes, thereby diminishing isolation efficacy. Furthermore, traditional FPBs often display high initial stiffness, characterized by a stark transition from initial to sliding stiffness (Fenz and Constantinou, 2007).

Figure 5.

Working principle of friction single-pendulum bearing. (a) Motion diagram. (b) Force diagram.

Double-pendulum bearings

The double-pendulum bearing (Deng et al., 2010), an evolution of the friction single-pendulum isolation technology, offers enhanced flexibility in performance tuning compared to its single-pendulum counterparts, showing promising development prospects. The structural components and isolation principles of the double-pendulum bearing closely mirror those of the single-pendulum variant, consisting of upper and lower bearing plates and a hinged slider that mitigates seismic energy through friction and a rocking motion.

At the heart of this bearing is the hinged slider, designed to seamlessly interface with both the upper and lower spherical sliding surfaces. During seismic activity, the upper bearing plate maintains a horizontal position, and thanks to the spherical nature of the sliding surfaces, the bearing employs both friction and rocking motions for energy dissipation. The spherical configuration of the sliding surfaces enables gravity-driven automatic re-centering of the slider, thereby minimizing residual displacement post-seismic events. A distinguishing feature of the double-pendulum bearing is its enhanced design, incorporating spherical sliding surfaces for both upper and lower friction points on the hinged slider. This design significantly increases its displacement capacity, offering double the displacement potential of a similarly sized FPB, as illustrated in Figure 6.

Figure 6.

Working principle of friction double-pendulum bearing.

Yan and Liu (2014) analyzed the motion of structures with double-pendulum bearings during seismic events using Lagrange equations and the Runge-Kutta method, generating time-history plots for displacements, velocities, and accelerations. They concluded that double-pendulum bearings offer substantial isolation efficiency. Han (2013), along with Wang et al. (2014) derived and solved nonlinear autonomous vibration differential equations for double-pendulum bearings, using MATLAB to represent phase plane characteristics and identify motion types and stability. Their findings indicated a globally asymptotically stable motion type with decaying vibrations. Feng et al. (2017) used a simplified model to assess the seismic response of smoke ducts with double-pendulum bearings, demonstrating significant mitigation of reaction and support shear forces during seismic events.

Deng et al. (2010) investigated the isolation efficacy of double-pendulum bearings, formulating hysteresis models and residual displacement calculation formulas based on theoretical analyses. Upon validating these models and formulas, their theoretical analysis and numerical simulations revealed that: (i) Double-pendulum bearings demonstrate superior hysteresis energy dissipation capabilities. (ii) The stiffness of double-pendulum bearings inversely correlates with the aggregate of the radii of the upper and lower sliding spherical surfaces. (iii) Post-seismic events, double-pendulum bearings do not ideally revert to their initial positions, with their self-centering capacity being contingent upon the friction coefficient and the radii of the sliding surfaces of the upper and lower bearings. (iv) Absent contact of the isolation bearing’s slider with the limit end, the maximum stress is localized at the port of the spherical hinge surface. Yu (2018) evaluated how parameters like curvature radius and friction coefficient impact isolation performance under different peak ground acceleration (PGA) levels. Double-pendulum bearings showed better performance than traditional FPBs, especially in seismic events with PGAs exceeding 0.4 g.

Fenz and Constantinou (2007) undertook an in-depth analysis of the mechanical behavior of friction double-pendulum bearings. Their research validated experimental outcomes with varied parameters for the concave surfaces and offered recommendations for enhancing the isolation capabilities of double-pendulum bearings, as well as considerations for isolation design. Similarly, Malekzadeh and Taghikhany (2010) conducted a comparative study on the seismic responses of structures equipped with ordinary FPBs versus those with double-pendulum bearings. Their investigation underscored the superior performance of double-pendulum bearings in terms of peak acceleration and displacement, affirming the advantages of double-pendulum bearings over traditional friction pendulum systems.

Multiple-pendulum bearings

In recent years, friction multi-pendulum bearings have garnered significant interest within the engineering community due to their adaptive properties during sliding, exhibiting distinct mechanical behaviors under various seismic intensities. By adjusting the geometric parameters and friction materials of the sliding surfaces, multi-pendulum bearings can provide variable stiffness and damping throughout their motion, effectively meeting isolation needs across different seismic scenarios (Shang, 2017). Among these, the triple-pendulum bearing is particularly well-suited for performance-based design. Morgan (2007) have noted several advantages of the triple-pendulum bearing over traditional rubber bearings, including the elimination of rubber aging concerns, enhanced durability, and self-centering properties. Furthermore, the triple-pendulum bearing requires over 60% less space than conventional single-pendulum bearings to achieve similar isolation effectiveness (Yan, 2018), significantly reducing construction costs.

As depicted in Figure 7, the triple-pendulum bearing consists of four concave surfaces and three independent pendulum mechanisms. Adjustments in physical quantities such as the curvature radius and slider height, along with the friction coefficients of each concave surface, allow the design of sliding stages to match various seismic response levels (Morgan, 2007; Morgan and Mahin, 2008). Although passive, the bearing’s stiffness, and damping change with the extent of sliding displacement, demonstrating adaptive behavior. This adaptivity’s principal benefit is its ability to tailor the isolation system to multi-level seismic inputs and performance targets. As the bearing transitions between sliding surfaces, stiffness and friction coefficients adjust accordingly. With three discrete sliding limits, this bearing, through thoughtful design, can meet “three-level” seismic design criteria (Chen et al., 2009).

Figure 7.

Working principle of friction three-pendulum bearing. (a) Stationary state. (b) Middle slider sliding state. (c) Lower slider sliding state. (d) Upper slider sliding state.

