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Viscous dampers have proven to be effective in enhancing the seismic performance of existing structures. Despite this, there is still a need for rapid and simplified design methods and formulae for viscous dampers that can take into account the elastic–plastic performance of structures. This study introduces a retrofit design method for existing structures using viscous dampers, based on the concept of uniform damping ratio (UDR), with the aim of fully utilizing each damper. The UDR concept assumes that each damper in the structure provides the same UDR when subjected to seismic excitations of identical intensity. In this method, the first step involves defining the equivalent damping ratio (EDR) of the damper. Then, based on the capacity spectrum of the structure, the response mitigation ratio can be determined, which helps to determine the additional EDR required from the dampers. Once the UDR and additional EDR from the viscous damper have been determined, the parameters of the dampers at each story can be rapidly obtained. To demonstrate the effectiveness of this method, a six-story reinforced concrete frame was utilized as a benchmark structure. A comparison between this UDR-based approach and a traditional design approach was also conducted. The study findings reveal that the UDR concept enables the maximum utilization of energy dissipation capacity of viscous dampers installed in the structure, leading to a more effective and economical design approach. [ABSTRACT FROM AUTHOR]

The inerter-based systems have proven to be effective for vibration control of adjacent structures. The interaction through the soil medium between adjacent structures in urban areas is generally accepted. However, existing studies concerning the inerter-based adjacent structures are primarily based on the assumption of a fixed base, without considering the inevitable interaction. To address this issue, this study incorporated the soil effects into the theoretical analysis of adjacent structures interconnected by an inerter system, and correspondingly develops an optimal design framework for such system. Employing a classic discrete model for structures and soil, the interaction behavior between inerter-based adjacent structures and soil was extensively studied in a comparative analysis. Based on the revealed interaction phenomena, the need for considering the soil condition in the design of an inerter system for adjacent structures was addressed, and a performance-demand-based optimal design framework was developed. The results indicated that for inerter-based adjacent structures spaced closely, the coupled interaction effect of soil and structure requires careful consideration, especially in soft soil conditions. Owing to the soil effects, the inerter system exhibited a weakened effectiveness for displacement reduction. A larger inner deformation of the inerter system is required to meet the demand for energy dissipation. With consideration of the soil condition, the proposed design method can satisfy the pre-specified target displacement demands for adjacent structures, simultaneously optimizing the control cost as an economical solution. [ABSTRACT FROM AUTHOR]

Summary: The passive tuned viscous mass damper (TVMD), i.e., a classic inerter system, has been proven as an efficient vibration mitigation device that is characterized by a damping‐enhancement effect for enhanced energy absorption and dissipation. However, due to the sensitivity of the tuning frequency, the effective frequency band of TVMD for vibration reduction is limited, so that the enhanced energy absorption and dissipation are limited. Dealing with this, this study proposes a novel variable friction TVMD (VF‐TVMD) by incorporating a sub‐device with variable friction forces into the TVMD, successively maximizing the energy dissipation efficiency of VF‐TVMD by employing a power‐flow‐based algorithm. A power‐flow analysis is performed for TVMD‐structures, which explicitly determine the optimal phase deviation of the dashpot‐deformation in TVMD with respect to structural displacement. Given this finding, the friction device in VF‐TVMD is employed by the proposed power‐flow‐based control strategy to adjust the asynchronous vibration between the TVMD and primary structure. Through the implementation of VF‐TVMD, the feasibility and effectiveness are illustrated by numerical examples. The results show that a desired phase lag of the TVMD with respect to the structure is −90° to guarantee TVMD the maximum power flow for energy dissipation. Benefitting from the variable friction force, the VF‐TVMD is more effective for structural vibration control and exhibits a more significant damping‐enhancement effect, in comparison with the TVMD. Applicable in a wider frequency band, the structural vibration can be significantly mitigated by the optimized VF‐TVMD or even by VF‐TVMD with un‐optimized stiffness and damping ratios. [ABSTRACT FROM AUTHOR]

