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High-rise structures and large-span bridges have low vibration frequencies and low intrinsic damping and hence are subjected to multimode vibrations under environmental excitation. Supplementing damping is a viable means to suppress such vibrations. The amount of supplemental damping is nevertheless limited as the damping devices in practice can on...
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... displacement, uðtÞ, and are in phase with the velocity, ˙ uðtÞ, is more appropriate (Caughey and Vijayaraghavan 1970;Inaudi and Makris 1996 where ζ; k are two factors. A damping force that is proportional to both displacement and velocity, and is in phase with velocity is also appropriate (Reid 1956;Makris 1997) fðu; ˙ uÞ ¼ ζkjuðtÞj ˙ uðtÞ ð 9Þ Fig. 3 shows the force-displacement behavior of damping models in Eqs. (8) and (9), wherein it is evident that the damping force is proportional to displacement, in phase with velocity, and independent of ...
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... outrigger system location is examined in this subsection. The parameter setting β ¼ 5 is the same as in the previous cases. For each location α ∈ ð0; 1 and a specific mode, the inertance μ is varied to find the optimal value that achieves the maximal damping (by equal modal damping principle). The optimal inertance μ opt ¯ ω 2 0n is plotted in Fig. 13(a) for the first three modes, and the corresponding maximal damping ratios are plotted in Fig. 13(b). It is seen that the optimal inertance decreases as the IDO location moves from the bottom to the top of the building. From the perspective of practical implementation, it is better to install the IDO at a higher position as a relatively ...
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... as in the previous cases. For each location α ∈ ð0; 1 and a specific mode, the inertance μ is varied to find the optimal value that achieves the maximal damping (by equal modal damping principle). The optimal inertance μ opt ¯ ω 2 0n is plotted in Fig. 13(a) for the first three modes, and the corresponding maximal damping ratios are plotted in Fig. 13(b). It is seen that the optimal inertance decreases as the IDO location moves from the bottom to the top of the building. From the perspective of practical implementation, it is better to install the IDO at a higher position as a relatively smaller inertance is able to achieve a comparable damping effect. When the IDO approaches the ...
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... multimode damping effect is concerned, the outrigger system is placed at α ¼ 1. Note that the maximally achievable damping is small for a mode when the outrigger is near antinodes of the corresponding mode shape (see Figs. 13 and 14). The stiffness ratio is assumed to be β ¼ 5.0. In practice, the first mode is usually of primary importance, and hence, the optimal inertance and viscous damper coefficient of the IDO is determined by targeting the first mode. Correspondingly, the equivalent NSDO is determined such that the same level of modal damping is provided by ...
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... further compare the performances of the NSDO and the IDO in suppressing multimode structural responses of the building under seismic loading, Fig. 23 plots the power spectra density (PSD) of top floor acceleration responses of the building respectively equipped with the IDO and the NSDO under the two earthquakes. It is shown that for the 1st mode vibration whose frequency lies in 0.1 Hz to 0.2 Hz, the NSDO and the IDO perform similarly in structural response reduction, as expected, ...
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... the earthquake-excited responses of the building are dominated by the 2nd mode rather than the 1st mode. In terms of the 2nd mode, the NSDOs substantially reduce the response amplitude as compared to that achieved by the IDO. For example, the 2nd mode amplitude of the building with the NSDOs is decreased by about 82% [from 0.1535 to 0.02707, see Fig. 23(a)] as compared to that of the building when equipped with the IDO under the El-Centro earthquake. In the case of the Northridge earthquake, a similar performance is seen in Fig. 23(b). The presented discussion assumes linear behaviors of the NSD in the NSDO. In fact, it is known that the typical NSD realized by precompressed springs ...
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... as compared to that achieved by the IDO. For example, the 2nd mode amplitude of the building with the NSDOs is decreased by about 82% [from 0.1535 to 0.02707, see Fig. 23(a)] as compared to that of the building when equipped with the IDO under the El-Centro earthquake. In the case of the Northridge earthquake, a similar performance is seen in Fig. 23(b). The presented discussion assumes linear behaviors of the NSD in the NSDO. In fact, it is known that the typical NSD realized by precompressed springs exhibits elastic nonlinear behaviors (stiffening effect in particular) at large deformations. This favorable characteristic has been well utilized to reduce the inelastic response of the ...