Xu (2020) performed shake table experiments on high-rise buildings equipped with triple-pendulum isolators compared to non-isolated models. The study documented the seismic responses of these structures under varied seismic intensities and analyzed the isolation benefits of triple-pendulum bearings across different seismic levels. The findings indicated that, relative to non-isolated models, the triple-pendulum isolated structures showed significant reductions in inter-story drift angles and absolute accelerations of the upper structure under various seismic intensities. Notably, as seismic intensity escalated, the isolation performance of the triple-pendulum bearings improved. However, the seismic response was notably affected by collisions among the bearings’ internal components. Such collisions led to a sharp increase in the maximum inter-story drift angle, potentially hastening structural failure. Li (2017) explored the sliding mechanism of triple-pendulum bearings, grounding the analysis in traditional FPB sliding theories. The study examined the forces and displacements under different sliding mechanisms and validated the theoretical analysis by correlating sliding theories with experimental observations. Utilizing experimental data, a finite element model of triple-pendulum bearings was developed for numerical simulations. The analysis outcomes revealed that triple-pendulum bearings could adaptively modify stiffness and damping in real-world scenarios, and the theoretical model was proven to predict such behaviors accurately and reliably.

Zhao (2017) developed an enhanced triple-pendulum bearing that integrates the super-elastic properties of shape memory alloys (SMAs) and the high damping capabilities of SMA helical springs, building upon traditional triple-pendulum designs. This innovative device comprises upper and lower bearing plates, nested sliders, and SMA helical springs connecting the four corners of the upper and lower plates. The unique sliding mechanism of this improved bearing reacts differently under various seismic forces due to the specific arrangement of sliders and SMA helical springs. This configuration allows the bearing’s stiffness and damping properties to vary within a certain displacement range, making it versatile enough to accommodate seismic events of varying intensities. As the sliding surfaces engage in a specific sequence, the isolation bearing’s equivalent stiffness, radius, and friction coefficient adjust accordingly. Continuing this line of innovation, Lee and Constantinou (2016) introduced a friction five-pendulum isolation bearing, which further extends the operational versatility of triple-friction pendulums. They developed an analytical model to accurately describe the isolator’s performance across various geometric and frictional states. This model is crucial for validating computational models and simplifying calculations in the analysis and design processes. The successful experimental testing of a quintuple friction pendulum isolator prototype confirms the reliability of both the analytical and computational models.

Other types of FPBs

Based on the classic FPB, Yao (2018) developed a novel segmented slip FPB incorporating a rotating fork mechanism, which enhances the system with self-centering capabilities. This innovative bearing operates in two distinct modes: under small slip conditions, it engages in swinging slip alone, using frictional damping to reduce seismic energy transmission to the superstructure. In contrast, during strong earthquake scenarios, the bearing undergoes both swinging and rotational slip, augmenting its frictional damping effectiveness. The bearing’s sliding contact surface is spherical, allowing for the adjustment of the isolation period by modifying the swing radius.

Zhang (2019) introduced an innovative semi-active tunable FPB that merges the seismic isolation and frictional damping energy dissipation features of traditional FPBs with the continuous adjustability provided by active control technology, as depicted in Figure 8(a). This design facilitates the continuous adjustment of the horizontal friction force, as supported by theoretical analysis. A scaled-down model for a single-pendulum configuration was meticulously designed and constructed. Through experimental investigations, the adjustability of the novel semi-active tunable FPB was validated, alongside the accuracy of the theoretical model. The experiments, carried out across various displacement amplitudes and oil pressure settings, affirmed the bearing’s adjustability and the alignment between theoretical predictions and empirical data. The horizontal friction force can be fine-tuned by altering the normal pressure distribution on the sliding block’s surface.

Figure 8.

Novel friction three-pendulum bearings. (a) Semi-active tunable FPB (Zhang, 2019). (b) 3D vibration isolation device (Cao et al., 2022).

Cui (2022) tackled the challenge of insufficient tensile resistance in existing FPBs by introducing a novel design: a friction double-pendulum bearing equipped with a damper. This design not only resists vertical tensile forces but also improves stiffness and energy dissipation capabilities. The expressions for stiffness and period were derived from basic mechanical principles. A numerical model was created in ABAQUS software to assess the bearing’s energy dissipation capacity and hysteresis behavior. The findings indicated that the innovative FPB with a damper exhibits a powerful energy dissipation mechanism, attributing approximately 95% of the energy dissipation to the damper’s function. Additionally, the damper’s presence significantly mitigates or eliminates plastic damage to the FPB. He (2022) introduced a tensile-resistant FPB design, connecting various components through lug connections to counteract tensile forces and restrict the bearing’s vertical displacement. This approach addresses the issue of component separation seen in conventional FPBs, markedly improving the isolation layer’s resistance to overturning. Moreover, this solution allows for the decoupling of horizontal displacements in two directions.

To further bolster the tensile resistance of FPBs, Roussis (2004), Roussis and Constantinou (2006) proposed a grooved tensile-resistant FPB. This model is adept at isolating near-fault seismic activities and can also withstand overturning moments in structures with aspect ratios exceeding 4.5. Analysis from 1/4 scale testing showed consistent performance under seismic actions at 0, 45, and 90°, specifically under conditions of unidirectional horizontal and vertical seismic coupling. Amarnath and Michael (2005) investigated the application of preloading to improve the tensile resistance of FPBs. Their studies demonstrated that preloading can provide tensile resistance while minimally affecting the horizontal performance of the bearing.

To address the issue of inadequate tensile resistance in FPBs and enhance their seismic performance, Li et al. (2024) introduced an adaptive magnetic levitation anti-pull FPB, integrating semi-active control with traditional FPBs. This advanced bearing features a sawtooth hysteresis curve, offering superior energy dissipation and limit control. The tensile resistance is influenced by limit displacement, coil turns of the U-shaped electromagnet, and input current. Zhuang et al. (2020) developed a multifunctional FPB and conducted quasi-static tests to examine the effects of vertical pressure, displacement amplitude, and loading frequency on its hysteresis behavior and mechanical performance, highlighting its exceptional energy dissipation capacity and adaptive potential.

