Nonlinear Fluid Viscous Dampers Research Articles

Seismic response of SMRFs retrofitted with bracing systems and nonlinear fluid viscous dampers under near and far field ground motion

Seismic response of SMRFs retrofitted with bracing systems and nonlinear fluid viscous dampers under near and far field ground motion

Simultaneous analysis and design optimization for seismic retrofitting of hysteretic structures with fluid viscous dampers

Fluid viscous dampers, if properly sized and placed, can significantly improve the performance and safety of existing structures during an earthquake. This has motivated the development of several approaches to optimize the design of fluid viscous dampers. The optimization approaches available typically have an iterative nature, and in every iteration, expensive time-history analyses are performed. This paper presents a novel optimization-based approach for retrofitting hysteretic structures with fluid viscous dampers that does not require the computation of time-history analyses. The sizing and placement of the dampers are defined using a simultaneous analysis and design optimization approach based on nonlinear programming. In this approach, the equations of motion are treated as equality constraints of the optimization problem. As a consequence, design sensitivity analysis methods are not needed to calculate the gradients of the objective and constraint functions. Two design scenarios are considered: structures with hysteretic behavior retrofitted with linear or nonlinear fluid viscous dampers. The optimization variables include the damping coefficients of the dampers and the structural response over time. The manufacturing cost of the dampers is minimized, with constraints on the inter-story drifts. A continuation scheme on the design-driving inter-story drift constraints is proposed to effectively solve the class of problems considered. The numerical results demonstrate that the proposed approach can solve complex design optimization problems using reasonable computational resources and time. It is also shown that, thanks to the proposed approach, additional constraints can be incorporated in the problem formulation with minimal modeling effort, and without the need to develop additional sensitivity analyses for computing the gradients of the added constraints. The Julia codes used in this study are freely available on GitHub: https://github.com/pollinico/SAND_opt_nonlinFVDs.

Seismic design of reinforced concrete buildings equipped with viscous dampers using simplified performance-based approach

Passive control systems, such as Fluid Viscous Dampers (FVDs), have gained significant consideration in the design of earthquake-resistant structures. However, simple analysis and design methods are scarce for more practical and feasible implementation. This study provides a simplified procedure for performance-based seismic design of Reinforced Concrete (RC) special moment resisting frame using nonlinear FVDs. It adopts an extended performance-based design approach, focusing on maximum displacement along with floor acceleration to control the overall behavior of the structure. The fundamental principle of the method is to achieve the fully stressed (effect of FVDs on response indices) design approach to place dampers, which is attained by placing dampers among the storeys where drifts exceed the pre-decided performance limits. Further, a uniform damage distribution concept is followed to maximize the dampers' capacity. This study examines a rectangular-shaped RC SMRF with dampers to get the required performance when subjected to design basis and maximum considered earthquake levels. To check the efficacy, the proposed method is contrasted with a practical design method and a standard placement method employed in previous studies for RC structures with dampers. The analysis shows that the structure meets the performance targets of the design basis and the maximum considered level of earthquake hazards using the proposed step-by-step procedure. The comparison with the other two methods confirmed that the structure with dampers improved seismic behavior with the suggested process. Structural engineers can refer to the proposed method for the design of RC buildings with FVDs.

A novel stochastic linearization technique for structures with nonlinear fluid viscous dampers including soil-structure interaction

A novel stochastic linearization technique for structures with nonlinear fluid viscous dampers including soil-structure interaction

Full-scale shaking table tests and numerical studies of structural frames with a hybrid isolation system

A typical hybrid isolation system (HIS) incorporating natural-rubber bearings (NRBs) and nonlinear fluid viscous dampers (NFVDs) is proposed for seismic protection of critical equipment in nuclear power industrial buildings (NPIBs) under strong earthquakes. Design procedure with a parametric study towards the HIS considering various stiffness and damping values is first investigated via extensive nonlinear time history analyses. Then a preliminary recommendation for the specific structural demands of the considered system is proposed to direct the seismic design for both member- and system-level tests. Through a suite of full-scale shaking table tests on two typical NPIBs, the efficiency and reliability of the HIS are verified, in comparison to the structure with conventional rubber isolation system (RIS). The shaking table test results exhibit a superior behavior of the HIS in structural dual control strategies, i.e., transient acceleration control in critical equipment and bearing deformation control. Also, the HIS presents stable and resilient performances in both negligible residual bearing deformation and undetectable damage to structural/nonstructural components (containing the seismic isolated devices, i.e., NRBs and NFVDs). Finally, a three-dimensional finite element (FE) structural model and a single-degree-of-freedom (SDOF) system are successively developed to simulate the dynamic responses of the test structures. The well-validated SDOF FE model, serving as a reliable alternative for the isolated NPIBs, can be further utilized to facilitate practical design.

