Abstract
In this paper, the development of non-linear building isolation systems is overviewed. The study summarizes commonly used linear building isolation systems in two categories, which are building base isolation systems and building inter-storey isolation systems. Typical isolators including Lead-Rubber Bearings Friction Pendulum Bearings inter-storey viscous damper and Tuned Mass Damper are reviewed. The analysis and design of linear building isolation systems are also reported. After that, non-linear building isolation systems are introduced from two aspects based on their dynamic characteristics. They are (i) non-linear stiffness isolators including Quasi-Zero Stiffness isolators and Non-linear Energy Sink and (ii) non-linear damping isolators including power-law viscous dampers and magnetorheological dampers. Practical implementations of these non-linear isolators are introduced. Finally, the analysis and design of non-linear building isolation systems are discussed. Traditional equivalent linearization approaches and advanced non-linear frequency design approaches are introduced. The promising applications of the non-linear frequency design approaches to building isolation systems are also demonstrated in this review paper.
1 Introduction
Severe earthquakes often result in significant damage to buildings, infrastructures, and cause casualties. For example, the 2011 Tohoku Earthquake in Japan caused over 20,000 deaths and missing, and 190,000 buildings were damaged (Okada et al., 2011; Takewaki et al., 2011). Protecting building structures under earthquakes is of great concern in earthquake-prone countries (Mazzolani, 2001; Azinovic et al., 2016; Tesfamariam, 2022; Zhang et al., 2022). To address this challenge, building isolation systems are applied to mitigate seismic hazards (Morgan, 2007; Mohammed and Mohd, 2011; Takewaki et al., 2013). The aim of applying building isolation is to reduce either the storey or inter-storey vibrations transmitted from the seismic ground motions (Hu, 2014). In practice, two types of passive building isolation systems are commonly used, which are the base isolation system (Jangid and Datta, 1995; Deb, 2004) and the super-structure isolation system, including the inter-storey isolation (De Domenico et al., 2019; Dona et al., 2022) and top floor isolation (Thakur, and Pachpor, 2012), as illustrated in Figure 1.
FIGURE 1
In order to reduce the effects of ground motions on the whole building structure, base isolation was applied to decouple the upper structure from the ground (Akehashi et al., 2018; De Luca and Guidi, 2019). In practice, Lead-Rubber Bearings (LRB) (Jangid, 2007) and Friction Pendulum Bearings (FPB) (Chen and Jia, 2021) are commonly used to implement building base isolation systems. Both LRB and FPB produce soft stiffness to isolate earthquakes and mitigate transmitted seismic energy by friction effects (Cardone et al., 2009; Deringol and Guneyisi, 2020). Friction dampers are often applied to inter-storey isolation to mitigate the relative displacement between two storeys of the building (Lee et al., 2008; Zhang et al., 2017). In addition, the top floor isolation is often implemented by a Tuned Mass Damper (TMD) to absorb vibration energies (Chey et al., 2010; Ghaedi et al., 2017). Detailed reviews of the existing building isolation systems are as follows.
1.1 Base isolation systems
LRB is one of the most commonly used base isolators in practice. An LRB is composed of laminated rubber layers with reinforced steel plates, and a central lead core providing damping to the building structure due to the large shear deformation (Figure 2A) (Kunde and Jangid, 2003; Zordan et al., 2014). The LRB was first invented in New Zealand in 1975 and has been applied to many building structures worldwide (Komuro et al., 2005; Providakis, 2008; Komur, 2016). For example, the Shimizu Corporation Tokyo Headquarters, one of the city’s leading office buildings in Japan, applied 32 LRB and 10 NRB (Natural Rubber Bearings) to achieve a structure natural period of 5.40s (Shimazaki and Nakagawa, 2015). Christchurch Women’s Hospital in New Zealand was well protected by 41 LRB base isolators in the 2010 Darfield (Canterbury) earthquake (Gavin and Wilkinson, 2010).
FIGURE 2
On the other hand, a similar type of base isolators known as the FPB was developed as shown in Figure 2B to improve the restoring capacity and durability of base isolation systems (Wang, 2002). An FPB is composed of two curved sliding surfaces providing horizontal restoring force and a hemispherical slider between the two sliding surfaces (Peng et al., 2022). The FPB base isolation systems are widely applied to solve the difficulties in isolating large displacements using LRB (Drozdov et al., 2007; Kravchuk et al., 2008; Chen and Xiong, 2022). For example, the world’s largest FPB with a 4 m diameter was installed on the Benicia Martinez Bridge in United States (Kravchuk et al., 2008). The international airport of San Francisco where 267 FPB base isolators have been in operation can bear earthquakes of up to eight Richter scale (Drozdov et al., 2007).
Both the LRB and FPB isolators have the same type of bi-linear force-displacement characteristics as illustrated in Figure 2C, where is the initial bearing elastic stiffness; is the post-yield stiffness,; is the effective stiffness; ; are the yield strength and yield deformation of the bearing, respectively; ; are the maximum force and displacement of the bearing, respectively (Ozdemir, 2015).
In practice, the stiffness and damping of the LRB and FPB are often linearized, so that linear system theories can be applied to the analysis and design of bearing-based building base isolation systems (Syed, 2011; Ye et al., 2019; De Domenico et al., 2020). For example, linear static analysis and linear response spectrum analysis were applied to the design of multi-storey buildings in Banglades (Syed, 2011). Ye et al. (2019) proposed a direct-displacement based design procedure for the LRB base isolation systems based on the equivalent linearization of base-isolated building structures. De Domenico et al. (2020) applied tuned fluid inerters to structures with friction pendulum isolators based on system linearization approaches. Other bearing base isolation systems including High Damping Rubber Bearing (HDRB) (Dezfuli and Alam, 2016), Sliding LRB (Zheng et al., 2020) were developed based on the LRB and FPB to improve the building isolation performance under earthquakes.
1.2 Super-structure isolation systems
Reducing inter-storey displacements during earthquakes is important to prevent large deformations of buildings (Valente and Milani, 2018). This is often resolved by applying energy dissipation or vibration absorption devices to building storeys (Symans et al., 2008). A common practice is to use inter-storey isolators. For example, Ryan and Earl (2010) applied LRB to conduct inter-storey isolations as shown in Figure 3ADe Domenico et al. (2019) introduced various inter-storey isolation systems based on Fluid Viscous Dampers (FVD) in Figure 3B. Palacios-Quinonero et al. (2019) applied multiple TMD to inter-storey isolation and adjacent building isolations as illustrated in Figure 3C. Viscous dampers are also applied to adjacent building isolations in Figure 3D by Kasagi et al. (2016), Fukumoto and Takewaki (2017), Hayashi et al. (2018), Makita et al. (2018), Kawai et al. (2020, 2021), Nakamura et al. (2021).
FIGURE 3
The design and arrangement of inter-storey dampers were studied including the optimization of the values, numbers, and position of the dampers (Singh and Moreschi, 2001; Fujita et al., 2010; Uemura et al., 2021; Akehashi and Takewaki, 2022a). The design optimization problem can be formulated as (De Domenico et al., 2019)where is the objective function depends on damping coefficients and is a constraint.
In general, there are various options to determine the objective function for system design. These may include the maximum top floor or inter-storey displacement (Constantinou and Tadjbakhsh, 1983), the total mechanical energy of the system (Gorgoze and Muller, 1992), transfer function amplitudes (Takewaki, 1997), life-cycle costs (Gidaris and Taflanidis, 2015), and damper costs (De Domenico and Hajirasouliha, 2021), etc. Evolutionary approaches and Pareto front were applied to solve the optimization problem, as well as determine the optimal placement of the inter-storey isolators based on a single bay model (Lavan and Dargush, 2009). Distribution of isolators among different bays was also investigated by researchers (Mezzi, 2010; Whittle et al., 2012; Takewaki and Akehashi, 2021). For example, Mezzi (2010) investigated seven different configurations of energy-dissipating braces for an 18-storey reinforced concrete frame, showing that random distributions of isolators in Figure 4A can offer better isolation performance than conventional regular distributions as illustrated in Figure 4B. However, the optimization of such complex decision problems is still challenging.