Jin (2019) proposed a variable parameter FPB to optimize isolation during small-to-medium earthquakes and control displacement during significant seismic events. This bearing adjusts damping and stiffness based on displacement, enhancing its engineering applicability. Pranes and Sinha (2000, 2004a, 2004b) introduced variable frequency pendulum bearings, showing their effectiveness in reducing torsional coupling and responses under near-fault ground motions. Panchal and Jangid (2008) analyzed the seismic performance of various structures with variable curvature FPBs, contributing to seismic isolation research.

Cao et al. (2022) introduced a 3D vibration isolation device combining a disc spring vertical isolation unit with a single friction pendulum horizontal isolation unit, as shown in Figure 8(b). Full-scale tests under compression-shear conditions demonstrated independent vertical and horizontal functionalities, with significant reductions in structural responses during horizontal seismic events and vertical subway vibrations. This device showed a reduction of over 80% in structural responses during horizontal seismic events and a 61% decrease in floor vertical acceleration responses under subway vibrations.

Seismic performance of friction pendulum isolation structure systems

Performance analysis

Isolation systems incorporating FPBs demonstrate dynamic behaviors that distinguish them from other structural systems, prompting in-depth investigations by various scholars. Sun (2013) applied time-frequency analysis techniques and utilized MATLAB/Simulink for wavelet packet decomposition and reconstruction of dynamic responses in dual-mass and multi-mass isolated structures. This study explored how the friction coefficient, slider radius, mass ratio, and the natural period of the upper structure influence the distribution of acceleration response energy within isolated structures. Findings revealed that in dual-mass isolated structures, the bulk of the acceleration energy in the upper structure is focused in the low-frequency range, with a negligible presence in the high-frequency range. Moreover, an increase in the friction coefficient and a reduction in slider radius resulted in greater acceleration energy in the upper mass, while variations in mass ratio and the natural period of the upper structure notably altered the acceleration energy distribution pattern. For multi-mass isolation structures, the analysis showed that a substantial portion of the energy is absorbed by the isolation layer, leaving only a minimal amount of acceleration energy in the upper structure. The acceleration energy in the upper structure predominantly falls within the low-frequency domain, whereas the isolation layer experiences high-frequency components, highlighting a “filtering” effect by the isolation bearings. Consistent with the findings from dual-mass systems, increasing the friction coefficient and reducing the slider radius were associated with higher acceleration energy in the upper mass. Almazan et al. (1998; Almazan and Llera, 2003) developed dynamic differential equations for isolated systems featuring FPBs through detailed theoretical analysis, considering the impact of “viscous” phenomena during sliding. Their studies underscored the notable influence of these “viscous” phenomena on the accuracy of computational outcomes during the sliding phase.

He and Wang (2013) explored the seismic isolation performance of friction pendulum isolation frame structures, focusing on multi-story reinforced concrete frames. They compared these structures, equipped with FPBs, to their non-isolated counterparts across various seismic intensity levels, including both frequent and rare events. Their findings highlighted that the isolation system extended the structure’s period, exhibited a “K”-shaped distribution in maximum floor acceleration across different layers, and maintained relatively small inter-story displacements, suggesting a primarily translational movement. Notably, under high seismic intensity, the base-level maximum inter-story shear force was significantly reduced, evidencing a pronounced isolation effect. Constantinou et al. (1991) performed shake table tests on a six-story scaled steel frame with FPBs. The tests, conducted under EL-Centro wave (0.78 g) excitation, showed that the isolated structure remained undamaged. Dynamic differential equations were used to forecast the structure’s response, with predictions closely aligning with actual experimental outcomes.

Yang (2014) assessed the seismic performance of asymmetric frame structures isolated with FPBs. By establishing coupled horizontal-torsional dynamic equations for horizontal seismic activity, the study analyzed eight-story asymmetric reinforced concrete frame’s dynamic responses, both with and without isolation. The findings demonstrated that isolation effectively mitigates both horizontal and torsional responses in asymmetric structures, yielding significant reductions in inter-story displacement, floor accelerations, torsional angles, and column forces when compared to non-isolated setups. Mokha et al. (1993) examined the mechanical behavior of FPBs under bi-directional dynamic loading, identifying coupling effects during bi-directional sliding. Ignoring these effects in analysis could lead to underestimating displacement amplitudes and overestimating shear forces in isolated structures. Rabiei and Khoshnoudian (2011) conducted a seismic analysis on a multi-story building using FPBs, focusing on vertical seismic excitation. Through the application of the Newmark-β method to derive motion equations, the study highlighted the significant impact of vertical seismic excitation on structures with FPBs in engineering applications.

Duan and Zhang (2021) tackled inter-story seismic control using FPBs by developing finite element models for both the bearings and the seismic isolation structures, as shown in Figure 9(a). They analyzed the effects of varying parameters, such as friction coefficient and slider radius, on system performance. The study found that increasing the friction coefficient improved initial stiffness and reduced top floor acceleration, while also decreasing relative displacement between the bearings’ plates. Expanding the slider radius reduced swing stiffness, further managing isolation layer deformation. Adjusting the isolation layer’s placement influenced the structure’s dynamic properties by altering modal participation mass coefficients, effectively modifying higher-order modes.

Figure 9.

Friction pendulum isolation structures. (a) Inter-story seismic isolation structures (Duan and Zhang, 2021). (b) Triple-pendulum isolation high-rise building (Xu, 2020). (c) Curved surface isolated structure (Liu et al., 2020).

Xu (2020) conducted a comprehensive study on high-rise building isolation using triple FPBs, combining theoretical analysis, experimental testing, and finite element analysis with optimization design techniques. Shaking table tests on high-rise building models demonstrated the bearings’ effective isolation capabilities under various seismic intensities (Figure 9(b)). Zhou (2019) performed shaking table tests on high-rise frame-shear structures with FPBs, addressing the tension separation phenomenon and proposing a scaling design method for accurate experimental replication, validated through analysis and testing.