Design methods for damped structures using viscous dampers have been proposed by different scholars. However, a parametric distribution among the installation locations of the dampers has not been fully considered. In this study, a conceptually optimized damping distribution pattern is introduced, in which, the nominal additional damping ratio supplied by dampers at each story is in positive correlation to the corresponding story drift. This conceptually optimized damping distribution pattern can reduce the total requirement of damping coefficient without changing the response mitigation effect. The target story drift mitigation ratio, which can be determined by the desired seismic performance demand, is adopted as the performance guidance in the design process. Given a target story drift mitigation ratio and the conceptually optimized damping distribution pattern, the required additional damping can be easily determined according to the design response spectra. A detailed design process is elaborated and a six-story regular benchmark model is employed to illustrate the proposed design method to achieve the target seismic performance. The results show that the required damping is optimized according to the specified damping distribution pattern and the proposed method is simple and effective. [ABSTRACT FROM AUTHOR]

Summary: Existing studies mainly focused on the mass enhancement effect of the inerter system within a seismically isolated structure. In this study, a new analytical perspective is introduced based on another attractive feature of the inerter system, namely, the damping enhancement effect. Accordingly, a ready‐to‐use optimal design method for isolated structure with the inerter system is proposed. First, the damping enhancement equation of the inerter system is reformulated in the form of the equivalent damping ratio. Then, the closed‐form design formulae of the inerter system are derived based on damping enhancement maximization and seismic demand. By taking the performance of both the primary structure and the isolation layer into consideration, the dual‐target‐oriented design strategy of the isolated structure is subsequently developed. And the closed‐form design formulae of the inerter system are then integrated into the strategy to produce a practical design method for isolated structure with the inerter system. A seven‐story isolated benchmark model is finally employed as the design case to exemplify the effectiveness of the proposed design method. Compared to the directly installed viscous damper, structural base shear force, inter‐story drift angle, and the deformation of the isolation layer are more effectively reduced with the addition of the inerter system, and the energy dissipation capacity of the damper within the inerter system is improved substantially. Furthermore, the derived closed‐form design formulae reduce the burden of iterative calculation and bring a high‐efficient design for isolated structure with the inerter system. [ABSTRACT FROM AUTHOR]

Summary: The incorporation of the inerter with tuned mass damper yields the inerter‐based tuned mass damper that has been verified as effective lightweight or performance‐enhanced control devices. This study theoretically proved an intrinsic effect, namely, the input energy reduction, that the inerter reduces the input energy transmitted into the controlled structures from ground motion. A generic tuned mass damper inerter (GTMDI) including two separating inerters (the total inertance keeps constant) is analyzed to facilitate a universal analysis of typical inerter‐based tuned mass dampers. Closed‐form displacement and power equations are derived for the GTMDI to reveal and clarify the working mechanisms, especially the functionality of inerters. Correspondingly, an energy‐based design framework is established for the design of a new GTMDI and the retrofitting of an existing tuned mass, in which the inertances distributed on the two separating inerters are optimized to make GTMDI outperform the conventional TMDI. Finally, a series of examples verified the discovered effect and derived power equation of GTMDI. In this study, two derived equations confirm that the GTMDI possesses dual benefits, referring to the input energy reduction and the enhanced dissipation power effects. The required physical mass of the GTMDI is relieved due to the reduced input energy, which essentially lays the foundation for lightweight control. The developed energy‐based design framework is suitable for utilizing the dual benefits of GTMDI with a clear physical basis, where the introduced two separating inerters are designed with optimized inertances to guarantee the displacement control demand with a minimized total energy cost. [ABSTRACT FROM AUTHOR]

Summary: Interactions among an inerter, spring, and energy dissipation element (EDE) in an inerter system can result in a higher energy dissipation efficiency compared to a single identical EDE, which is referred to as the damping enhancement effect. Previous studies have mainly concentrated on the vibration mitigation effect of the inerter system without an explicit consideration or utilization of the damping enhancement mechanism. In this study, the theoretical essence of the damping enhancement effect is discovered, and a universal design principle is proposed for an inerter system. A fundamental equation is found and demonstrated on the basis of closed‐form stochastic responses, which establishes a bridge between the damping deformation enhancement factor (DDEF) and the response mitigation ratio, thus clarifying the relationship of the damping enhancement effect and the response mitigation effect. Inspired by the equation, a novel damping‐enhancement‐based strategy is proposed to determine the key parameters of an inerter system. Following the performance‐demand‐based design philosophy, the parameters of the inerter system can be determined in the design condition of a target‐damping‐enhancement effect. Through the implementation of the damping enhancement equation, the damping parameter of an inerter system can be directly obtained by the prespecified DDEF and the displacement response mitigation ratio. The influence of parameters on the response mitigation effect and the damping enhancement effect is then investigated to determine ways of obtaining the other two parameters in an inerter system. Finally, design examples are conducted to verify the proposed strategy and the theoretical relationship revealed by the damping enhancement equation. The results show that the proposed design strategy explicitly utilizes the damping enhancement effect for vibration control, where the target of the DDEF is effective in enhancing the efficiency of the EDE for energy dissipation. In the design condition of the target DDEF, the implementation of the proposed damping enhancement equation provides an inerter system with a practical equation to determine the key parameters of an inerter system in a direct manner. [ABSTRACT FROM AUTHOR]