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... displacement, uðtÞ, and are in phase with the velocity, ˙ uðtÞ, is more appropriate (Caughey and Vijayaraghavan 1970;Inaudi and Makris 1996 where ζ; k are two factors. A damping force that is proportional to both displacement and velocity, and is in phase with velocity is also appropriate (Reid 1956;Makris 1997) fðu; ˙ uÞ ¼ ζkjuðtÞj ˙ uðtÞ ð 9Þ Fig. 3 shows the force-displacement behavior of damping models in Eqs. (8) and (9), wherein it is evident that the damping force is proportional to displacement, in phase with velocity, and independent of ...
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... outrigger system location is examined in this subsection. The parameter setting β ¼ 5 is the same as in the previous cases. For each location α ∈ ð0; 1 and a specific mode, the inertance μ is varied to find the optimal value that achieves the maximal damping (by equal modal damping principle). The optimal inertance μ opt ¯ ω 2 0n is plotted in Fig. 13(a) for the first three modes, and the corresponding maximal damping ratios are plotted in Fig. 13(b). It is seen that the optimal inertance decreases as the IDO location moves from the bottom to the top of the building. From the perspective of practical implementation, it is better to install the IDO at a higher position as a relatively ...
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... as in the previous cases. For each location α ∈ ð0; 1 and a specific mode, the inertance μ is varied to find the optimal value that achieves the maximal damping (by equal modal damping principle). The optimal inertance μ opt ¯ ω 2 0n is plotted in Fig. 13(a) for the first three modes, and the corresponding maximal damping ratios are plotted in Fig. 13(b). It is seen that the optimal inertance decreases as the IDO location moves from the bottom to the top of the building. From the perspective of practical implementation, it is better to install the IDO at a higher position as a relatively smaller inertance is able to achieve a comparable damping effect. When the IDO approaches the ...
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... multimode damping effect is concerned, the outrigger system is placed at α ¼ 1. Note that the maximally achievable damping is small for a mode when the outrigger is near antinodes of the corresponding mode shape (see Figs. 13 and 14). The stiffness ratio is assumed to be β ¼ 5.0. In practice, the first mode is usually of primary importance, and hence, the optimal inertance and viscous damper coefficient of the IDO is determined by targeting the first mode. Correspondingly, the equivalent NSDO is determined such that the same level of modal damping is provided by ...
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... further compare the performances of the NSDO and the IDO in suppressing multimode structural responses of the building under seismic loading, Fig. 23 plots the power spectra density (PSD) of top floor acceleration responses of the building respectively equipped with the IDO and the NSDO under the two earthquakes. It is shown that for the 1st mode vibration whose frequency lies in 0.1 Hz to 0.2 Hz, the NSDO and the IDO perform similarly in structural response reduction, as expected, ...
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... the earthquake-excited responses of the building are dominated by the 2nd mode rather than the 1st mode. In terms of the 2nd mode, the NSDOs substantially reduce the response amplitude as compared to that achieved by the IDO. For example, the 2nd mode amplitude of the building with the NSDOs is decreased by about 82% [from 0.1535 to 0.02707, see Fig. 23(a)] as compared to that of the building when equipped with the IDO under the El-Centro earthquake. In the case of the Northridge earthquake, a similar performance is seen in Fig. 23(b). The presented discussion assumes linear behaviors of the NSD in the NSDO. In fact, it is known that the typical NSD realized by precompressed springs ...
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... as compared to that achieved by the IDO. For example, the 2nd mode amplitude of the building with the NSDOs is decreased by about 82% [from 0.1535 to 0.02707, see Fig. 23(a)] as compared to that of the building when equipped with the IDO under the El-Centro earthquake. In the case of the Northridge earthquake, a similar performance is seen in Fig. 23(b). The presented discussion assumes linear behaviors of the NSD in the NSDO. In fact, it is known that the typical NSD realized by precompressed springs exhibits elastic nonlinear behaviors (stiffening effect in particular) at large deformations. This favorable characteristic has been well utilized to reduce the inelastic response of the ...
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Long-span bridges have low vibration frequencies and small intrinsic damping, and hence are subjected to large-amplitude vibrations, e.g., vortex-induced vibrations (VIVs), which jeopardize the serviceability and safety of the bridge structures. This study proposes a novel concept to supplement damping to such bridges for multimode vibration mitiga...