Enhancing Seismic Resilience of Existing Reinforced Concrete Building Using Non-Linear Viscous Dampers: A Comparative Study

After the catastrophic destruction of the October 2005 Kashmir earthquake, the first building code of Pakistan was developed in 2007. The sole purpose of the building code of Pakistan (BCP) was to incorporate advancements in earthquake-resistant design to fortify structures and ensure the safety of citizens against future seismic events. After 2007, the BCP was not revised till 2021 to include the changes over time. However, the recently updated version of BCP 2021 highlights that the seismicity of many regions in Pakistan is high, which is not truly reflected in the BCP 2007. Therefore, the advancements in earthquake-resistant design due to the growing concerns about the potential risks of seismicity in the region have been incorporated into the updated version of the BCP. However, there are concerns among researchers that many structures designed on the 2007 code may need seismic fortification. Therefore, the current study focuses on the seismic fortification of existing systems that were developed using previous codes. Non-linear viscous fluid dampers are used to improve the seismic resilience of existing structures. This study compares the seismic performance of an existing reinforced concrete building with and without non-linear viscous dampers and subjected to a non-linear dynamic analysis. The performance of the building is evaluated in terms of story displacement, story drift, story acceleration, and energy dissipation mechanisms. Adding the non-linear fluid viscous dampers in the structure caused a decrease in the inter-story drift by around 31.16% and the roof displacement was reduced by around 36.58%. In addition to that, in a controlled structure, more than 70% of energy was dissipated by the fluid viscous dampers. These results indicate that adding the non-linear fluid viscous dampers to the existing structure significantly improved the vibration performance of the system against undesirous vibrations. The outcomes of this study also provide a very detailed insight into the usage of non-linear viscous dampers for improving the seismic performance of existing buildings and can be used to develop effective strategies to mitigate the impact of seismic events on already built structures.

Damage indices of steel moment-resisting frames equipped with fluid viscous dampers

ABSTRACT Deformations, accelerations, shear forces, and energy demands are normally utilized to evaluate the performance of steel frames equipped with fluid viscous dampers (FVDs). This study aims to quantify damage indices (DI) and their distributions along the structural height for steel frames (3, 6, 9, and 20 stories) equipped with FVDs. The damage model incorporating both deformation and hysteretic plastic energy is adopted to quantify damage developed in structures. A set of 20 pairs of ground motions is used to perform nonlinear time history analyses. Influences of structural property and FVD features (supplementary damping ratio and velocity power ) on DI are investigated. The results show that FVDs with lower α would reduce DI. However, nonlinear FVDs lead to higher DI compared to linear ones when >30%, particularly for 9- and 20-story structures. Nonlinear FVDs () are more effective than linear ones in reducing DI during low-intensity earthquakes. The results further demonstrate that the distribution of DI along the structural height is mostly determined by structural properties, FVD characteristics, ground motion intensity, and the type of damage model used.

Shock Vibration Control of SDOF Systems with Tubular Linear Eddy Current Dampers

The nonlinear dynamic characteristic of a tubular linear eddy current damper (TLECD) and the transient responses to shock excitations of a single-degree-of-freedom (SDOF) system with the TLECD are studied. First, the nonlinear force-velocity relationship of the TLECD is discussed using the finite element simulation and mathematical model fitting. Next, the influences of three forms of shock excitation and various mechanical parameters of the TLECD on shock vibration control of an SDOF system with the TLECD are investigated. Moreover, for the SDOF systems with the TLECD or the nonlinear fluid viscous dampers (FVD) at the same maximum displacement and maximum damper force, the time to reach the maximum displacement, the time to reach one-third of the maximum displacement, the energy input of the external loading, and the energy dissipation of dampers are analyzed and compared. Finally, the shock response spectrums (SRSs) of the SDOF system and the design flowchart for the TLECD are presented to provide a reference for shock vibration control of the SDOF system with the nonlinear TLECD and the design of TLECDs. The results show that there is an optimal dimensionless critical relative velocity that minimizes the dimensionless maximum damping force for reaching the target maximum displacement, and compared to the FVD, the TLECD greatly shortens the time to reach one-third of the maximum displacement.