FIGURE 4
Existing analysis and design of building isolation systems are often based on the linear or bi-linear characteristics of isolators, which often have limited performance in isolating near-fault earthquakes compared with far-fault long-period earthquakes (Providakis, 2009; Gur et al., 2014; Ozuygur and Noroozinejad Farsangi, 2021; Akehashi and Takewaki, 2022b). Near-fault earthquakes often contain extensive pulses and high-frequency vibrations can be amplified to the super-structures by linear base isolation systems as illustrated in Figure 5 (Ho et al., 2018). Developing non-linear base isolation systems can solve these challenges and deal with both near and far-fault earthquakes. For example, the optimal acceleration transmissibility shown in Figure 5 can be achieved by applying power-law non-linear damping based building base isolation system (Ho et al., 2018). Non-linear dampers applied to inter-storey isolation systems also have better performance in reducing inter-storey drifts than linear dampers (Fujita et al., 2014).
FIGURE 5
Therefore, developing non-linear building isolation systems, as well as systematic analysis and design approaches, is necessary for the development of the next-generation’s building isolation systems. Current research on the development of non-linear building isolation systems will be reviewed in the following sections.
2 Non-linear stiffness for building isolation
2.1 The quasi-zero stiffness isolator
The QZS isolator enables an isolation system to achieve low resonance in vibration while keep a high supporting capacity in static scenarios, which has demonstrated great advantages especially in solving low-frequency vibration isolation problems (Niu et al., 2013; Li et al., 2020; Yan et al., 2022). The QZS is a non-linear mount composed of a negative stiffness component and a positive stiffness component as shown in Figure 6A, where ; are the vertical and horizontal stiffness, respectively; ; are the length of the vertical and horizontal spring under the load . The force-displacement () characteristic of a QZS is illustrated in Figure 6B, showing the high static () low dynamic () stiffness property.
FIGURE 6
In practice, there are many ways to realize a QZS isolation system. For example, a QZS can be simply achieved by using a disk spring shown in Figure 7A (Zhou et al., 2022). Dai et al. (2018) and Chai et al. (2022) developed a series of bio-inspired QZS isolators as illustrated in Figure 7B, which have been applied to solve vibration isolation problems in vehicle suspensions (Feng and Jing, 2019) and hand-held jackhammers (Jing et al., 2019). A convex ball-roller mechanism was developed to enable QZS isolation for rotor systems in Figure 7C (Zhang et al., 2020). Buckled beams can naturally produce negative stiffness in Figure 7D (Liu et al., 2013), and U-shape beam structures were developed and applied to building base isolation systems as demonstrated in Figure 7E (Ene et al., 2016).
FIGURE 7
In building isolation systems, the QZS isolators are often applied to isolate vertical vibrations that are frequently observed in near-fault seismic events (Liu et al., 2018). Zhou et al. (2019) studied the base isolation of a 3-dimensional 7-storey frame concrete building by using both the disk spring with QZS and the equivalent linear spring. The results demonstrate a significant acceleration reduction of the building structure at the expense of a slight increase in displacement response compared to a fixed seismic isolation system in Figure 8.
FIGURE 8
Chen et al. (2022) developed an integrated QZS system composed of horizontal spring and LRB damper to isolate horizontal seismic input to buildings (Figure 9A). The schemes of QZS based vertical and horizontal isolation systems are shown in Figure 9B. In addition, Liu et al. (2020) developed a novel 3-dimensional seismic isolator combining the QZS system to prevent the vertical and rotational vibration of buildings. Valeev et al. (2019) reported a two-component material with the QZS property for building vibration isolation (Figure 9C).
FIGURE 9
2.2 Non-linear energy sink
The TMD has been used as a vibration absorber in high-rise buildings and landscape towers such as Shanghai Tower (632 m high) (Zhou et al., 2018), Taipei 101 Tower (508 m high), New York Citicorp Center (279 m high), Boston John Hancock Tower (457 m high), and Sydney Tower (305 m high) (Chung et al., 2013). However, a TMD only works for a particular modal frequency of the building over a narrow frequency band (Saidi et al., 2006). The tuning strategy of a TMD is vitally important but usually complex due to the complexity of building structures (Ferreira et al., 2018).
To address the issues in linear TMD isolation systems, a series of non-linear TMD systems were developed (Alexander and Schilder, 2009). One of the most commonly studied non-linear TMD is the NES (Gomez et al., 2021). A typical NES is shown in Figure 10A, which integrates the TMD and QZS to achieve wider damping frequency and better robustness without increasing the resonance peak (Ding and Chen, 2020). Gourdon et al. (2007) compared the vibration isolation performance of a 2-Degree of Freedom (2DoF) system by using NES and TMD and the results indicate the NES has much better isolation performance than linear TMD as shown in Figure 10B. If the vertical damper of the NES is replaced by a linear spring, the system becomes a KDamping isolation system as shown in Figure 10C, which has been applied to energy absorption of vehicle vibrations (Papaioannou et al., 2019) and seismic isolation of bridges (Sapountzakis et al., 2016).
FIGURE 10
Recently, Wang et al. (2020) applied a track NES to the top of a 32-storey high-rise building, showing that a track NES is robust against changes in structural stiffness and maintains high energy absorption efficiency of building isolation systems. Luo et al. (2014) and Wierschem et al. (2014) conducted experiments on large-scale model building structures with multiple NES devices. In their studies, three historic earthquake ground motions were scaled down and implemented by a large-scale shake table, proving the efficiency of the NES based vibration mitigation in earthquakes. The design of NES isolation systems is often conducted by using non-linear dynamic analysis approaches such as the Harmonic Balance Method (HBM) (Luongo and Zulli, 2012) and the Non-linear Normal Modes (NNM) approach (Ahmadabadi and Khadem, 2012). But these approaches are often difficult to be applied to complex building isolation systems (Li et al., 2021).
3 Non-linear damping for seismic isolation
3.1 Non-linear viscous damper
In order to improve the seismic isolation performance of traditional linear building isolation systems, non-linear viscous damping has been applied to both the base and super-structure isolation of buildings. In general, the force-velocity relationship for a non-linear viscous damper can be written as (Milanchian and Hosseini, 2019).where is the damping force, is the damping coefficient, is the velocity, and is the velocity exponent.
Many studies on non-linear damping-based building isolation systems have been carried out by researchers. The non-linearly damped inter-storey isolation system is illustrated in Figure 11A (Dong et al., 2016). Martinez-Rodrigo and Romero (Martinez-Rodrigo and Romero, 2003) found that by applying non-linear inter-storey viscous dampers, the forces in the dampers can be reduced by more than 35% while having a structural performance similar to that with using linear dampers. Since large damper forces have important implications on the overall retrofitting cost, manufacturers generally strive for achieving such a non-linear behaviour in their products (De Domenico and Hajirasouliha, 2021). Kangda and Bakre (2018) studied the seismic isolation of adjacent buildings, observing that at low damping ratio, non-linear dampers perform better than linear dampers in reducing absolute accelerations. The optimal placement of non-linear dampers for building structures was investigated by Fujita et al. (2014, 2021), showing that the velocity exponent plays a key role in vibration suppression under low level seismic input. Moreover, a non-linear damper is much more effective than a linear damper under very rare earthquakes having seismic intensities larger than the design earthquakes.