Citations
... An alternative approach to systems based on translational mass is using rotational masses. Gyroscopes (Yamada et al., 1997;He et al., 2017;Curadelli and Amani, 2022;Nagarajaiah et al., 2022) consist of rotating masses that generate a moment, which is a function of the angular velocity, that is useful for stabilizing the response of the structure. Depending on its orientation, it can be used to control the bending and torsional responses of the structure. ...
... Matteo et al. (2017) Movable façade damping system:Kareem (1995) andMoon (2009) Stiffness modification device Passive negative stiffness:Nagarajaiah et al. (2022) Passive viscous dampers:Wang et al. (2015) Passive friction dampers:Malhotra et al. (2020) Aerodynamic Cross-section shape design WT-based corners modification:Kwok et al. (1988),Tamura et al. (2005), Irwin(2008), Tse et al. (2009), Tanaka et al. (2012), Kwok (2013) and Gu et al. (2020) CFD-based drag minimization: Kareem et al. (2013), Bernardini et al. (2015), Mooneghi and Kargarmoakhar (2016), Elshaer et al. (2017) and Ding and Kareem (2018) CFD-based performance constraints: Cid Montoya et al. (2021a) and Abdelwahab et al. (2023) 3D shape design Twinsting: Elshaer et al. (2016) and Kim et al. (2018) Openings: Miyashita et al. (1993), Kim et al. (2017), Elshaer and Bitsuamlak (2018) and Marsland et al. (2022) Tappering: Kim et al. (2017) and Chen et al. (2021) Façade design Façade roughness and porosity: Belloli et al. (2014) and Skvorc and Kozmar (2023) Façade shape configuration: Pomaranzi et al. (2020) and Jafari and Alipour (2021a) Active Structural Stiffness control device Active variable stiffness (AVS): Dong et al. (2011) Semi-active magneto-rheological (MR) dampers: Spencer et al. (1997) and Baheti and Matsagar (2022) Semi-active electro-rheological (ER) dampers: Gavin (1998) Semi-active friction dampers: Xu et al. (2001) Active cable/tendon control: Yang and Samali (1983) and Reinhorn et al. (1987) Inertial control device Active mass damper (AMD): Kareem et al. (1999), Yamazaki et al. (1992), Ricciardelli et al. (2003), Shi et al. (2012) and Zhou et al. (2022) Multiple active mass dampers (MAMD): Yang et al. (2017) and Talib et al. (2019) Semi-active tuned mass dampers (SATMD): Hrovat et al. (1983) and Ricciardelli et al. (2000) Semi-active variable stiffness tuned mass dampers (SAVS-TMD): Varadarajan and Nagarajaiah (2011) Semi-active tuned liquid dampers (SATLD): Abe et al. (1998) Semi-active tuned liquid column dampers (SATLCD): Yalla et al. (2001) and Balendra et al. (2001) Semi-active movable façade damping system: Zhang et al. (2022) Hybrid mass damper (HMD): Tan et al. (2012) and Demetriou and Nikitas (2016) Active gyroscope stabilizer (AGS): Yamada et al. (1997), He et al. (2017), Curadelli and Amani (2022) and Nagarajaiah et al. (2022) Twin rotor dampers (TRD): Bäumer and Starossek (2016) and Terrill and Starossek (2022) Aerodynamic Façade shape control device Active cross-section: Ding and Kareem (2020) and Hareendran et al. (2023) Active plates: Abdelaziz et al. (2021) Active porosity and roughness: Karanouh and Kerber (2015) and Hou et al. ...
Controlling wind-induced responses is a challenging and fundamental step in the design of wind-sensitive critical infrastructures (CI). While passive design modifications and passive control devices are effective alternatives to a certain extent, further actions are required to fulfill design specifications under some demanding circumstances. Active countermeasures, such as active dampers, active aerodynamic devices, and operational control systems, stand out as a smart alternative that allows extra control over wind-induced responses of tall buildings, long-span bridges, wind turbines, and solar trackers. To make this possible, CI are equipped with operational technology (OT) and cyber-physical systems (CPS). However, as with any other OT/CPS, these systems can be threatened by cyberattacks. Changing their intended use could result in severe structural damage or even the eventual collapse of the structure. This study analyzes the potential consequences of cyberattacks against wind-sensitive structures equipped with OT/CPS based on case studies reported in the structural control literature. Several cyberattacks, scenarios, and possible defenses, including cyber-secure aero-structural design methods, are discussed. Furthermore, we conceptually introduce and analyze a new cyberattack, the ''Wind-Leveraged False Data Injection'' (WindFDI), that can be specifically developed by taking advantage of the positive feedback between wind loads and the misuse of active control systems.