Liu et al. (2020) addressed excessive deformation of isolation layers and its impact on structural safety during severe seismic events by introducing an innovative isolation structure with bearings positioned along a curved surface (Figure 9(c)). They developed a simplified dual-degree-of-freedom dynamic model to extract critical system dynamics parameters, such as precession, nutation, and pendulum frequencies. Through shake table experiments on steel frame models with isolation layer surface angles of 0°, 4°, and 8°, they assessed the impact of these parameters on seismic response. The findings indicated that structures with curved surface bearings exhibited more rounded force-displacement hysteresis loops and reduced horizontal displacement of the isolation layer by 30% to 40% under a peak ground acceleration of 0.3 g, compared to flat plane bearings. Although there was a slight increase in acceleration, the curved surface design effectively minimized the displacement of the isolation layer.

Li et al. (2015) examined structures isolated with two types of FPBs and additional viscous dampers, focusing on their behavior under near-fault and far-field seismic activities. They discovered that near-fault excitations led to increased upper structure displacement with higher damping ratios, while other responses were either stable or decreased; contrastingly, under far-field conditions, all dynamic responses tended to rise with increased damping ratios. The incorporation of additional viscous dampers was particularly effective in mitigating the larger horizontal displacements characteristic of FPBs under near-fault conditions, highlighting the critical role of the damping ratio coefficient in design. A 20% damping ratio for viscous dampers was recommended for optimal performance.

He (2022) utilized dynamic time-history analysis to assess the performance of an innovative anti-pullout isolation bearing, comparing it to traditional FPBs with equivalent periods on a standard frame structure. The anti-pullout bearings demonstrated a reduced discrepancy in inter-story displacements within the isolation layer during rare seismic events, thereby diminishing the potential for structural overturning. Moreover, structures with anti-pullout bearings showed a controlled increase in floor accelerations relative to their non-isolated counterparts. As the peak ground acceleration and the number of floors rose, the difference in peak accelerations progressively expanded. Kim et al. (2009) delved into the potential of FPBs for nuclear power plant control rooms, conducting a comprehensive theoretical and experimental comparative analysis to confirm their applicability within nuclear facilities. Vern et al. (2010) investigated the suitability of FPBs for liquid storage tanks, concluding that these bearings are particularly beneficial for tall and wide tanks. Nonetheless, they also noted an associated risk of tank overturning under near-fault seismic conditions, pointing out an area of concern that requires careful consideration in the application of FPBs.

Engineering applications

After years of dedicated research and development, the field of FPBs has seen remarkable progress, culminating in their integration into engineering practices and design standards across various countries. By 2007, both the United States and Japan had already incorporated isolation design methodologies involving FPBs into their building codes. Following their lead, China introduced two seismic design codes specifically for FPBs: one targeting highway bridges (JT/T 852-2013, 2013) and “Friction pendulum isolation bearings for buildings” (GB/T 37358-2019, 2019). Reports suggest that in the United States and Japan, the number of structures employing FPBs ranges from hundreds to thousands (Chen et al., 2008). Additionally, the Beijing Modern International City stands as a pioneering example of the practical engineering application of FPBs in China, signifying their growing acceptance and implementation in major construction projects worldwide. This global adoption underscores the effectiveness and reliability of FPBs in enhancing seismic resilience in infrastructure.

The Padma Bridge (Figure 10(a)) (Li et al., 2023), situated in Bangladesh, stands as a critical transport link under the Belt and Road Initiative and a key element of the Pan-Asian Railway network, representing the largest bridge endeavor to date. Spanning 6.15 km, this integrated road and rail bridge navigates a challenging environment prone to natural adversities such as earthquakes, strong winds, and floods. To mitigate these risks, the bridge incorporates the world’s most substantial dual-curved surface friction pendulum seismic isolation bearings, designed to significantly reduce seismic forces exerted on the structure during earthquakes, thereby safeguarding its operational integrity. These specialized bearings exhibit distinctive features; their hysteresis curve displays a standard bilinear pattern, facilitating reduced stiffness restoration during oscillatory movements. This attribute effectively lengthens the vibrational period of the bridge’s superstructure, preventing resonance with the seismic waves’ intrinsic frequencies. Additionally, the lateral force generated by the friction pendulum isolation bearings escalates with lateral displacement under a consistent vertical load, enhancing the bridge’s seismic isolation capacity. The robust and comprehensive hysteresis curves, consistently full across varying sliding displacements and vertical loads, underscore the bearings’ superior isolation performance. Furthermore, the high degree of congruence among the hysteresis loops under reciprocal loading indicates the system’s stable mechanical performance, highlighting the innovative engineering behind the Padma Bridge’s design to ensure resilience against natural disasters.

Figure 10.

Typical engineering applications of friction pendulum isolation structures. (a) Padma bridge. (b) CenturyLink field. (c) San Francisco international airport. (d) Taipei arts center.

In Europe, the aftermath of the 2009 L’Aquila earthquake in Italy saw a rapid adoption of seismic isolation technologies, with over 5000 FPBs and 2500 friction double-pendulum bearings deployed in new constructions within Italy in less than a year. The advancement and application of friction pendulum isolation technology have significantly accelerated, finding widespread use in both new builds and retrofitting projects (Gino et al., 2020; Sorace and Terenzi, 2014), as well as in special seismic isolation structures (Alexandros and Yiannis, 2021; Kazantzi and Vamvatsikos 2021). In the United States, the CenturyLink Field (Figure 10(b)), an American football stadium in Seattle, utilized four FPBs to safeguard its roof structure. Additionally, the Emergency Operations Center in Washington State incorporated FPBs, achieving a 50% reduction in base shear and enhancing the building’s resilience to withstand seismic events surpassing the 6.8 magnitude of the Nisqually earthquake. The terminal building of San Francisco International Airport (Figure 10(c)), recognized as the largest isolated structure globally, incorporated 267 FPBs to bolster structural integrity against earthquake impacts.