FIGURE 11
Additional non-linear damping to building base isolation systems can bring significant benefit to seismic isolations. Deringol and Guneyisi (2021) investigated the effectiveness of non-linear fluid viscous dampers in seismic isolation with LRB shown in Figure 11B. The study found that the non-linear damper can significantly mitigate long-period seismic vibrations (T > 4s) with optimized velocity exponents and positions. Menga et al. (2021) found that non-linear damped base isolation can provide desired isolation performance over a wider range of excitation spectra than a linear damper. Lang et al. (2009) theoretically proved that a power-law non-linear damping can produce desired vibration isolation performance over both resonant and non-resonant frequency ranges. This property has been applied to the development of non-linear building isolation systems. For example, Lang et al. (2013) studied the design of power-law non-linear viscous damping for high-rise building base isolation systems under both long-period sinusoidal and random ground motions, where the energy transmissibility is applied as the objective function for non-linear damping design. The prominent advantages of non-linear damping in high-frequency seismic isolation have been proven by Ho et al. (2018), Guo et al. (2012), and Zhu et al. (2020), which can profoundly improve the building isolation performance under both far-fault and near-fault earthquakes.
3.2 Implementation of non-linear damping
In general, a desired non-linear damping characteristic cannot be achieved naturally by materials and pure mechanical design. Specific mechanical structures and materials only produce limited non-linear properties. For example, Ilbeigi et al. (2012) developed a non-linear displacement-dependent damper by introducing a varying cross-section piston guide in a damper as shown in Figure 12A. Bian and Jing (2019) applied a horizontal damper to an X shape isolator to achieve non-linear damping as shown in Figure 12B. Tang and Brennan (2013) found that a horizontal damper attached to a vibration isolator in Figure 12C can be represented by an unplugged Van der Pol equation.
FIGURE 12
In order to achieve desired non-linear damping properties, magnetorheological (MR) damper and semi-active control approaches were employed (Yao et al., 2002). The structure of MR dampers is shown in Figure 13A, where by controlling the external magnetic field, the MR fluid can produce various damping coefficients (Li et al., 2019). A novel semi-active control of MR dampers was developed in Laalej et al. (2012) as illustrated in Figure 13B, where is the desired non-linear force to be achieved; ; are the MR damper control current and MR damper power amplifier input voltage, respectively. The semi-active control strategy was verified by experiments in Ho et al. (2013) as shown in Figure 13C.
FIGURE 13
In addition, Ho et al. (2018) and Zhu et al. (2020) developed an open-loop semi-active control strategy based on a viscous damper with four linear damping coefficients for the base isolation of the Sosokan building (Japan) model. Ma et al. (2020) obtained desired non-linear damping force by controlling an electromagnetic shunt damping device.
4 Analysis and design of non-linear seismic isolation systems
4.1 Building isolation system analyses
In order to study the dynamic properties of building isolation systems, a building structure is often simplified as a Multiple-Degree-of-Freedom (MDoF) mass-spring-damper system (Figure 14A) (Silva-Navarro and Abundis-Fong, 2017). For example, Yamamoto et al. (2011) studied the input energy and energy input rate to a base-isolated building during an earthquake based on an MDoF N-storey shear building model. Liu et al. (2018) investigated the effectiveness of FVDs in building inter-storey isolation based on a 7DoF building model. The N-storey building model was also applied to the analysis and design of LRB base isolation systems (Kodakkal et al., 2019), TMD isolation systems (Giaralis and Taflanidis, 2018), as well as many non-linear and adjacent building isolation systems (Milanchian and Hosseini, 2019).
FIGURE 14
In general, an MDoF system can be easily simulated by using Runge-Kutta method (Soni et al., 2011), but it is often with low fidelity and only be used for conceptual studies of building isolation systems. To address this issue, more complex truss frame structures were considered in building isolation analyses (Figure 14B) (Takewaki, 2000), where structure mechanics approaches can be applied to compute the building responses under seismic input. For example, Eltahawy and Ryan (2020) studied the application of a 3-dimensional isolation system to the reduction of non-structural component damage caused by vertical excitations based on a frame building model. Takewaki (2000) proposed a systematic procedure by using the transfer function, in order to find the optimal damper positioning to minimize the dynamic compliance of a planar building frame. High fidelity Finite Element (FE) models are also used in the analysis of building isolation systems (Figure 14C), but they are often complex and with high computational costs in practical use (Wang et al., 2021).
4.2 Linearization approaches
In order to study the effects of non-linear building isolation systems, non-linear isolators are usually linearized as an equivalent linear isolator, so that the linear system theories can be applied for system analysis. For example, effective stiffness and damping of LRB are often evaluated for the analysis and design of LRB building isolation systems (Hwang and Chiou, 1996). In general, the linearization of the building isolation system is to find equivalent linear stiffness or damping, so that the output displacement of the linearized isolated building is equal to that of the non-linearly isolated building (Liu et al., 2014). In practice, the most commonly used linearization method was proposed by Rosenblueth and Herrera (1964) and has been adopted by many seismic codes (Eurocode eight; AASHTO; NTC). For example, Ma et al. (2013) applied the equivalent linearization method to the analysis and design of base-isolated buildings with many hysteretic devices. Zhang et al. (2020) studied the linearization of a flag-shaped isolation system, based on which the inter-storey brace isolation systems were optimized. Zordan et al. (2014) derived the equivalent damping ratio of an LRB isolated building model based on over 12 ground motions. Shinozuka et al. (2015) applied the stochastic linearization method investigate the LRB based building base isolation under random ground motions.
For the design of non-linear isolators, the equivalent linearization is often conducted based on the equivalent force or energy of the isolator. The equivalent linearization is therefore to solve the optimization problem (Zhu et al., 2022):where and are the non-linear and equivalent linear force of the isolator, respectively; represents the mean value. To solve equivalent linear damping problems, Elliott et al. (2015) studied the equivalent linear damping of power-law non-linear damping under both harmonic and random excitations. Bajric and Hogsberg (2018) derived equivalent linear damping of a hysteretic system under both low and high levels of excitation amplitudes. Zhu et al. (2022) developed a novel data-driven modelling approach for building isolation systems based on the mobility analysis method, where the design of non-linear isolation damping was conducted based on the equivalent linearization method.
4.3 Non-linearity frequency design approaches
Basically, both linear and linearization approaches only work in a narrow region around the working point of the system as illustrated in Figure 15A (Zhu et al., 2021). In practice, a large class of non-linear systems can be represented by Volterra series, which enables the analysis of non-linear systems over a much wider range of operations around a working point. The Volterra series is an extension of Taylor expansion to non-linear dynamic relationships, based on which the non-linear frequency response functions, such as the Generalized Frequency Response Functions (GFRFs) (George, 1959), the Non-linear Output Frequency Response Functions (NOFRFs) (Lang and Billings, 2005), the Output Frequency Response Fucntions (OFRF) (Lang et al., 2007) and the Associated OFRF (AOFRF) (Zhu and Lang, 2018), were developed for non-linear system frequency analysis and design.
FIGURE 15
Among these non-linear frequency response functions, the OFRF and AOFRF are one-dimensional functions, and have been applied to the design of non-linear dynamical systems. The concept of the OFRF was first developed by Lang et al. (2007), using which the system output frequency response can be written as a polynomial function of non-linear characteristic parameters:where is the system output frequency response; are the functions of frequency variable and are dependent on the linear characteristic parameters of the system; are system non-linear design parameters; denotes integer vectors. Figure 15B shows an example of OFRF (Zhu and Lang, 2017), the spectrum of the output force of a non-linear system is represented by a polynomial function of and which are two non-linear design parameters of system non-linearity.