... After applying the Laplace transformation [10,33,50,51] ...
Flexible high-rise buildings are extremely vulnerable to wind, especially when synchronously subjected to alongwind and crosswind forces. In this scenario, acceleration-sensitive targets (such as delicate instruments) are at risk of damage. Moreover, occupant comfort and structural safety may be degraded due to excessive bi-directional vibrations. To resolve this problem, a bi-directional rail variable friction pendulum-tuned mass damper (BRVFP-TMD) is used to achieve optimal bi-directional wind-induced vibration control. The modeling of the BRVFP-TMD for bi-directional high-rise buildings under bi-directional winds was performed. Further, the physical interaction forces of the BRVFP-TMD with a multi-degree-of-freedom structure and the governing equations for the modal structure with the BRVFP-TMD were derived, with experimental results confirming the effectiveness of the linear variable friction force. For the BRVFP-TMD with a lightly damped structure, acceleration optimizations were conducted to obtain closed-form solutions for optimal parameters. However, the deployment position of the tuned mass damper (TMD) was found to degrade the optimal control performance significantly. Therefore, for the convenience of engineers, improved optimal solutions were obtained by considering the actual deployment position of the TMD and the influence of inherent structural damping. The stochastic linearization method was used to evaluate the effect of linear hysteretic damping (HD) with equivalent viscous damping (VD) in the field of random theory. Accordingly, a closed-form expression for the VD ratio was proposed to represent HD. Numerical verifications of a Chinese landmark (Canton Tower) subjected to bi-directional winds were assessed through time history and frequency decomposition analyses. The results verified the effectiveness, correctness, and necessity of the BRVFP-TMD; the improved optimal solutions were also confirmed. Compared with the closed-form solution, which neglects the deployment position of the TMD, and the classic TMD, the improved optimal solutions of the BRVFP-TMD demonstrated superior performance in mitigating both structural displacement and acceleration. The vibration reduction ratios achieved were 44.55% for the displacement at the top of the mast and 46.69% for the acceleration at the top of the main tower.
... Several analytical and experimental studies of NSD in the form of an adaptive negative stiffness system (ANSS) have demonstrated efficient control performance. ANSS has been applied to BI structures, tall buildings and bridges, showing an efficient seismic and wind response reduction [36][37][38][39]. A modification of ANSS gives rise to a negative stiffness amplifying damper (NSAD) proposed by Wang et al. [40] uses a negative stiffness system combined with a flexibly supported VD (represented by classical Maxwell damping element). ...
Liquid storage tanks (LSTs) have become indispensable to civil engineering infrastructure. LSTs are used not only for storing harmless fluids but also explosive, toxic, and hazardous substances. Thus, the ability of LSTs to withstand significant seismic activity without damage is a major worry. Strong pulse-type characteristics in near fault (NF) type of ground motions have shown significant base and sloshing displacements for a commonly adopted structural control measure: base isolation (BI). The current study introduces negative stiffness and inerter dampers (NSIDs) as supplemental response control measures to LSTs with BI (BILSTs). Conventional supplemental damping applications in the isolation system are helpful in displacement reduction at the isolator level, but the upper structure response gets severely affected. This study presents NSIDs, characterised by the damping magnification effect, as supplemental dampers to BILSTs. The continuous liquid mass within the tank is represented by discrete lumped masses referred to as sloshing, impulsive, and rigid mass. The stiffness constants of these lumped masses are derived by considering the tank wall and stored liquid physical parameters. The optimal supplemental damping parameters are deduced by developing contour plots describing the sloshing and base displacement response reduction (mitigation) ratios. Through analytical studies conducted using real earthquake records, it has been demonstrated that appropriately designed Negative Stiffness and Inerter Devices (NSIDs) yield enhanced performance for Base Isolated Liquid Storage Tanks (BILSTs). These optimised combinations of NSIDs effectively mitigate isolator displacement, base shear, lumped sloshing mass displacement, and sloshing mass height in response to both near-field (NF) and far-field (FF) base excitations.