The Bosporus Viaduct Bridge in Turkey underwent seismic retrofitting using over 500 FPBs, designed for a maximum displacement exceeding 600 mm (Zhou and Gong, 2010). At the Taipei Arts Center (Figure 10(d)), FPBs were integrated into the main structure, which is characterized by an uneven mass distribution. In Ishikawa Prefecture, Japan, a construction company’s technical research laboratory was outfitted with friction double-pendulum bearings, which experienced a maximum displacement of only 5 mm during a 6.7 magnitude earthquake in 2000. In Istanbul, Turkey, the Basaksehir Hospital, spanning 950,000 square meters with more than 2600 beds, was equipped with over 2000 friction triple-pendulum isolation bearings. Following the 2011 Christchurch earthquake, the Christchurch Art Gallery in New Zealand adopted friction triple-pendulum bearings to safeguard its invaluable art collection. A bridge over Lake Natoma in California, USA, measuring 690 m in length, utilized 48 FPBs to achieve structural resilience against design-level seismic forces, achieving a cost savings of $1 million attributed to the application of FPBs.

The Bolu Viaduct Highway Bridge in Turkey, which bridges Europe, was significantly damaged during the 7.2 magnitude Duzce earthquake in 1999, particularly its energy dissipating devices and pot-type rubber bearings (Chen et al., 2009). In response, the American Society of Civil Engineers sent a team to investigate and contribute to the redesign efforts, ultimately deciding to reinforce the structure using friction pendulum isolation devices. To accommodate variations in pier height and fault crossing locations, three different specifications of FPBs were utilized. The bridge was outfitted with a total of 536 FPBs, each designed to accommodate a horizontal displacement capacity with a safety margin of at least 1.5 times. As per American design standards, all bearings were subject to prototype dynamic testing. The I-40 Bridge, crossing the Mississippi River, is an essential conduit for transportation, commerce, and safety in the Memphis area, situated on the southeastern edge of the New Madrid seismic zone - a region notorious for experiencing three of the strongest earthquakes in the Midwest United States during the 19th century. The incorporation of FPBs into the bridge’s design ensures its resilience against a 7.0 magnitude earthquake occurring along the New Madrid fault. Thanks to the implementation of FPBs, this bridge, now over 40 years old, is expected to continue functioning normally even after severe seismic events. The transition to FPBs for the bridge’s reinforcement resulted in a construction cost saving of $16 million compared to traditional reinforcement methods. This cost efficiency was achieved by reducing the required strength of the superstructure, piers, and foundations as much as possible.

Future directions

Many types of FPBs have been developed over the years, yet there is an urgent need to deepen the understanding of these systems among professionals across various stages such as product design, production, testing, construction, and supervision. Despite the significant achievements, FPBs still face a myriad of challenges. For instance, in the design phase, the tendency to set small displacement limits to control costs can lead to collisions between upper and lower bearing plates under intense seismic activities. Although FPBs require more steel compared to rubber bearings and steel is considered more fire-resistant, the friction material in these bearings may vaporize in a fire, causing significant deviations from expected friction performance. Furthermore, installations in adverse environmental conditions like dampness or water immersion often result in the corrosion of steel components, affecting the friction coefficient and causing malfunctions, thus increasing maintenance demands. Theoretically, FPBs have a longer lifespan, but issues such as uneven wear on sliding surfaces, molecular cross-linking, and bearing jamming frequently occur during use, necessitating higher manufacturing standards and resulting in higher costs. Additionally, these bearings have weaker tensile resistance and require higher aspect ratios for buildings, necessitating larger auxiliary devices and leading to overall cost increases.

To enhance their functionality while balancing the interplay of functionality, safety, and economic factors in seismic isolation structures, optimizing and upgrading existing types of FPBs is necessary. These three factors critically determine the application and promotion of FPBs. To address the current issues, the following research directions are proposed:

High-performance friction surface materials

FPBs, commonly used in base isolation configurations, face critical issues due to factors like rusting, molecular cross-linking, and wear on the friction surface, which can lead to jamming during earthquakes. The complex environment of building isolation layers, including debris, dust, foreign objects, and water vapor, can damage the friction surface. Severe vertical seismic components may cause the FPBs sliders to create pits on the friction sliding surface, leading to damage. Inconsistent wear on each sliding surface within the isolation layer leads to uneven structural loading, underscoring the need for the development of high-performance friction surface materials. Emerging materials such as advanced composites, self-lubricating materials, and coatings with enhanced wear resistance could significantly improve the durability and performance of FPBs.

Comprehensive experimental and numerical simulations

Numerical simulation offers an economical and effective validation method, yet experimental research remains the most convincing approach to assess the performance and seismic mitigation effects of FPBs. Comprehensive and systematic performance tests on various types of FPBs, establishing refined models to simulate their behavior accurately, and conducting scaled and full-scale tests on isolation structures are essential to examine the performance and seismic mitigation effects of various types of FPBs. Advanced simulation techniques, such as finite element analysis (FEA) with improved material models, and high-fidelity hybrid simulation methods, could provide deeper insights into FPB behavior under seismic loads.

Enhanced analysis and design methods

Enhancing practical analysis and design methods for isolation structural systems with FPBs involves establishing design response spectra and developing corresponding software tools. FEA can be used to optimize FPB parameters by simulating stress distributions and deformation patterns, while machine learning (ML) techniques can predict performance under various conditions and identify optimal configurations. This integrated approach ensures effective interaction between the structure and the isolation system, preventing suboptimal designs.

Additionally, research on performance-based and energy-based analysis methods is crucial for developing multi-level FPBs aligned with seismic design objectives. By incorporating AI and ML into predictive modeling, engineers can rapidly evaluate numerous design iterations, improve maintenance schedules, and enhance safety measures. Developing user-friendly software that integrates these advanced techniques will facilitate the practical application of cutting-edge research, ultimately enhancing the resilience and efficiency of FPB-based isolation systems.