Based on the concept of OFRF, Peng and Lang (2008) proposed the least squares based evaluation of the OFRF representation. Guo et al. (2012) and Ho et al. (2018) conducted the OFRF based design of non-linearly damped building base isolation systems by minimizing the energy transmissibility of the buildings. Fujita et al. (2014) investigated the optimal placement of inter-storey non-linear damper using the OFRF design approach. Considering that the OFRF only considers the relationship between system output frequency responses and non-linear design parameters, recently, Zhu and Lang. (2018) developed a novel AOFRF concept to deal with the non-linear system design by determining both the system’s linear and non-linear characteristic parameters.
5 Conclusion
This paper has reviewed the development of the analysis and design of passive non-linear building isolation systems. The building isolation systems are divided into two categories, which are the base isolation systems and the super-structure isolation systems. The current analysis and design of typical LRB and FPB base isolation systems, viscous damping inter-storey isolation systems, and TMD top floor isolation systems have been overviewed. Moreover, commonly used non-linear isolators for base and super-structure isolation systems, including the QZS, NES, and non-linear viscous damper, as well as their implementations, have been summarized. It can be concluded that these non-linear isolation systems are promising solutions to both near-fault and far-fault seismic isolations.
Finally, the analysis and design approaches of non-linear building isolation systems have been introduced. These approaches include the linearization approaches and the non-linear frequency design approaches. The increasing applications of these approaches demonstrate a systematic analysis and design of non-linear building isolation systems are really needed in engineering practice. The solutions include but are not limited to the investigation of effective modelling and simulation approaches for non-linear building isolation systems, the development of systematic non-linear analysis approaches, the specification of effective design objectives in both the frequency and time domain, as well as the development of non-linear system design approaches.
Statements
Author contributions
YPZ contributes to the writing of the whole review paper; ZQL supports the review of the analysis and design of non-linear systems and helped with the proofreading; KF and IT support the review of building isolation systems.
Funding
This work was supported by the United Kingdom EPSRC: EP/R032793/1, and UK Royal Society: IE150298.
Conflict of interest
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Publisher’s note
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.
References
1
AhmadabadiZ. N.KhademS. E. (2012). Nonlinear vibration control of a cantilever beam by a nonlinear energy sink. Mech. Mach. Theory50, 134–149. 10.1016/j.mechmachtheory.2011.11.007
2
AkehashiH.KojimaK.FujitaK.TakewakiI. (2018). Critical response of nonlinear base- isolated building considering soil-structure interaction under double impulse as substitute for near-fault ground motion. Front. Built Environ.4, 34. 10.3389/fbuil.2018.00034
3
AkehashiH.TakewakiI. (2022a). Bounding of earthquake response via critical double impulse for efficient optimal design of viscous dampers for elastic-plastic moment frames. Jpn. Archit. Rev.5 (2), 131–149. 10.1002/2475-8876.12262
4
AkehashiH.TakewakiI. (2022b). Resilience evaluation of elastic-plastic high-rise buildings under resonant long-duration ground motion. Jpn. Archit. Rev.5 (4), 373–385. 10.1002/2475-8876.12280
5
AlexanderN. A.SchilderF. (2009). Exploring the performance of a nonlinear tuned mass damper. J. Sound Vib.319 (1-2), 445–462. 10.1016/j.jsv.2008.05.018
6
AzinovićB.KilarV.KorenD. (2016). Energy-efficient solution for the foundation of passive houses in earthquake-prone regions. Eng. Struct.112, 133–145. 10.1016/j.engstruct.2016.01.015
7
BajrićA.HøgsbergJ. (2018). Estimation of hysteretic damping of structures by stochastic subspace identification. Mech. Syst. Signal Process.105, 36–50. 10.1016/j.ymssp.2017.11.042
8
BianJ.JingX. (2019). Superior nonlinear passive damping characteristics of the bio-inspired limb-like or X-shaped structure. Mech. Syst. Signal Process.125, 21–51. 10.1016/j.ymssp.2018.02.014
9
CardoneD.DolceM.PalermoG. (2009). Direct displacement-based design of seismically isolated bridges. Bull. Earthq. Eng.7 (2), 391–410. 10.1007/s10518-008-9069-2
10
ChaiY.JingX.ChaoX. (2022). X-shaped mechanism based enhanced tunable QZS property for passive vibration isolation. Int. J. Mech. Sci.218, 107077. 10.1016/j.ijmecsci.2022.107077
11
ChenX.IkagoK.GuanZ.LiJ.WangX. (2022). Lead-rubber-bearing with negative stiffness springs (LRB-NS) for base-isolation seismic design of resilient bridges: A theoretical feasibility study. Eng. Struct.266, 114601. 10.1016/j.engstruct.2022.114601
12
ChenX.XiongJ. (2022). Seismic resilient design with base isolation device using friction pendulum bearing and viscous damper. Soil Dyn. Earthq. Eng.153, 107073. 10.1016/j.soildyn.2021.107073
13
ChenZ.JiaP. (2021). Seismic response of underground stations with friction pendulum bearings under horizontal and vertical ground motions. Soil Dyn. Earthq. Eng.151, 106984. 10.1016/j.soildyn.2021.106984
14
CheyM. H.ChaseJ. G.ManderJ. B.CarrA. J. (2010). Semi-active tuned mass damper building systems: Design. Earthq. Eng. Struct. Dyn.39 (2), 119–139. 10.1002/eqe.934
15
ChungL. L.WuL. Y.LienK. H.ChenH. H.HuangH. H. (2013). Optimal design of friction pendulum tuned mass damper with varying friction coefficient. Struct. control health Monit.20 (4), 544–559. 10.1002/stc.514
16
ConstantinouM. C.TadjbakhshI. G. (1983). Optimum design of a first story damping system. Comput. Struct.17 (2), 305–310. 10.1016/0045-7949(83)90019-6
17
DaiH.JingX.WangY.YueX.YuanJ. (2018). Post-capture vibration suppression of spacecraft via a bio-inspired isolation system. Mech. Syst. Signal Process.105, 214–240. 10.1016/j.ymssp.2017.12.015
18
De DomenicoD.HajirasoulihaI. (2021). Multi-level performance-based design optimisation of steel frames with nonlinear viscous dampers. Bull. Earthq. Eng.19 (12), 5015–5049. 10.1007/s10518-021-01152-7
19
De DomenicoD.RicciardiG.TakewakiI. (2019). Design strategies of viscous dampers for seismic protection of building structures: A review. Soil Dyn. Earthq. Eng.118, 144–165. 10.1016/j.soildyn.2018.12.024
20
De DomenicoD.RicciardiG.ZhangR. (2020). Optimal design and seismic performance of tuned fluid inerter applied to structures with friction pendulum isolators. Soil Dyn. Earthq. Eng.132, 106099. 10.1016/j.soildyn.2020.106099
21
De LucaA.GuidiL. G. (2019). State of art in the worldwide evolution of base isolation design. Soil Dyn. Earthq. Eng.125, 105722. 10.1016/j.soildyn.2019.105722
22
DebS. K. (2004). Seismic base isolation–An overview. Curr. Sci.2004, 1426–1430.
23
DeringölA. H.GüneyisiE. M. (2021). Influence of nonlinear fluid viscous dampers in controlling the seismic response of the base-isolated buildings. Structures34, 1923–1941. 10.1016/j.istruc.2021.08.106
24
DeringölA. H.GüneyisiE. M. (2020). Single and combined use of friction-damped and base-isolated systems in ordinary buildings. J. Constr. Steel Res.174, 106308. 10.1016/j.jcsr.2020.106308
25
DezfuliF. H.AlamM. S. (2016). Seismic vulnerability assessment of a steel-girder highway bridge equipped with different SMA wire-based smart elastomeric isolators. Smart Mater. Struct.25 (7), 075039. 10.1088/0964-1726/25/7/075039
26
DingH.ChenL. Q. (2020). Designs, analysis, and applications of nonlinear energy sinks. Nonlinear Dyn.100 (4), 3061–3107. 10.1007/s11071-020-05724-1
27
DonàM.BernardiE.ZontaA.SalerE.da PortoF. (2022). “Assessment of the inter-story isolation technique applied to an existing school building,” in Current perspectives and New directions in mechanics, modelling and design of structural systems (United States: CRC Press), 233–239.