Energy-based fragility curves of building structures equipped with viscous dampers

The performance of systems equipped with fluid viscous dampers (FVDs) has been extensively analyzed only by determining the deformations, accelerations, and forces. However, with current analysis and methodology for quantifying structural damage, focusing on energy as an evaluation criterion is conceptually very attractive. The energy concept is able to capture structural characteristics simultaneously as deformation, force, and the number of hysteretic loops. Therefore, the aim of this paper is to introduce a comprehensive investigation to estimate the probability of collapse (P[collapse]) of three steel buildings (3-, 9-, and 20-story) equipped with linear and nonlinear FVDs based on plastic energy demand EPD. To assess the seismic collapse, nonlinear static pushover analyses (NSPA) were utilized to compute the plastic energy capacity EPc with significant contributions of higher modes, and incremental dynamic analyses were performed subjecting 20-pairs of earthquake records to produce a response curve of EPD until it caused collapse. Then, the fraction P[collapse] at a given intensity level was be estimated when the EPD exceeds the EPC; subsequently, the analytical fragility curves were developed. The results demonstrate that the supplemental FVDs can substantially reduce (i.e., by 30–100%) the P[collapse]of steel buildings. P[collapse] based on EPD experiences lower values than those based on inter-story-drift demand (θD). In most cases based on EPD, buildings with nonlinear FVDs have a relatively lower P[collapse] than linear FVDs. Although, in the case of the θD, the linear FVDs are effective than nonlinear ones in reducing P[collapse].

Seismic vulnerability assessment of reinforced concrete buildings having nonlinear fluid viscous dampers

Seismic resilience is the residual capacity of a damaged system for recovering and sustaining an acceptable level of performance as a consequence of a seismic event. Firstly, this paper summarizes the current calculation framework of seismic resilience using fragility analyses. After that, a new metric based on vulnerability analyses is developed to calculate seismic resilience. Finally, a typical hospital building is adopted as a single building and then retrofitted with supplemental Energy Dissipation Systems (EDS) to show the applicability of the new metric and compare it with the current calculation model of the seismic resilience. The considered supplemental EDS is the Nonlinear Fluid Viscous Damper (NFVD) located as the diagonal damper-brace system. The seismic performance of the supplemental EDSs is to enhance structural performance by reducing induced lateral displacements and as a result the level of physical damages and losses. To this end, Incremental Dynamic Analysis (IDA) is implemented to achieve the damage fragility and vulnerability curves. A comparison of the fragility, vulnerability, and functionality curves indicates that NFVDs are potentially useful for attenuating seismic damages to structural and non-structural components.

Energy dissipation demand and distribution for multi-story buildings with fluid viscous dampers

The seismic response of structures with fluid viscous dampers (FVDs), which is a predominant type of structural control techniques, can be analysed from the perspective of energy. In such structures, the imposed seismic energy is mainly dissipated by the structural plastic energy, EP, and the energy dissipated by FVDs, Ed2, which quantify the structural cumulative damage and FVD’s seismic reduction effect, respectively. Research conducted in the past focuses on investigating the EP demand of systems without supplemental damping devices, but little knowledge is available for the EP and Ed2 demand in multi-story buildings equipped with FVDs. To fill this gap, this paper conducted a comprehensive investigation based on four steel-moment resisting buildings with different height (3-, 6-, 9-, and 20-stories, respectively) equipped with linear or nonlinear FVDs. The effect of structural property and FVDs properties, characterised by the supplemental damping ratio ξadd and velocity power α, on the EP and Ed2‘s overall demand and distributions among stories were illustrated. The results indicate coupling effects of structural property, ξadd and α, on the EP and Ed2 demands. In most cases, the increase of ξadd and the decrease of α can reduce the EP demand and increase the Ed2 response. However, the increasing of ξadd is not effective if it is larger than 20% and the FVDs with α = 0.3 are not recommended in relative high-rise buildings. The distribution pattern shows a trend of linearly decreasing along the height, but those in the high-rise buildings are disturbed by high-mode effects.