Integration with advanced structural control techniques

Although friction pendulum isolation technology has seen successful applications in seismic protection and strengthening of various structures such as buildings, lifeline engineering, industrial equipment, and historical monuments, there is ample room for development. Integrating FPBs with other advanced structural control techniques to explore their applicability in novel, complex, specialized, and highly flexible structures forms the next frontier in seismic mitigation structural systems, aiming to expand the research and application domains of this technology. Techniques such as smart materials, active control systems, and real-time monitoring using IoT (Internet of Things) devices could be integrated with FPBs to create more adaptive and resilient seismic protection systems.

Summary

Friction pendulum isolation bearings, as pivotal structural isolation devices, have garnered substantial attention within the realm of earthquake engineering. Following years of diligent research and development, researchers have delved extensively into FPBs, yielding a plethora of types characterized by diverse structural forms and exceptional mechanical properties. This paper presents a comprehensive review elucidating the mechanical attributes and research advancements of FPBs, encompassing the spectrum of friction materials employed, as well as single, double, and multiple-pendulum configurations, alongside other variants. Furthermore, a succinct overview of their seismic performance and utilization in isolated structures is provided.

These bearings epitomize low sensitivity and high stability, effectively attenuating seismic excitations and furnishing steadfast isolation safeguards to structures. Moreover, FPBs boast robust self-centering capabilities, coupled with exemplary isolation and energy dissipation mechanisms. These inherent characteristics facilitate prompt restoration to operational norms post-earthquake occurrences, thereby curtailing structural damage and maintenance expenditures, while markedly augmenting the seismic resilience of edifices.

It is imperative to acknowledge that notwithstanding the strides made in theoretical and practical realms, FPBs encounter challenges and impediments in real-world engineering applications. Notably, further research is warranted in the realm of friction material selection and optimization to fortify bearing durability and abrasion resistance. Additionally, due considerations must be accorded to diverse structural attributes and seismic milieu during bearing design and construction endeavors to ensure efficacy and reliability. This paper encapsulates extant predicaments and challenges confronting the research and development landscape of friction pendulum isolation bearings, with the aim of furnishing reference points and suggestions for prospective investigations.

In conclusion, friction pendulum isolation bearings epitomize a burgeoning isolation apparatus replete with vast developmental prospects and substantive application value within the sphere of earthquake engineering. Future research endeavors should pivot towards optimizing friction materials, refining bearing design, and enhancing performance to bolster seismic resistance and engineering application efficacy, thus furnishing more efficacious technical underpinnings for earthquake disaster mitigation and structural integrity.

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 authors gratefully acknowledge the support received from “National Natural Science Foundation of China (No. 52108440, 52125802),” “Natural Science Foundation of Jiangsu Province (No. BK20210253),” “Key Laboratory of Structural Engineering of Jiangsu Province (Suzhou University of Science and Technology) (No. ZD2201),” “Postdoctoral Fellowship Program of CPSF (No. GZB20240151),” “Jiangsu Funding Program for Excellent Postdoctoral Talent (No. 2024ZB680).”

ORCID iD

Gang Xu

References

Alexandros

Yiannis

(2021) Optimizing the seismic response of base-isolated liquid storage tanks using swarm intelligence algorithms. Computers & Structures 243: 106407.

Almazan

Llera

JCDL

(2003) Physical model for dynamic analysis of structures with FPS isolators. Earthquake Engineering & Structural Dynamics 32: 1157–1184.

Almazan

Lallera

JCDE

Inaudi

(1998) Modelling aspects of structures isolated with friction pendulum system. Earthquake Engineering & Structural Dynamics 27: 845–867.

Amarnath

Michael

(2005) Testing and modeling of prestressed isolators. Journal of Structural Engineering 131(6): 857–866.

ATC (Applied Technology Council) (2005) Field Manual: Postearthquake Safety Evaluation of Buildings. Redwood, CA: Applied Technology Council.

Bondonet

Filiatrault

(1997) Frictional response of PTFE sliding bearings at high frequencies. Journal of Bridge Engineering 2(4): 139–148.

Cao

Pan

Sun

, et al. (2022) Mechanical properties and isolation effect of disc spring – single friction pendulum 3D vibration isolation device. Journal of Building Structures 43(7): 44–53.

Chen

Yang

Liu

(2008) Design and application of friction pendulumbeari ng for seismicisolated bridges. Industrial Construction 39: 256–261.

Chen

Yang

Liu

(2009) Design and application of friction pendulum bearing for seismic isolated bridges. Industrial Construction 39(S1): 256–261.

10.

Cheng

Wang

(2006) Review and prospect of seismic achievements in China. Seismic Design Engineering 8: 4–7.

11.

Constantinou

Mokha

Reinhorn

(1990) Teflon bearings in base isolation II: modeling. Journal of Structural Engineering 116(2): 455–474.

12.

Constantinou

Reinhorn

Zayas

(1991) Experimental study of friction pendulum isolation system. Journal of Structural Engineering 117: 1201–1217.

13.

Cui

(2022) Theoretical analysis and numerical simulation of double-concave friction pendulum isolation bearing with damper. Building Structure 52(S1): 1016–1022.

14.

Deng

Gong

Zhou

(2010) Study on the theoretical analysis and numerical simulation of double concave friction pendulum isolation bearing. Journal of Guangzhou University 9(4): 71–77.

15.

Dolce

Cardone

Croatto

(2005) Frictional behavior of steel-PTFE interfaces for seismic isolation. Bulletin of Earthquake Engineering 3(1): 75–99.

16.

Duan

Zhang

(2021) Shaking table test of inter-story isolation structure based on friction pendulum system. Journal of Shenyang Jianzhu University (Natural Science) 37(6): 1040–1048.

17.

Feng

Chen

Wang

, et al. (2017) Seismic response of isolated gas duct using DCFP bearing. Mechanics in Engineering 39(5): 472–478.

18.

Fenz

Constantinou

(2007) Spherical sliding isolation bearings with adaptive behavior: experimental verification. Earthquake Engineering & Structural Dynamics 37(2): 185–205.