28
DongB.SauseR.RiclesJ. M. (2016). Seismic response and performance of a steel MRF building with nonlinear viscous dampers under DBE and MCE. J. Struct. Eng.142 (6), 04016023. 10.1061/(asce)st.1943-541x.0001482
29
DrozdovY. N.NadeinV. A.PuchkovV. N. (2007). Tribological behavior of frictional seismic dampers of pendulum type. J. Frict. Wear28 (2), 119–127. 10.3103/s1068366607020018
30
ElliottS. J.TehraniM. G.LangleyR. S. (2015). Nonlinear damping and quasi-linear modelling. Philosophical Trans. R. Soc. A Math. Phys. Eng. Sci.373 (2051), 20140402. 10.1098/rsta.2014.0402
31
EltahawyW.RyanK. L. (2020). Performance of flexible frame building with horizontal and 3D seismic isolation when subjected to 3D ground shaking. Earthq. Spectra36 (4), 1823–1843. 10.1177/8755293020942562
32
EneD.KishikiS.YamadaS.JiaoY.KonishiY.TerashimaM.et al (2016). Experimental study on the bidirectional inelastic deformation capacity of U‐shaped steel dampers for seismic isolated buildings. Earthq. Eng. Struct. Dyn.45 (2), 173–192. 10.1002/eqe.2621
33
FengX.JingX. (2019). Human body inspired vibration isolation: Beneficial nonlinear stiffness, nonlinear damping & nonlinear inertia. Mech. Syst. Signal Process.117, 786–812. 10.1016/j.ymssp.2018.08.040
34
FerreiraF.MoutinhoC.CunhaÁ.CaetanoE. (2018). Proposal of optimum tuning of semiactive TMDs used to reduce harmonic vibrations based on phase control strategy. Struct. Control Health Monit.25 (4), e2131. 10.1002/stc.2131
35
FujitaK.KasagiM.LangZ. Q.GuoP. F.TakewakiI. (2014). Optimal placement and design of nonlinear dampers for building structures in the frequency domain. Earthq. Struct.7 (6), 1025–1044. 10.12989/eas.2014.7.6.1025
36
FujitaK.MoustafaA.TakewakiI. (2010). Optimal placement of viscoelastic dampers and supporting members under variable critical excitations. Earthq. Struct.1 (1), 43–67. 10.12989/eas.2010.1.1.043
37
FujitaK.WatayaR.TakewakiI. (2021). Robust optimal damper placement of nonlinear oil dampers with uncertainty using critical double impulse. Front. Built Environ.7, 744973. 10.3389/fbuil.2021.744973
38
FukumotoY.TakewakiI. (2017). Dual control high-rise building for robuster earthquake performance. Front. Built Environ.3, 12. 10.3389/fbuil.2017.00012
39
GavinH. P.WilkinsonG. (2010). Preliminary observations of the effects of the 2010 Darfield earthquake on the base-isolated Christchurch Women’s Hospital. J. R. Soc. N. Z. Earthq. Eng.43 (4), 360–367.
40
GeorgeD. A. (1959). Continuous nonlinear systems.(No. TR-355). Cambridge, Massachusetts: Massachusetts Inst of Tech Cambridge Research Lab of Electronics.
41
GhaediK.IbrahimZ.AdeliH.JavanmardiA. (2017). Invited Review: Recent developments in vibration control of building and bridge structures. J. Vibroengineering19 (5), 3564–3580. 10.21595/jve.2017.18900
42
GiaralisA.TaflanidisA. A. (2018). Optimal tuned mass-damper-inerter (TMDI) design for seismically excited MDOF structures with model uncertainties based on reliability criteria. Struct. Control Health Monit.25 (2), e2082. 10.1002/stc.2082
43
GidarisI.TaflanidisA. A. (2015). Performance assessment and optimization of fluid viscous dampers through life-cycle cost criteria and comparison to alternative design approaches. Bull. Earthq. Eng.13 (4), 1003–1028. 10.1007/s10518-014-9646-5
44
GomezF.FermandoisG. A.SpencerB. F.Jr (2021). Optimal design of nonlinear energy sinks for mitigation of seismic response on structural systems. Eng. Struct.232, 111756. 10.1016/j.engstruct.2020.111756
45
GourdonE.AlexanderN. A.TaylorC. A.LamarqueC. H.PernotS. (2007). Nonlinear energy pumping under transient forcing with strongly nonlinear coupling: Theoretical and experimental results. J. Sound Vib.300 (3-5), 522–551. 10.1016/j.jsv.2006.06.074
46
GuoP. F.LangZ. Q.PengZ. (2012). Analysis and design of the force and displacement transmissibility of nonlinear viscous damper based vibration isolation systems. Nonlinear Dyn.67 (4), 2671–2687. 10.1007/s11071-011-0180-6
47
GurS.MishraS. K.ChakrabortyS. (2014). Performance assessment of buildings isolated by shape-memory-alloy rubber bearing: Comparison with elastomeric bearing under near‐fault earthquakes. Struct. Control Health Monit.21 (4), 449–465. 10.1002/stc.1576
48
GürgözeM.MüllerP. C. (1992). Optimal positioning of dampers in multi-body systems. J. Sound Vib.158 (3), 517–530. 10.1016/0022-460x(92)90422-t
49
HayashiK.FujitaK.TsujiM.TakewakiI. (2018). A simple response evaluation method for base-isolation building-connection hybrid structural system under long-period and long-duration ground motion. Front. Built Environ.4, 2. 10.3389/fbuil.2018.00002
50
HoC.LangZ. Q.SapińskiB.BillingsS. A. (2013). Vibration isolation using nonlinear damping implemented by a feedback-controlled MR damper. Smart Mater. Struct.22 (10), 105010. 10.1088/0964-1726/22/10/105010
51
HoC.ZhuY. P.LangZ. Q.BillingsS. A.KohiyamaM.WakayamaS. (2018). Nonlinear damping based semi-active building isolation system. J. Sound Vib.424, 302–317. 10.1016/j.jsv.2018.03.023
52
HuJ. W. (2014). Response of seismically isolated steel frame buildings with sustainable lead-rubber bearing (LRB) isolator devices subjected to near-fault (NF) ground motions. Sustainability7 (1), 111–137. 10.3390/su7010111
53
HwangJ. S.ChiouJ. M. (1996). An equivalent linear model of lead-rubber seismic isolation bearings. Eng. Struct.18 (7), 528–536. 10.1016/0141-0296(95)00132-8
54
IlbeigiS.JahanpourJ.FarshidianfarA. (2012). A novel scheme for nonlinear displacement-dependent dampers. Nonlinear Dyn.70 (1), 421–434. 10.1007/s11071-012-0465-4
55
JangidR. S.DattaT. K. (1995). Seismic behaviour of base-isolated buildings: A state-of-the art review. Proc. Institution Civ. Engineers-Structures Build.110 (2), 186–203. 10.1680/istbu.1995.27599
56
JangidR. S. (2007). Optimum lead–rubber isolation bearings for near-fault motions. Eng. Struct.29 (10), 2503–2513. 10.1016/j.engstruct.2006.12.010
57
JingX.ZhangL.FengX.SunB.LiQ. (2019). A novel bio-inspired anti-vibration structure for operating hand-held jackhammers. Mech. Syst. signal Process.118, 317–339. 10.1016/j.ymssp.2018.09.004
58
KangdaM. Z.BakreS. (2018). The effect of LRB parameters on structural responses for blast and seismic loads. Arabian J. Sci. Eng.43 (4), 1761–1776. 10.1007/s13369-017-2732-7
59
KasagiM.FujitaK.TsujiM.TakewakiI. (2016). Automatic generation of smart earthquake-resistant building system: Hybrid system of base-isolation and building-connection. Heliyon2 (2), e00069. 10.1016/j.heliyon.2016.e00069
60
KawaiA.MaedaT.TakewakiI. (2021). Critical response of high-rise buildings with deformation-concentration seismic control system under double and multi impulses representing pulse-type and long-duration ground motions. Front. Built Environ.7, 649224. 10.3389/fbuil.2021.649224
61
KawaiA.MaedaT.TakewakiI. (2020). Smart seismic control system for high-rise buildings using large-stroke viscous dampers through connection to strong-back core frame. Front. Built Environ.6, 29. 10.3389/fbuil.2020.00029
62
KodakkalA.SahaS. K.SepahvandK.MatsagarV. A.DuddeckF.MarburgS. (2019). Uncertainties in dynamic response of buildings with non-linear base-isolators. Eng. Struct.197, 109423. 10.1016/j.engstruct.2019.109423
63
KomurM. A. (2016). Soft-story effects on the behavior of fixed-base and LRB base-isolated reinforced concrete buildings. Arabian J. Sci. Eng.41 (2), 381–391. 10.1007/s13369-015-1664-3
64
KomuroT.NishikawaY.KimuraY.IsshikiY. (2005). Development and realization of base isolation system for high-rise buildings. J. Adv. Concr. Technol.3 (2), 233–239. 10.3151/jact.3.233
65
KravchukN.ColquhounR.PorbahaA. (2008). “Development of a friction pendulum bearing base isolation system for earthquake engineering education,” in Proceedings of the 2008 American Society for Engineering Education Pacific Southwest Annual Conference, June 22–25, 2008, Pittsburgh, Pennsylvania, 22–25.