Keywords: seismic isolation; energy dissipation devices; tuned mass damper; negative stiffness device; inerter system; damped structures EN seismic isolation energy dissipation devices tuned mass damper negative stiffness device inerter system damped structures 2819 1 05/20/20 20200415 NES 200415 1. Although the development of new technologies generally follows established practice and underlies basic working principles, existing design methods for conventional devices are not always straightforwardly applicable to these new devices. Based on the obtained experimental results, the proposed device proves to be an effective strategy to increase the ductility and to mitigate the structural damage in the structural members, as the energy dissipation is mostly concentrated in the low-cost energy dissipation device. Seismic isolation, energy dissipation devices, tuned mass damper, negative stiffness device, inerter system, damped structures. [Extracted from the article]

Various inerter systems utilizing velocity-dependent damping for vibration control have been developed. However, a velocity-dependent damping element may exhibit relatively poor performance compared to a displacement-dependent damping element (DDE) of equivalent damping ratio, when the structural deformation is small in the early stage of the seismic response. To address this issue, the advantage of DDE in generating a larger control force in the early stage of excitation is promoted here and enhanced by a supplemental inerter-spring-system, thus realizing a proposed novel displacement-dependent damping inerter system (DDIS). First, the influence of various DDIS-parameters is carried out by resorting to the stochastic linearization method to handle non-linear terms. Then, seismic responses of the DDIS-controlled system are evaluated in the time domain taking the non-linearity into account, thus validating the accuracy of the stochastic dynamic analysis. Several design cases are considered, all of which demonstrated damping enhancement and timely control achieved by the DDIS. The results show that the energy dissipation as well as reduction of structural displacement and acceleration accomplished by the proposed system are significant. DDIS suppresses structural responses in a timely manner, as soon as the peak excitation occurs. In addition, it is demonstrated that interactions among the inerter, spring, and DDE, which constitute the damping-enhancement mechanism, lead to a higher energy-dissipation efficiency compared to the DDE alone. [ABSTRACT FROM AUTHOR]

In the design of damped structures, the additional equivalent damping ratio (EDR) is an important factor in the evaluation of the energy dissipation effect. However, previous additional EDR estimation methods are complicated and not easy to be applied in practical engineering. Therefore, in this study, a method based on energy dissipation is developed to simplify the estimation of the additional EDR. First, an energy governing equation is established to calculate the structural energy dissipation. By means of dynamic analysis, the ratio of the energy consumed by dampers to that consumed by structural inherent damping is obtained under external excitation. Because the energy dissipation capacity of the installed dampers is reflected by the additional EDR, the abovementioned ratio can be used to estimate the additional EDR of the damped structure. Energy dissipation varies with time, which indicates that the ratio is related to the duration of ground motion. Hence, the energy dissipation during the most intensive period in the entire seismic motion duration is used to calculate the additional EDR. Accordingly, the procedure of the proposed method is presented. The feasibility of this method is verified by using a single-degree-of-freedom system. Then, a benchmark structure with dampers is adopted to illustrate the usefulness of this method in practical engineering applications. In conclusion, the proposed method is not only explicit in the theoretical concept and convenient in application but also reflects the time-varying characteristic of additional EDR, which possesses the value in practical engineering. [ABSTRACT FROM AUTHOR]