Analysis of bilinear hysteretic structures with nonlinear fluid viscous dampers using modified stochastic linearization technique

Viscous dampers are increasingly used to design seismic resistant structures in modern construction due to their ability to reduce structural and non-structural damage by absorbing a large portion of the earthquake input energy. To facilitate the design of such complex nonlinear systems, this study aims to propose new non-Gaussian probability density functions (PDFs) to improve the accuracy in the determination of the seismic response of bilinear hysteretic structures equipped with linearized nonlinear viscous dampers. The employed linearization method is based on a stochastic linearization technique using stationary response velocity PDFs, while the difference between the governing nonlinear differential equation and the equivalent linear equation is minimized. To generate suitable functions, a Genetic Algorithm (GA) optimization method is adopted for both hard and soft soil-based structures equipped with nonlinear viscous dampers using three different power coefficients. The computational error of the employed modified stochastic linearization technique is then evaluated for single-degree-of-freedom (SDOF) systems under a set of five thousand randomly generated earthquake excitations with peak ground accelerations (PGAs) of 0.2 g to 0.6 g. The results indicate that the proposed method can significantly reduce (up to 80%) the computational errors. Subsequently, the lateral roof displacements of 5-story structures equipped with nonlinear viscous dampers are obtained under a set of natural ground motions using different linearization methods. It is shown that the proposed functions lead to the least error for both hard and soft soil-based structures compared to the accurate results.

Influence of nonlinear fluid viscous dampers in controlling the seismic response of the base-isolated buildings

Recently, many buildings have originally been designed as base-isolated to mitigate the structural vibration. However, buildings with base isolation systems can undergo displacement/amplification demand due to the inherent nonlinear behaviour of the base isolators, especially in earthquake-prone regions. Hence, in some cases it could be necessary to control the seismic response of the base-isolated buildings using supplemental damping device. This paper investigated the effectiveness of nonlinear fluid viscous damper (NFVD) considering design parameters for the base-isolated buildings with lead rubber bearing (LRB). For this, 10-storey benchmark steel moment resisting frame isolated with LRB having a series of isolation periods (T) of 3, 3.5, 4, and 5 s was used. These base-isolated frames consist of three bays and NFVDs having different damping exponents (α) of 0.15, 0.30, 0.50, and 0.70 were inserted in the mid, corner, and all bays of each base-isolated frame at the ground level. The case studied frames were modelled with a finite element program in which LRB elements were characterized by bi-linear hysteretic behaviour while NFVD elements were represented considering the Maxwell model having an elastic spring and a viscous dashpot in series. The nonlinear response of the frames with LRB and NFVD were evaluated by the nonlinear time history analyses using five ground motion records. The analysis of the results were comparatively evaluated considering certain engineering demand parameters such as the storey, bearing, and relative displacements, roof and inter-storey drift ratios, absolute acceleration, base shear, base moment, input energy, and hysteretic curves. One of the main findings of this study is that the base-isolated building with the passive damping device as control attenuation satisfactorily responded when associated with appropriated design parameters.

Mitigating the seismic pounding of multi-story buildings in series using linear and nonlinear fluid viscous dampers

Seismic-induced pounding between adjacent buildings may have serious consequences, ranging from minor damage up to total collapse. Therefore, researchers try to mitigate the pounding problem using different methods, such as coupling the adjacent buildings with stiff beams, connecting them using viscoelastic links, and installing damping devices in each building individually. In the current paper, the effect of using linear and nonlinear fluid viscous dampers to mitigate the mutual pounding between a series of structures is investigated. Nonlinear finite-element analysis of a series of adjacent steel buildings equipped with damping devices was conducted. Contact surfaces with both contactor and target were used to model the mutual pounding. The results indicate that the use of linear or nonlinear dampers leads to the significant reduction in the response of adjacent buildings in series. Moreover, the substantial improvement of the performance of buildings has been observed for almost all stories. From the design point of view, it is concluded that dampers implemented in adjacent buildings should be designed to resist maximum force of 6.20 or 1.90 times the design independent force in the case of using linear or nonlinear fluid viscous dampers, respectively. Also, designers should pay attention to the design of the structural elements surrounding dampers, because considerable forces due to pounding may occur in the dampers at the maximum displaced position of the structure.