... Sarlis et al. [21,22] developed physical devices to achieve negative stifness, which is a signifcant component for some causal RILD models. Nagarajaiah et al. [23] investigated the multimode response mitigation efects of dampers with negative stifness and inerter systems. Luo et al. [24] used a Maxwell negativestifness damper to causally realize RILD. ...
Compared with conventional linear viscous damping (LVD), rate-independent linear damping (RILD) mitigates floor response acceleration in low-frequency structures more effectively without compromising the control performance of displacement responses during long-period or low-frequency earthquakes. Although theoretical and experimental attempts have been made to overcome the noncausality of RILD devices and realize RILD using passive or semiactive devices, only a few studies have highlighted the impulse-response precursor and modal analysis method of multistory structures incorporated into RILD devices. This study investigated the impulse-response precursor of a noncausal RILD system and proposed a novel modal decomposition method for the structures equipped with nonproportionally distributed RILD devices. Additionally, real-time hybrid simulation was conducted to validate the effectiveness of the proposed modal analysis method and the feasibility of realizing ideal RILD using mechanical devices. This study is the first to demonstrate the differences between RILD and LVD devices in terms of controlling the modal responses of low-frequency structures and how RILD can lower the floor response acceleration more effectively compared to LVD.
... Reviewing of the above non-TMD type solutions indicates that the key to directly applying dampers on wind turbines is how to install them in a place with relative large deformation or using a damping amplification mechanism. However, many passive controls of wind turbines are emphasized on utilizing transversal displacement, while the benefit of use of rotation is not well-recognized [53,54]. Moreover, the seismic response reduction effect of supplemental devices under near-fault pulse-like ground motions is relatively limited, typically for experimental investigations. ...
Wind turbine (WT) with a long period is a dynamic sensitive but lightly damped structure, which may be prone to earthquakes, especially for the near-fault pulse-like records containing large amplitude of velocity pulse with a period close to WT's period. An efficient and convenient solution to enhance the damping effect of WT, amplifying damping transfer system (ADTS), is applied by transferring the upper rotation of the wind turbine to its bottom with an amplified damping mechanism. The feasibility of the ADTS is experimentally validated through free vibration tests, sinusoidal excitation tests, and shaking table tests for both non-pulse-like earthquakes and pulse-like earthquakes. Test results of free vibration validate that more than 6.2% extra damping ratio is provided by the ADTS to the tested WT model; while the supplemental stiffness of ADTS shifts the frequency of the tested WT model from 2.16 Hz to 2.61 Hz. Sinusoidal tests show ADTS reduces the displacement (acceleration) response of the tested WT by about 73.88% (58.16%) when subjected to resonant frequency. It is also observed that the ADTS is effective in controlling the seismic responses of non-pulse-like earthquakes and pulse-like earthquakes, providing at least 30% of the reduction in displacement and acceleration. Simulations with high accuracy indicate that the pulse signal usually concentrates the majority of the input energy of near-fault pulse-like earthquakes; while the ADTS can absorb most of the input energy (over 90%), protecting the WT away from undergoing excessive vibration.
... As per the literature survey, several research works have been conducted on the performance of structures with passive control devices under seismic excitation [71][72][73][74]. However, a few works have been carried out on passive control devices such as TMDI-NSD and their optimum parameters [87,88]. The previous work published by Zhang et al. [65] studied the optimum design of the TMD-NSD device on an undamped structure system using only H 2 and H ∞ methods. ...