Highlights • Uniform damping ratio design concept is raised for structure with metallic dampers. • Dampers are expected to have the same damping ratio under certain dynamic excitations. • Stiffness and damping parameters of metallic dampers can be designed individually. • Design procedure can be simplified with a demand-oriented design scheme based on UDR. • Elastoplastic properties of both the structure and dampers are considered. Abstract This study proposes a novel design concept, referred to as the uniform damping ratio (UDR) concept, to improve the seismic energy dissipation efficiency of damped structures with metallic yielding dampers (MYDs) by maximizing the use of the capability of each damper. Furthermore, this new concept can simplify the design procedure of structures with MYDs. The UDR concept implies that all installed MYDs have the same equivalent damping ratio under dynamic excitations, which enables each MYD to be fully utilized. The UDR concept can simplify the estimation process of the additional equivalent damping ratio of a damped structure and decouple the stiffness and damping effects caused by MYDs, which can be designed separately. A performance demand-oriented design procedure is presented based on the UDR concept considering the nonlinear properties of an original structure and MYDs under an intense earthquake. The design procedure involves the following three steps: (1) determine seismic performance demand and obtain the elastic and elastoplastic properties of the original structure using pushover analysis; (2) determine key design parameters based on the formulae derived under the UDR concept; (3) verify seismic performance via nonlinear dynamic analyses. In addition, a few empirical suggestions are provided for determining the key design parameters more efficiently. A nine-story steel frame structure with MYDs is used to exemplify the UDR-based design procedure. The seismic performance demand of the structure with designed MYDs is achieved, and the energy dissipation capacity of all installed MYDs is sufficiently utilized. The proposed UDR concept is found to be effective, and the procedure based on this concept is efficient and simple. [ABSTRACT FROM AUTHOR]

In this study, a direct static design method for structures with metal yielding dampers is proposed based on a new design target called the seismic capacity redundancy indicator (SCRI). The proposed method is applicable to the design of elastic-plastic damped structures by considering the influence of damper on different structural performance indicators separately without the need for iteration or nonlinear dynamic analysis. The SCRI-a quantitative measure of the seismic capacity redundancy-is defined as the ratio of the seismic demand required by the target performance limit to the design seismic demand. Changes in the structural SCRI are correlated with the parameters of the supplemental dampers so that the dampers can be directly designed according to a given target SCRI. The proposed method is illustrated through application to a 12-story reinforced-concrete frame, and increment dynamic analysis is performed to verify the effectiveness of the proposed method. The seismic intensity corresponding to the target structural performance limit is regarded as a measure of the structural seismic capacity. The required seismic intensity increases after the structure is equipped with the designed metal yielding dampers according to the expected SCRI. It is concluded that the proposed method is easy to implement and feasible for performance-based design of metal yielding dampers. [ABSTRACT FROM AUTHOR]

In this study, a demand-based optimal design method is proposed for an oscillator (a single-degree-of-freedom system) with a parallel-layout viscous inerter damper (PVID). The proposed design method overcomes some deficiencies of the existing method, which is based on the fixed-point theory and is mainly suitable for tuned mass dampers. Moreover, for the fixed-point method, the inherent damping of the primary structure is neglected, and the global optimal solution cannot be obtained. The proposed method can obtain a more rational and practical design for the actual design by minimizing both the response and the cost. The design problem of a PVID-equipped oscillator is transformed into a multi-objective optimization problem that can be solved using the ε-constraint approach, which is consistent with the concept of demand-based design. The dynamic response of the oscillator and the force of the PVID (i.e., the cost factor) are evaluated according to theories of random vibration to reduce the number of calculations required. A computer program is developed to perform demand-based parametric design of a PVID-equipped oscillator. Several design cases were examined under different excitation conditions using the computer program, and dynamic time history analyses were then conducted to verify the designs obtained. The results show that the proposed optimal design method identifies satisfactory designs more effectively than the existing method by obtaining PVID design parameter values that better meet the performance demand and simultaneously minimize the cost. [ABSTRACT FROM AUTHOR]