66
KundeM. C.JangidR. S. (2003). Seismic behavior of isolated bridges: A-state-of-the-art review. Electron. J. Struct. Eng.3, 140–170. 10.56748/ejse.335
67
LaalejH.LangZ. Q.SapinskiB.MartynowiczP. (2012). MR damper based implementation of nonlinear damping for a pitch plane suspension system. Smart Mater. Struct.21 (4), 045006. 10.1088/0964-1726/21/4/045006
68
LangZ. Q.BillingsS. A. (2005). Energy transfer properties of non-linear systems in the frequency domain. Int. J. Control78 (5), 345–362. 10.1080/00207170500095759
69
LangZ. Q.BillingsS. A.YueR.LiJ. (2007). Output frequency response function of nonlinear Volterra systems. Automatica43 (5), 805–816. 10.1016/j.automatica.2006.11.013
70
LangZ. Q.GuoP. F.TakewakiI. (2013). Output frequency response function based design of additional nonlinear viscous dampers for vibration control of multi-degree-of-freedom systems. J. Sound Vib.332 (19), 4461–4481. 10.1016/j.jsv.2013.04.001
71
LangZ. Q.JingX. J.BillingsS. A.TomlinsonG. R.PengZ. K. (2009). Theoretical study of the effects of nonlinear viscous damping on vibration isolation of sdof systems. J. Sound Vib.323 (1-2), 352–365. 10.1016/j.jsv.2009.01.001
72
LavanO.DargushG. F. (2009). Multi-objective evolutionary seismic design with passive energy dissipation systems. J. Earthq. Eng.13 (6), 758–790. 10.1080/13632460802598545
73
LeeS. K.ParkJ. H.MoonB. W.MinK. W.LeeS. H.KimJ. (2008). Design of a bracing-friction damper system for seismic retrofitting. Smart Struct. Syst.4 (5), 685–696. 10.12989/sss.2008.4.5.685
74
LiC.ChangK.CaoL.HuangY. (2021). Performance of a nonlinear hybrid base isolation system under the ground motions. Soil Dyn. Earthq. Eng.143, 106589. 10.1016/j.soildyn.2021.106589
75
LiD. D.KeoghD. F.HuangK.ChanQ. N.YuenA. C. Y.MenictasC.et al (2019). Modeling the response of magnetorheological fluid dampers under seismic conditions. Appl. Sci.9 (19), 4189. 10.3390/app9194189
76
LiH.LiY.LiJ. (2020). Negative stiffness devices for vibration isolation applications: A review. Adv. Struct. Eng.23 (8), 1739–1755. 10.1177/1369433219900311
77
LiuD.LiuY.ShengD.LiaoW. (2018). Seismic response analysis of an isolated structure with QZS under near-fault vertical earthquakes. Shock Vib.2018, 1–12. 10.1155/2018/9149721
78
LiuD.ZhangY.FangS.LiuY. (2020). Horizontal-vertical-rocking coupled response analysis of vertical seismic isolated structure under near-fault earthquakes. Shock Vib.2020, 1–10. 10.1155/2020/6519808
79
LiuT.ZordanT.BriseghellaB.ZhangQ. (2014). An improved equivalent linear model of seismic isolation system with bilinear behavior. Eng. Struct.61, 113–126. 10.1016/j.engstruct.2014.01.013
80
LiuX.HuangX.HuaH. (2013). On the characteristics of a quasi-zero stiffness isolator using Euler buckled beam as negative stiffness corrector. J. Sound Vib.332 (14), 3359–3376. 10.1016/j.jsv.2012.10.037
81
LiuY.WuJ.DonàM. (2018). Effectiveness of fluid-viscous dampers for improved seismic performance of inter-storey isolated buildings. Eng. Struct.169, 276–292. 10.1016/j.engstruct.2018.05.031
82
LuoJ.WierschemN. E.HubbardS. A.FahnestockL. A.QuinnD. D.McFarlandD. M.et al (2014). Large-scale experimental evaluation and numerical simulation of a system of nonlinear energy sinks for seismic mitigation. Eng. Struct.77, 34–48. 10.1016/j.engstruct.2014.07.020
83
LuongoA.ZulliD. (2012). Dynamic analysis of externally excited NES-controlled systems via a mixed Multiple Scale/Harmonic Balance algorithm. Nonlinear Dyn.70 (3), 2049–2061. 10.1007/s11071-012-0597-6
84
MaC. F.ZhangY. H.TanP.KennedyD.WilliamsF. W.ZhouF. L. (2013). Non-stationary seismic response analysis of base-isolated buildings with many hysteretic devices. Comput. Struct.123, 39–47. 10.1016/j.compstruc.2013.04.003
85
MaH.YanB.ZhangL.ZhengW.WangP.WuC. (2020). On the design of nonlinear damping with electromagnetic shunt damping. Int. J. Mech. Sci.175, 105513. 10.1016/j.ijmecsci.2020.105513
86
MakitaK.MuraseM.KondoK.TakewakiI.KepnerW. G.BurnsI. S. (2018). Modeling urban hydrology and green infrastructure using the AGWA urban tool and the KINEROS2 model. Front. Built Environ.4, 1–15. 10.3389/fbuil.2018.00058
87
Martinez-RodrigoM.RomeroM. L. (2003). An optimum retrofit strategy for moment resisting frames with nonlinear viscous dampers for seismic applications. Eng. Struct.25 (7), 913–925. 10.1016/s0141-0296(03)00025-7
88
MazzolaniF. M. (2001). Passive control technologies for seismic-resistant buildings in Europe. Prog. Struct. Eng. Mater.3 (3), 277–287. 10.1002/pse.83
89
MengaN.BottiglioneF.CarboneG. (2021). Nonlinear viscoelastic isolation for seismic vibration mitigation. Mech. Syst. Signal Process.157, 107626. 10.1016/j.ymssp.2021.107626
90
MezziM. (2010). “Innovative configurations and morphologies using dissipating bracing systems,” in Proceedings of the 9th US National and 10th Canadian Conference on Earthquake Engineering, Toronto, Ontario, Canada, 25-29 July 2010.