This paper presents a study on optimizing the combination of a tuned mass damper inerter and a negative stiffness damper (TMDI-NSD) for better performance of structures against seismic actions. The experimental data obtained from the literature were used in the optimization of a hybrid combination of TMDI-NSD subjected to harmonic excitation considering different stability maximization criteria (SMC). The H2 optimization technique was used to obtain the optimum tunning parameter using the numerical method, while the closed form of the optimum technique was used to obtain the optimum tunning parameter through the SMC optimization technique. The maximum dynamic amplification factor (DAFmax) was considered for a comparison of TMDI-NSD. The results show that the performance of a TMDI-NSD combination is superior compared to that of a TMD. In addition, it is found that the performance of SMC is less compared to H2 & H∞ criteria, but the performance of H2 & H∞ is equivalent. The DAFmax value increases with the increase in the mass ratio for the TMDI-NSD combination, whereas it declines with the rise in the mass ratio for TMD. Besides, the performance of the damped primary system under seismic load with and without the TMDI-NSD combination was analyzed. Twenty real earthquake ground motion data were considered in the analysis. The response of the primary system mitigated with the TMD and TMDI-NSD combination was evaluated in terms of the broad frequency range efficiency and peak value. It is observed that the damped primary system with TMDI-NSD combination using under-optimization criteria is superior to TMDI-NSD with respect to the displacement response. However, when considering the acceleration response, the SMC performs better compared to H2 & H∞ optimization criteria. The acceleration and displacement response for the primary structural system is reduced by 60% and 75%, respectively, by using TMDI-NSD of SMC optimization. Finally, the investigation of the single primary degree of freedom for a system with a TMDI-NSD combination indicates that all three optimization criteria under real seismic excitation perform better.
... Note that Laplace transformation in terms of the signum function has been illustrated by Satish [36] and Liu [37,38]. The following nondimensionalized terms are introduced, as listed in Table 1. ...
The hysteretic damping tuned mass damper (HD-TMD), which exhibits linear damping force, has been achieved by variable friction devices. Such devices own the advantages of stable mitigation capacity and easy maintenance compared to viscous damping devices. Previous studies have mainly concentrated on the vibration mitigation effect of the HD-TMD system without explicit consideration of structural acceleration control. In this context, seismic optimizations of HD-TMD for structural acceleration control were presented, and the effective damping of HD-TMD was investigated. H∞ optimizations of the HD-TMD were considered for undamped and lightly damped structures with fixed-point theory, where the closed-form solutions of optimal and improved parameters were derived. Parametric analysis for the dynamic amplification factors (DAFs) of structural acceleration revealed that the closed-form solutions effectively tuned the DAF into double peaks and reduced the maximum response overall frequency. H2 optimizations were conducted with residue theory for the optimization of the undamped structure, and the optimal parameters of HD-TMD subjected to stochastic ground excitation were obtained by numerical searching and curve-fitting techniques. Effective damping of the HD-TMD was consequently examined using the stochastic stationary process in which the damping effect additionally provided to the structure was measured. The effectiveness of the proposed optimal solutions for the HD-TMD in the form of an available engineering variable friction device was thereby corroborated by twenty sets of seismic ground motions. Spectrum's results indicated that the proposed optimal parameters greatly improved the absolute structural acceleration response and provided excellent seismic mitigation capacity for structural displacement response. The response of the equivalent SDOF demonstrated almost the same trend of absolute structural acceleration reduction, which revealed the successful application of effective damping of HD-TMD for designers. Detailed analysis of the earthquake record indicated the functionality and effectiveness of the proposed methods of HD-TMD with the average absolute structural acceleration reduction ratio of 65.86% and 42.66% for maximum reduction and standard deviation reduction, respectively.
... Besides TMD, there are many other damping enhancement solutions using novel dampers [32][33][34][35][36][37][38][39][40] and magnification strategies, 41,42 which have been successfully applied at other infrastructures. In terms of wind turbines, braced-friction damper system, 43 braced-viscous damper system, 44 scissor-jack braced viscous damper, 45 and magnetorheological dampers, 46,47 etc., were typically applied to control the vibration of wind turbines. ...
This paper proposed a novel amplifying damping transfer system (ADTS) as a new damping enhancement solution for high-rise structures like wind turbines. The proposed ADTS can transfer the upper rotation of turbine tower to its bottom with damping amplification mechanism. Hence, viscous damper can be installed on wind turbines in a very convenient and efficient way. The dynamic characteristics of wind turbines equipped with ADTS were parametrically investigated concerning the influence of the damping, stiffness, and position of the ADTS based on complex frequency analysis. It was found that each mode has a maximum damping ratio, which is affected by the ADTS stiffness and position. The optimal ADTS position of the first mode is about 0.7 H (turbine height), and the optimal positions of the second mode are at 0.3 H and 0.86 H. The proposed ADTS considerably attenuated both drift and acceleration responses of wind turbines caused by winds and earthquakes. For example, as compared to the optimized tuned mass damper, ADTS further decreases the displacement (acceleration) of wind turbine tower by about 22% (38%).