19.

GB/T 37358-2019 (2019) Friction Pendulum Isolation Bearings for Buildings. Beijing, China: China National Standardization Administration.

20.

Gino

Anerdi

Castaldo

, et al. (2020) Seismic upgrading of existing reinforced concrete buildings using friction pendulum devices: a probabilistic evaluation. Applied Sciences 10(24): 8980.

21.

Gong

Zhou

(2010) State of the art and prospect of the research and application of friction pendulum isolation technology (I): types and performance of friction pendulum bearings. Earthquake Resistant Engineering and Retrofitting 32(3): 1–10.

22.

Gong

Deng

Zhou

(2011) Theoretical analysis and numerical simulation research on friction pendulum isolation bearings. Journal of Disaster Prevention and Mitigation Engineering 31(1): 56–62.

23.

Han

(2013) Nonlinear Vibration of DCFP and Impact Analysis of Large Span Structure Using DCFP. PhD Thesis, Lanzhou University of Technology, Lanzhou, China.

24.

(2022) Isolation device of tension pull-friction pendulum and its isolation effect analysis. PhD Thesis, Institute of Engineering Mechanics, China Earthquake Administration, Harbin, China.

25.

Wang

(2013) Theoretical research of isolation frame structure based on friction pendulum foundation sliding. Noise and Vibration Control 33(1): 212–217.

26.

Jin

(2019) Theoretical Study and Numerical Simulation of Variable Parameter Friction Pendulum Bearings. PhD Thesis, Huazhong University of Science and Technology, Wuhan, China.

27.

JT/T 852-2013 (2013) Friction Pendulum Seismic Isolation Bearing for Highway Bridges. Beijing, China: Ministry of Transport of the People’s Republic of China.

28.

Kazantzi

Vamvatsikos

(2021) Practical performance-based design of friction pendulum bearings for a seismically isolated steel top story spanning two RC towers. Bulletin of Earthquake Engineering 19(2): 1231–1248.

29.

Kim

Lee

Kim

(2009) Application of friction pendulum system to the main control room of a nuclear power plant. Canadian Journal of Civil Engineering 36(1): 63–72.

30.

Kumar

Whittaker

Constantinou

(2015) Characterizing friction in sliding isolation bearings. Earthquake Engineering & Structural Dynamics 44(9): 1409–1425.

31.

Lee

Constantinou

(2016) Quintuple friction pendulum isolator-behavior, modeling and validation. Earthquake Spectra 32(3): 1607–1626.

32.

(2017) Hysteretic Research and Practical Engineering Calculation of Triple Friction Pendulum Bearing. PhD Thesis, Beijing Jiaotong University, Beijing, China.

33.

Wang

(2015) Response analysis of friction pendulum typical structure with supervental damping under near fult groud motions. Industrial Construction 45(S1): 279–285.

34.

Zhao

, et al. (2023) Type test and performance analysis of friction pendulum isolated bearing for padama bridge. Structural Engineers 39(1): 107–115.

35.

Zhang

(2024) Mechanical properties of the adaptive uplift - restraint friction pendulum bearing based on the magnetic activity theory. China Earthquake Engineering 46(1): 52–58.

36.

Liu

Fang

, et al. (2020) Study on dynamic response and shaking table test of isolated structure with isolation bearings arranged along curved surface. Journal of Building Structures 43(3): 1–12.

37.

Malekzadeh

Taghikhany

(2010) Adaptive behavior of double concave friction pendulum bearing and its advantages over friction pendulum systems. Scientia Iranica 17(2): 81–88.

38.

Mokha

Constantinou

Reinhorn

(1990) Teflon bearings in base isolation I: testing. Journal of Structural Engineering 116(2): 438–454.

39.

Mokha

Constantinou

Reinhorn

(1991) Further results on frictional properties of Teflon bearings. Journal of Structural Engineering 117(2): 622–626.

40.

Mokha

Constantinou

Reinhorn

(1993) Verification of friction model of teflon bearings under triaxial load. Journal of Structural Engineering 119(1): 240–261.

41.

Morgan

(2007) The Use of Innovative Base Isolation Systems to Achieve Complex Performance Objectives. PhD Thesis, University of California, Berkeley, CA.

42.

Morgan

Mahin

(2008) The optimization of multi-stage friction pendulum isolators for loss mitigation considering a range of seismic hazard. In: The 14th WCEE, Beijing, China, 12∼17 October 2008.

43.

New Zealand Treasury (2013) Budget speech 2013-supporting the rebuilding of the Christchurch. Available at: https://www.treasury.govt.nz/budget/2013/speech/06.htm.

44.

Panchal

Jangid

(2008) Seismic isolation of bridge using variable curvature friction pendulum system. In: The 14th WCEE, Beijing, China, 12–17 October 2008.

45.

Pigouni

Castellano

Infanti

, et al. (2020) Full-scale dynamic testing of pendulum isolators (Curved surface sliders). Soil Dynamics and Earthquake Engineering 130: 105983.

46.

Pranes

Sinha

(2000) VFPI: an isolation device for aseimic design. Earthquake Engineering & Structural Dynamics 29: 603–627.

47.

Pranes

Sinha

(2004a) Aseismic design of structure equipment systems using variable frequency pendulum isolator. Nuclear Engineering and Design 231: 129–139.

48.

Pranes

Sinha

(2004b) Behavior of torsionally coupled structures with variable frequency pendulum isolator. Journal of Structural Engineering 130(7): 1041–1054.

49.

Rabiei

Khoshnoudian

(2011) Response of multistory friction pendulum base isolated buildings including the vertical component of earthquakes. Canadian Journal of Civil Engineering 38(10): 1045–1059.

50.

Roussis

(2004) Experimental and Analytical Studies of Structures Seismically Isolated with an Upliftrestraint Isolation System. PhD Thesis, State University of New York at Buffalo, Buffalo, NY.