91
MilanchianR.HosseiniM. (2019). Study of vertical seismic isolation technique with nonlinear viscous dampers for lateral response reduction. J. Build. Eng.23, 144–154. 10.1016/j.jobe.2019.01.026
92
MohammedJ.MohdZ. J. (2011). Seismic isolation in buildings to be a practical reality: Behaviour of structure and installation technique. J. Eng. Technol. Res.3 (4), 99–117. 10.5897/JETR2022.0733
93
MorganT. A. (2007). The use of innovative base isolation systems to achieve complex seismic performance objectives. Berkeley: University of California.
94
NakamuraT.FujitaK.TakewakiI. (2021). A simple critical response evaluation method for base-isolation building-connection hybrid system under double impulse as representative of near-fault ground motion. Front. Built Environ.7, 790584. 10.3389/fbuil.2021.790584
95
NiuF.MengL. S.WuW. J.SunJ. G.SuW. H.MengG.et al (2013). Recent advances in quasi-zero-stiffness vibration isolation systems. Appl. Mech. Mater.397, 295–303. 10.4028/www.scientific.net/amm.397-400.295
96
OkadaN.YeT.KajitaniY.ShiP.TatanoH. (2011). The 2011 eastern Japan great earthquake disaster: Overview and comments. Int. J. Disaster Risk Sci.2 (1), 34–42. 10.1007/s13753-011-0004-9
97
OzdemirG. (2015). Formulations of equivalent linearization of lead-rubber bearings for incorporating the effect of lead core heating. Earthq. Spectra31 (1), 317–337. 10.1193/041913eqs107m
98
OzuygurA. R.Noroozinejad FarsangiE. (2021). Influence of pulse-like near-fault ground motions on the base-isolated buildings with LRB devices. Pract. Periodical Struct. Des. Constr.26 (4), 04021027. 10.1061/(asce)sc.1943-5576.0000603
99
Palacios-QuiñoneroF.Rubió-MassegúJ.RossellJ. M.KarimiH. R. (2019). Design of inerter-based multi-actuator systems for vibration control of adjacent structures. J. Frankl. Inst.356 (14), 7785–7809. 10.1016/j.jfranklin.2019.03.010
100
PapaioannouG.VoutsinasA.KoulocherisD.AntoniadisI. (2019). Dynamic performance analysis of vehicle seats with embedded negative stiffness elements. Veh. Syst. Dyn.58, 307–337. 10.1080/00423114.2019.1617424
101
PengT.YanB.LiF. (2022). The hysteresis model of the friction pendulum bearing based on the moment balance theory. Ain Shams Eng. J.13 (4), 101707. 10.1016/j.asej.2022.101707
102
PengZ. K.LangZ. Q. (2008). The effects of nonlinearity on the output frequency response of a passive engine mount. J. Sound Vib.318 (1-2), 313–328. 10.1016/j.jsv.2008.04.016
103
ProvidakisC. P. (2008). Effect of LRB isolators and supplemental viscous dampers on seismic isolated buildings under near-fault excitations. Eng. Struct.30 (5), 1187–1198. 10.1016/j.engstruct.2007.07.020
104
ProvidakisC. P. (2009). Effect of supplemental damping on LRB and FPS seismic isolators under near-fault ground motions. Soil Dyn. Earthq. Eng.29 (1), 80–90. 10.1016/j.soildyn.2008.01.012
105
RosenbluethE.HerreraI. (1964). On a kind of hysteretic damping. J. Eng. Mech. Div.90 (4), 37–48. 10.1061/jmcea3.0000510
106
RyanK. L.EarlC. L. (2010). Analysis and design of inter-story isolation systems with nonlinear devices. J. Earthq. Eng.14 (7), 1044–1062. 10.1080/13632461003668020
107
SaidiI.HaritosN.GadE. F.WilsonJ. L. (2006). Floor vibrations due to human excitation-damping perspective. Earthq. Eng. Aust.2006, 257–264.
108
SapountzakisE. J.SyrimiP. G.PantazisI. A.AntoniadisI. A. (2016). KDamper concept in seismic isolation of bridges. Proc. 1st ICONHIC2016, 28–30.
109
ShimazakiD.NakagawaK. (2015). Seismic isolation systems incorporating with RC core walls and precast concrete perimeter frames-shimizu corporation Tokyo headquarter. Int. J. High-Rise Build.4 (3), 181–189. 10.21022/IJHRB.2015.4.3.181
110
ShinozukaM.ChaudhuriS. R.MishraS. K. (2015). Shape-memory-alloy supplemented lead rubber bearing (SMA-LRB) for seismic isolation. Probabilistic Eng. Mech.41, 34–45. 10.1016/j.probengmech.2015.04.004
111
Silva-NavarroG.Abundis-FongH. F. (2017). “Evaluation of autoparametric vibration absorbers on N-story building-like structures,” in Nonlinear dynamics (Cham: Springer), 177–184.
112
SinghM. P.MoreschiL. M. (2001). Optimal seismic response control with dampers. Earthq. Eng. Struct. Dyn.30 (4), 553–572. 10.1002/eqe.23
113
SoniD. P.MistryB. B.JangidR. S.PanchalV. R. (2011). Seismic response of the double variable frequency pendulum isolator. Struct. Control Health Monit.18 (4), 450–470. 10.1002/stc.384
114
SyedI. A. (2011). Simplified design guidelines for seismic base isolation in multi-storey buildings for Bangladesh National Building Code (BNBC). Int. J. Phys. Sci.6 (23), 5467–5486. 10.5897/IJPS11.795
115
SymansM. D.CharneyF. A.WhittakerA. S.ConstantinouM. C.KircherC. A.JohnsonM. W.et al (2008). Energy dissipation systems for seismic applications: Current practice and recent developments. J. Struct. Eng.134 (1), 3–21. 10.1061/(asce)0733-9445(2008)134:1(3)
116
TakewakiI.AkehashiH. (2021). Comprehensive review of optimal and smart design of nonlinear building structures with and without passive dampers subjected to earthquake loading. Front. Built Environ.7, 631114. 10.3389/fbuil.2021.631114
117
TakewakiI.MoustafaA.FujitaK. (2013). Improving the earthquake resilience of buildings: The worst case approach. Berlin: Springer, 159.
118
TakewakiI.MurakamiS.FujitaK.YoshitomiS.TsujiM. (2011). The 2011 off the Pacific coast of Tohoku earthquake and response of high-rise buildings under long-period ground motions. Soil Dyn. Earthq. Eng.31 (11), 1511–1528. 10.1016/j.soildyn.2011.06.001
119
TakewakiI. (1997). Optimal damper placement for minimum transfer functions. Earthq. Eng. Struct. Dyn.26 (11), 1113–1124. 10.1002/(sici)1096-9845(199711)26:11<1113:aid-eqe696>3.0.co;2-x
120
TakewakiI. (2000). Optimal damper placement for planar building frames using transfer functions. Struct. Multidiscip. Optim.20 (4), 280–287. 10.1007/s001580050158
121
TangB.BrennanM. J. (2013). A comparison of two nonlinear damping mechanisms in a vibration isolator. J. Sound Vib.332 (3), 510–520. 10.1016/j.jsv.2012.09.010
122
TesfamariamS. (2022). Performance-based design of tall timber buildings under earthquake and wind multi-hazard loads: Past, present, and future. Front. Built Environ.8, 848698. 10.3389/fbuil.2022.848698
123
ThakurV. M.PachporP. D. (2012). Seismic analysis of multistoried building with TMD (tuned mass damper). Int. J. Eng. Res. Appl. (IJERA)2, 319–326.