... Recently, damped outriggers were proposed for bridge vibration mitigation [40,41], where the concept was verified by analytical and numerical analyses. This study further provides a method for optimal design of a suspension bridge with damped outriggers at multiple locations. ...
Long-span suspension bridges are subjected to wind-induced vibrations due to their large flexibility and low damping. Damped outriggers have been proposed recently to supplement damping and suppress multimode vibrations of main girders of long-span bridges, e.g., vortex-induced vibrations. However, when installed at multiple positions including tower-girder junction points and girder ends to further improve multimode damping effect, damping effects of the damped outriggers are interdependent. Additionally, the frequency curves of adjacent modes with respect to varying parameters of the damping devices could approach and intersect with each other, making it difficult to track mode orders and modal damping variations in design optimization. This study therefore proposes an optimization method to design damped outrigger parameters for maximizing multimode damping of the bridge. First, the bridge with damped outriggers is modeled generally using finite element method for dynamic analysis. Subsequently, two critical issues in the design, i.e., the mode tracking and multi-objective optimization, are respectively addressed by using the modal assurance criterion and the genetic algorithm. The proposed method is then applied to the Xihoumen Bridge with a main span of 1650 m. The results show that through the proposed optimization, 6 out of 7 modes vulnerable to vortex-induced vibrations can reach a damping ratio over 1.0%, which cannot be achieved by using damped outriggers of a uniform size. Furthermore, the required damper coefficients are decreased by 49.4%. The flexibility of the outriggers has been considered in the design. The developed method is promising in the design of other types bridge damping devices, e.g., multiple tuned mass dampers.
... However, their performances are quite different, because the NSD provides almost frequency-independent negative stiffness while the negative stiffness equivalently realized by the inerter increases rapidly as vibration frequency increases. Such differences lead to varied performances of the NSD and inerter-based absorbers in vibration suppression of high-rise structures 36,37 and stay cables 38 which are subjected to multi-mode vibrations. Particularly, as in the comparative study of a tall building with a damped outrigger, respectively, enhanced by an NSD and an inerter, 36 the inerter when tuned to the first mode has nearly no damping effect on the second mode and higher modes. ...
... The optimal inertance and viscous coefficient of the IDO can be determined based on equal modal damping. 36 Figure 2(a) shows the variation of optimal inertance with respect to mode number and IDO location. Figure 2(b) shows maximal damping ratios achieved by the optimal IDO and Fig. 2(c) shows the corresponding viscous coefficient of the damper in the optimal IDO. ...
... The 60-story St. Shangri-La Palace, Philippines, is considered for simulation. 10,13,36 The total height of the building is 210 m, and the bending stiffness and mass per unit length of its simplified model are EI = 1.818e13 N · m 2 and m = 9.0308e4 kg/m. ...
Damped outrigger is a viable means for reducing dynamic responses of tall buildings. This study focuses on generalized damped outrigger (GDO) systems. A GDO is composed of a damper for energy dissipation, a negative stiffness device and an inerter for damping enhancement. The GDO system incorporates GDOs at different floors of the tall building optimized to varied structural modes. Frequency equation of a tall building simplified as a cantilever beam with multiple GDOs is first derived by complex modal analysis. A finite different model of such a system is used for verification. Parametric analyses are then performed to compare damping effects of different GDO systems. It is found that a negative stiffness damped outrigger (NSDO) or inerter damped outrigger (IDO) needs to be optimized for maximizing damping of a specific mode. GDOs, respectively, tuned to different modes can largely improve the multimode damping effects. The optimal parameters of the GDOs are slightly different from those in the case when they are installed separately. With both negative stiffness and nonzero inertance, a GDO still needs to be tuned to a specific mode because multimode damping is sensitive to the damper coefficient. The combination of an NSDO optimized to the first mode and an IDO tuned to a higher mode seems the best solution. The IDO additionally improves the first mode damping provided by the NSDO and the two-mode damping is not sensitive to the damper coefficient of the NSDO. The findings are confirmed through seismic response analyses of a tall building with different GDO systems.