Effects of using different arrangements and types of viscous dampers on seismic performance of intermediate steel moment frames in comparison with different passive dampers

In this paper, the effect of using different passive control systems on the seismic performance of an eight-story intermediate steel moment frame was investigated. For this purpose, ten steel frames equipped with the linear and nonlinear fluid viscous dampers with three different arrangements, viscoelastic damper, Pall friction damper, and metallic damper (TADAS) were modeled and designed according to the ASCE 7-16 and AISC 360-16 provisions. To investigate the seismic behavior of each system, nonlinear time history analyses were performed using eleven ground motion records in OpenSees software. The seismic responses of the frames were studied and compared in terms of the maximum roof displacement, maximum story drift, maximum base shear, input energy, and dissipated energy through the dampers for different types and arrangements of dampers. The results revealed that the structures with dampers had an outstanding seismic performance compared to the original structure. Among the three arrangements considered for the viscous dampers, the toggle arrangement had a significantly better seismic performance compared to the Chevron and Diagonal damper arrangements. Also, nonlinear viscous dampers dissipated much more seismic input energy compared to linear viscous dampers that resulted in improved seismic performance of the frames. In addition, among the friction, metallic, and viscoelastic dampers, the friction damper had the most beneficial effects for the structures studied.

Performance‐based seismic retrofitting of frame structures using negative stiffness devices and fluid viscous dampers via optimization

AbstractIn this paper, an optimization approach for the seismic retrofitting of inelastic moment resisting frames (MRFs) equipped with nonlinear fluid viscous dampers (FVDs) and negative stiffness devices (NSDs) is presented. The goal of the optimization is to minimize a cost‐related objective function, which accounts for the cost of the supplemental FVDs and NSDs. The mechanical properties and the topological layout of both the FVDs and NSDs are considered as design variables and simultaneously optimized during the optimization process. A loss estimation analysis is utilized as a performance constraint, where the PEER framework is adopted. The structural response is evaluated using a nonlinear time history analysis (NTHA), which accounts for the nonlinear behavior of the MRF elements, FVDs, and NSDs. The optimization problem is formulated using differentiable functions only, making it suitable for an efficient gradient‐based optimization solution scheme. The gradients are efficiently derived using the adjoint sensitivity analysis approach. Two numerical examples show the robustness and efficiency of the presented methodology, where the optimized design relies on NSDs and FVDs in both examples.

A new modified stochastic linearization technique to analyze structures with nonlinear fluid viscous dampers

Nonlinear viscous dampers can efficiently improve the seismic performance of structures by dissipating large amounts of earthquake-induced energy. In common practice, the spectral analysis of structures with nonlinear viscous dampers is generally conducted based on an estimated equivalent damping ratio. To this end, the stochastic linearization technique can be used as an effective probabilistic approach to take into account the evolutionary characteristics of the input earthquake excitation. This study aims to present optimal non-Gaussian probability density functions to improve the accuracy of the stochastic linearization technique for nonlinear viscous dampers in both firm and soft soil-based structures. It is shown that by using the optimum probability density functions, the computational error of the stochastic linearization technique for a single-degree-of-freedom structure under simulated ground motions, with a range of peak ground accelerations between 0.1 and 0.6 g, is reduced by up to 70%. The efficiency of the proposed probability density functions is then demonstrated for multi-degree-of-freedom structures, by estimating the roof displacements of a six-story steel frame with nonlinear viscous dampers under a set of natural ground motions using different linearization methods. The comparison of the stochastic linearization technique estimated responses with the exact values confirms that using the proposed probability density functions leads to considerably lower errors in both firm and soft soil-based structures compared with the other linearization techniques.