124
UemuraR.AkehashiH.FujitaK.TakewakiI. (2021). Global simultaneous optimization of oil, hysteretic and inertial dampers using real-valued genetic algorithm and local search. Front. Built Environ.7, 795577. 10.3389/fbuil.2021.795577
125
ValeevA.TokarevA.ZotovA. (2019). “Material with quasi-zero stiffness for vibration isolation in civil and industrial structures and buildings,” in IOP Conference Series: Earth and Environmental Science, 4–6 March, 2019, Russky Island, Russian Federation. IOP Publishing. 272 (3), 032048.
126
ValenteM.MilaniG. (2018). Alternative retrofitting strategies to prevent the failure of an under-designed reinforced concrete frame. Eng. Fail. Anal.89, 271–285. 10.1016/j.engfailanal.2018.02.001
127
WangJ.WierschemN. E.WangB.SpencerB. F.Jr (2020). Multi‐objective design and performance investigation of a high‐rise building with track nonlinear energy sinks. Struct. Des. Tall Special Build.29 (2), e1692. 10.1002/tal.1692
128
WangX.XieL.ZengD.YangC.LiuQ. (2021). Seismic retrofitting of reinforced concrete frame-shear wall buildings using seismic isolation for resilient performance. Structures34, 4745–4757. 10.1016/j.istruc.2021.10.081
129
WangY. P. (2002). Fundamentals of seismic base isolation. Taiwan: International training programs for seismic design of building structures hosted by National Certer of Research on Earthquake Engineering.
130
WhittleJ. K.WilliamsM. S.BlakeboroughA. (2012). Performance of structural members in seismic retrofitted frames with viscous dampers. UK: University of Oxford.
131
WierschemN. E.LuoJ.Al-ShudeifatM.HubbardS.OttR.FahnestockL. A.et al (2014). Experimental testing and numerical simulation of a six-story structure incorporating two-degree-of-freedom nonlinear energy sink. J. Struct. Eng.140 (6), 04014027. 10.1061/(asce)st.1943-541x.0000978
132
YamamotoK.FujitaK.TakewakiI. (2011). Instantaneous earthquake input energy and sensitivity in base‐isolated building. Struct. Des. Tall Special Build.20 (6), 631–648. 10.1002/tal.539
133
YanB.YuN.WuC. (2022). A state-of-the-art review on low-frequency nonlinear vibration isolation with electromagnetic mechanisms. Appl. Math. Mech.43 (7), 1045–1062. 10.1007/s10483-022-2868-5
134
YaoG. Z.YapF. F.ChenG.LiW.YeoS. H. (2002). MR damper and its application for semi-active control of vehicle suspension system. Mechatronics12 (7), 963–973. 10.1016/s0957-4158(01)00032-0
135
YeK.XiaoY.HuL. (2019). A direct displacement-based design procedure for base-isolated building structures with lead rubber bearings (LRBs). Eng. Struct.197, 109402. 10.1016/j.engstruct.2019.109402
136
ZhangQ.XiaS.XuD.PengZ. (2020). A torsion–translational vibration isolator with quasi-zero stiffness. Nonlinear Dyn.99 (2), 1467–1488. 10.1007/s11071-019-05369-9
137
ZhangR.PhillipsB. M.TaniguchiS.IkenagaM.IkagoK. (2017). Shake table real-time hybrid simulation techniques for the performance evaluation of buildings with inter-story isolation. Struct. Control Health Monit.24 (10), e1971. 10.1002/stc.1971
138
ZhangY.FungJ. F.JohnsonK. J.SattarS. (2022). Review of seismic risk mitigation policies in earthquake-prone countries: Lessons for earthquake resilience in the United States. J. Earthq. Eng.26 (12), 6208–6235. 10.1080/13632469.2021.1911889
139
ZhengW.WangH.HaoH.BiK.ShenH. (2020). Performance of bridges isolated with sliding-lead rubber bearings subjected to near-fault earthquakes. Int. J. Struct. Stab. Dyn.20 (02), 2050023. 10.1142/s0219455420500236
140
ZhouY.ChenP.MosquedaG. (2019). Analytical and numerical investigation of quasi-zero stiffness vertical isolation system. J. Eng. Mech.145 (6), 04019035. 10.1061/(asce)em.1943-7889.0001611
141
ZhouY.ChenP.MosquedaG. (2022). Numerical studies of three-dimensional isolated structures with vertical quasi-zero stiffness property. J. Earthq. Eng.26 (7), 3601–3622. 10.1080/13632469.2020.1813662
142
ZhouZ.WeiX.LuZ.JeremicB. (2018). Influence of soil‐structure interaction on performance of a super tall building using a new eddy‐current tuned mass damper. Struct. Des. Tall Special Build.27 (14), e1501. 10.1002/tal.1501
143
ZhuY. P.LangZ. Q. (2017). Design of nonlinear systems in the frequency domain: An output frequency response function-based approach. IEEE Trans. control Syst. Technol.26 (4), 1358–1371. 10.1109/tcst.2017.2716379
144
ZhuY. P.LangZ. Q.FujitaK.TakewakiI. (2022). The design of nonlinear damped building isolation systems by using mobility analysis. Front. Built Environ.8, 971260. 10.3389/fbuil.2022.971260
145
ZhuY. P.LangZ. Q.GuoY. Z. (2021). Nonlinear model standardization for the analysis and design of nonlinear systems with multiple equilibria. Nonlinear Dyn.104 (3), 2553–2571. 10.1007/s11071-021-06429-9
146
ZhuY. P.LangZ. Q.KawanishiY.KohiyamaM. (2020). Semi-actively implemented non-linear damping for building isolation under seismic loadings. Front. Built Environ.6, 19. 10.3389/fbuil.2020.00019
147
ZhuY. P.LangZ. Q. (2018). The effects of linear and nonlinear characteristic parameters on the output frequency responses of nonlinear systems: The associated output frequency response function. Automatica93, 422–427. 10.1016/j.automatica.2018.03.070
148
ZordanT.LiuT.BriseghellaB.ZhangQ. (2014). Improved equivalent viscous damping model for base-isolated structures with lead rubber bearings. Eng. Struct.75, 340–352. 10.1016/j.engstruct.2014.05.044
Summary
Keywords
earthquake, seismic isolation, building base isolation, inter-storey isolation, non-linear isolation systems, non-linear system design
Citation
Zhu Y-P, Lang ZQ, Fujita K and Takewaki I (2023) Analysis and design of non-linear seismic isolation systems for building structures—An overview. Front. Built Environ. 8:1084081. doi: 10.3389/fbuil.2022.1084081
Received
29 October 2022
Accepted
16 December 2022
Published
05 January 2023
Volume
8 - 2022
Edited by
Ehsan Noroozinejad Farsangi, University of British Columbia, Canada
Reviewed by
Said Elias Rahimi, University of Twente, Netherlands
Peyman Narjabadifam, University of Bonab, Iran
Aleksandra Bogdanovic, Institute of Earthquake Engineering and Engineering Seismology (IZIIS), North Macedonia
Vasant Annasaheb Matsagar, Indian Institute of Technology Delhi, India
Updates
Copyright
© 2023 Zhu, Lang, Fujita and Takewaki.
This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Z. Q. Lang, z.lang@sheffield.ac.uk
This article was submitted to Earthquake Engineering, a section of the journal Frontiers in Built Environment
Disclaimer
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