51.

Roussis

Constantinou

(2006) Experimental and analytical studies of structures seismically isolated with an uplift-restraining friction pendulum system. Earthquake Engineering & Structural Dynamics 35(5): 595–611.

52.

Ryuichi

Hironori

Nobuo

, et al. (2008) Experimental study on durability of sliding bearings under long duration dynamic loading. In: The 14th WCEE, Beijing, China, 12–17 October 2008.

53.

Shang

(2017) Seismic Behavior Analysis of Isolated Building Using Triple Friction Pendulum Bearings. PhD Thesis, Lanzhou University of Technology, Lanzhou, China.

54.

Sorace

Terenzi

(2014) A viable base isolation strategy for the advanced seismic retrofit of an R/C building. Contemporary Engineering Sciences 7(17): 817–834.

55.

Sun

(2013) Seismic-isolated Performance of the Base -isolated Structure with the Friction Pendulum System. PhD Thesis, Zhengzhou University, Zhengzhou, China.

56.

Tsepelas

Constantinou

(1994) NCEER-taisei Corporation Research Program on Sliding Seismic Isolation Systems for Bridges: Experimental and Analytical Study of a System Consisting of Sliding Bearings and Fluid Restoring Force/damping Devices. Buffalo, NY: National Center for Earthquake Engineering Research.

57.

Vern

Shrimali

Bharti

(2010) Parametric analysis of liquid storage tanks base isolated by curved surface sliding bearings. Soil Dynamics and Earthquake Engineering 30(1): 21–31.

58.

Wang

Han

(2014) Autonomous system of double concave friction pendulum and its validation analysis. Journal of Lanzhou University of Technology 40(1): 114–117.

59.

Wei

(2008) Review and prospect of earthquake relief work in urban and rural construction of China. In: The 14th WCEE, Beijing, China, 12∼17 October 2008.

60.

(2020) Study on Isolation and Design Optimization of High-Rise Buildings on Triple Friction Pendulum Bearings. PhD Thesis, Southeast University, Nanjing, China.

61.

(2020) Seismic performance and design approach of unbonded post-tensioned precast sandwich wall structures with friction devices. Engineering Structures 204: 110037.

62.

Guo

(2023) Seismic resilient shear wall structures: a state-of-the-art review. Science China Technological Sciences 66(6): 1640–1661.

63.

Guo

(2023a) Self-centering rotational joints for seismic resilient steel moment resisting frame. Journal of Structural Engineering 149(2): 04022245.

64.

Guo

, et al. (2023b) Development and investigation of a self-centering cable brace with variable slip stiffness for braced frame structure. Journal of Building Engineering 76: 107383.

65.

Guo

, et al. (2024) Seismic resilience enhancement for building structures: a comprehensive review and outlook. Structures 59: 105738.

66.

Yan

(2018) Dynamic Response Analysis of Base-Isolated High-Rise Building with Triple Friction Pendulum. PhD Thesis, Southeast University, Nanjing, China.

67.

Yan

Liu

(2014) The isolation effect of friction double-pendulum isolation bearings. Journal of Hefei Union University 36(3): 106–109.

68.

Yang

(2014) A Research of the Vibration Islolation Performance of the Asymmetric FPS-type Isolated Structure and its Damping Effect Combined with TMD. PhD Thesis, Lanzhou University of Technology, Lanzhou, China.

69.

Yao

(2018) Research on Mechianical Properties of Segmented Sliding Friction Pendulun Isolation Bearings. PhD Thesis, Southwest Jiaotong University, Chengdu, China.

70.

(2018) Study on Seismic-Isolated Structures Based on Double Concave Friction Pendulum Bearings. PhD Thesis, Beijing Jiaotong University, Beijing, China.

71.

Zayas

Low

Mahin

(1987) The FPS Earthquake Resisting System: Technical Report UCB/EERC-87/01. Berkeley, CA: University of California at Berkeley.

72.

Zayas

Piepenbrock

Al-hussaini

(1993) Summary of testing of the friction pendulum seismic isolation system. In: The ATC-17-1 Seminar on Seismic Isolation, San Francisco, CA, 11–12 March 1993. Applied Technology Council.

73.

Zayas

Kartonum

Constantinou

, et al. (1997) Testing of friction pendulum seismic isolation bearings for bridges. In: The 4th World Congress on Joint Sealants and Bearing Systems for Concrete Structures, Sacramento, CA, 13–18 July 1997.

74.

Zhang

(2019) Research on the Theory and Application of a New Semi-active Controlled Base-Isolated Structure. PhD Thesis, Tsinghua University, Beijing, China.

75.

Zhao

(2017) Seismic Response Analysis of Story Isolation Structure Based on Modified SMA-Triple Friction Pendulum Bearing. PhD Thesis, Lanzhou University of Technology, Lanzhou, China.

76.

Zhao

Taucer

Rossetto

(2009) Field investigation on the performance of building structures during the 12 May 2008 Wenchuan earthquake in China. Engineering Structures 31(8): 1707–1723.

77.

Zhou

(1996) The earthquake damage and lessons learned from the Hanshin earthquake in Japan. Seismic Engineering 1: 39–42.

78.

Zhou

(2019) Experimental research on seimic performance of friction pendulum isolated high-rise frame-shear wall structures. PhD Thesis, Institute of Engineering Mechanics, China Earthquake Administration, Harbin, China.

79.

Zhou

Gong

(2010) State of the art and prospect of the research and application of friction pendulum isolation technology (II). Earthquake resistant engineering and Retrofitting 32(4): 1–19.

80.

Zhu

(2018) Study on Isolation Performance of Friction Pendulum Isolated Structure and Analysis of Bearing Performance. PhD Thesis, Kunming University of Science and Technology, Kunming, China.

81.

Zhuang

Liu

, et al. (2020) Seismic response analyses of a single-layer spherical lattice shell structure with a multifunctional FPB system. Journal of Vibration and Shock 39(8): 79–87.