Probabilistic seismic performance of steel structures with FVDs designed by DDBD procedure

In this paper, the probabilistic seismic performance of steel moment-resisting frames (MRFs) equipped with fluid viscous dampers (FVDs) designed based on the deterministic direct displacement-based design (DDBD) method is investigated by taking into account the effect of the aleatory and epistemic uncertainties . For probabilistic analysis, two intensity measure (IM)-based approaches, including the determination of the mean annual frequency (MAF) of exceeding design target and the ratio of factored demand to factored capacity (F.D/F.C) in fragility/hazard design format, have been used. The maximum drift ratio has been selected as the demand parameter, and for controlled structures, the geometric mean of spectral acceleration, Sa avg , has been selected as the suitable IM. For numerical analysis, three 4, 8 and 12-story steel MRFs fitted with linear and nonlinear FVDs and designed based on the deterministic DDBD method have been considered. By performing the incremental dynamic analysis (IDA), the exceeding probability and F.D/F.C ratios have been determined for different nonlinearity levels of FVDs. The results show that the seismic performance of the structure designed using DDBD method has been significantly affected by the uncertainties. Moreover, the structures with nonlinear FVDs have a higher exceeding probability and F.D/F.C ratio than linear dampers due to their low damping coefficient in the deterministic DDBD method as well as minor capability of controlling displacements in higher velocities. In addition, considering the epistemic uncertainty has led to an increase in the F.D/F.C ratio up to 20%, while the probabilistic evaluation results altered slightly by the type of input record. • Uncertainties in performance of the structures with FVDs designed by DDBD. • Linear FVDs caused a higher capacity intensity for an IMC, compared to nonlinear FVDs. • In structures with nonlinear FVDs, F.D/F.C has increased up to 1.74. • Epistemic uncertainty affected the F.D/F.C ratio which is not negligible. • UD method for distributing FVDs improved the probabilistic performance of controlled structures.

Predicting the seismic collapse capacity of adjacent SMRFs retrofitted with fluid viscous dampers in pounding condition

Severe damages of adjacent structures due to structural pounding during earthquakes have emphasized the need to use some seismic retrofit strategy to enhance the structural performance. The purpose of this paper is to study the influence of using linear and nonlinear Fluid Viscous Dampers (FVDs) on the seismic collapse capacities of adjacent structures prone to pounding and proposing modification factors to modify the median collapse capacity of structures considering the effects of pounding. The factors can be used to predict the collapse capacity of structures in pounding condition. A seismic retrofit strategy employs FVDs installed in 3-, 6- and 9-story Special Moment Resisting Frames (SMRFs). The SMRFs were assumed to have different values of separation distance according to the seismic code. To model pounding phenomenon, linear viscoelastic contact elements were used in the OpenSees software. Furthermore, to determine the seismic collapse capacities of each structure, the proposed algorithm was applied to remove the collapsed structure during the incremental dynamic analysis. The results of the analyses illustrate that the existence of FVDs can substantially improve the seismic behavior of structures having a significant influence on the collapse capacities of colliding structures. Moreover, considering the adjacent SMRFs in one or two sides of the main structure can significantly affect the median collapse capacity of the main structure itself. Finally, the proposed modification factors can be successfully used to estimate the effects of pounding on the collapse capacities of adjacent structures.

A Simplified Design Strategy of Nonlinear Fluid Viscous Dampers for MDOF Structures

Energy dissipation devices are increasingly used as vibration mitigation systems owing to their efficiency. Therefore, many attempts were made to facilitate their design process. The design of fluid viscous dampers is summarized in the selection of suitable damping values and their location in the structure. This paper presents a strategy that estimates the damping coefficient value for nonlinear fluid viscous dampers in a straightforward manner. This minimizes the design time, and thus, more flexibility is offered for further design considerations. Combining a methodology that predicts a linear damping coefficient based on the concept of target-damping ratio, then, applying an equivalent energy-consumption approach to determine the nonlinear damping coefficient. This research gives a description of the method and its implementation by studying a structure equipped with a set of additional fluid viscous dampers. The results illustrate the efficiency and simplicity of the method.