Metallic yielding dampers (MYDs) can effectively improve the seismic performance of structures and are used in many practical engineering applications. In this paper, a simple elastic–plastic design method of a structure with MYDs is proposed based on the elastic–plastic response reduction curve (EPRRC). In widely used traditional design methods based on the elastic response reduction curve, the elastic–plastic behavior of the main structure is neglected. However, such methods may overestimate the vibration control effect of MYDs, especially their effect on acceleration reduction, which is demonstrated in this study. The EPRRC, which can directly reflect the relationship between MYDs’ characteristic parameters and the responses of the structure with MYDs in the elastic–plastic range, is proposed to improve the reliability of a structure with MYDs. Then, the corresponding design procedures are presented. To illustrate and verify the effectiveness of the proposed design method, a six-story reinforced concrete frame is analyzed by time history analysis. In conclusion, the proposed design method for the structure with MYDs can adequately satisfy the seismic performance targets under different seismic levels. [ABSTRACT FROM AUTHOR]

• An elastic-plastic design method is proposed based on EPRRC using viscous dampers. • Inelastic behaviour of primary structure can be directly considered. • Reduction in storey drift and shear force can be simultaneously realized. • Modular design flowchart is presented to facilitate ease of retrofit design. Installation of viscous dampers has been demonstrated to be an effective method to perform seismic retrofitting of a structure. However, most of the existing design methods are based on the elastic stage of the primary structure. The proposed study presents an alternate method for retrofit design of a structure using viscous dampers whilst considering inelastic behaviour of the primary structure. The said method makes use of the elastic–plastic response reduction curve (EPRRC) to reflect the relationship between characteristic parameters of the viscous damper, supporting brace, and response of the viscous-damper-equipped primary structure. Use of this method ensures that reduction in storey drift as well as shear force is simultaneously realized within the EPRRC coincident reduction region. Thus, parameters concerning the required dampers and supporting braces can be obtained from EPRRC in accordance with target performances of the damped structure. Comparison between a traditional elastic response reduction curve (ERRC) and EPRRC indicates that ERRC tends to overestimate the performance of damped structures. Nonlinear time-history analysis was performed to verify the effectiveness of the proposed method when applied to a benchmark model. Additionally, probabilistic reliability of the said method was determined via incremental dynamic analysis. Results demonstrate that the proposed design method can effectively satisfy design requirements under different seismic intensities. [ABSTRACT FROM AUTHOR]

Negative stiffness-incorporated dampers have been widely accepted as effective vibration mitigation systems for flexible structural stiffness adjustment and enhanced energy dissipation. However, current investigations and optimal designs of negative stiffness-incorporated structures are limited to the linear elastic assumption of primary structures, potentially causing stability issues and unsatisfactory control performance. In this case, this study derives the stability criterion for negative stiffness amplifying damper (NSAD)-incorporated nonlinear structures and establishes stability-oriented design as well as modification formulae. The theoretical foundation of NSADs and nonlinear primary structures are initially introduced, based on which the stability criterion is derived according to the Routh–Hurwitz stability criterion. Following the existing design of linear elastic assumption, an endurance time acceleration series is generated subsequently to examine the proposed stability criterion for NSAD-equipped nonlinear structures. Consequently, the stability-oriented design method and corresponding modification formulae are proposed for near-field and far-field earthquakes, of which the effectiveness is validated through design cases. The results underscore the importance of considering structural nonlinearity for ensuring stability and designing NSAD-equipped nonlinear structures, demonstrating the feasibility of using the proposed correction factors to guarantee the stability of NSAD-equipped nonlinear structures subjected to multi-type earthquakes with various intensities. Additionally, the established design framework successively provides a high-efficiency energy dissipation device for seismic control of nonlinear structures, simultaneously generating easy-to-use design formulae for NSADs by combining the linear structure-based design and modification factors, facilitating direct design of nonlinear structures. • Negative stiffness amplifying damper (NSAD) for nonlinear primary structures. • Modification factors of the negative stiffness ratio guarantee structural stability. • Stability-oriented design of NSAD with target performances of nonlinear structures. • Design formulae of NSAD combining linear structure design and modification factors. • Enhanced energy dissipation and robustness for nonlinear vibration mitigation. [ABSTRACT FROM AUTHOR]

• Input energy reduction of storage tank by parallel inerter isolation system (PIIS). • Precise control of specific/multiple sloshing height modes of storage tanks by PIIS. • Preliminary design approach for PIIS in rigid base using analytical design formulas. • Advantageous feature-oriented design of PIIS with soil-structure interaction (SSI). • Recommended scenarios for incorporating SSI in PIIS design with control targets. Inerter-based isolation systems are effective in providing seismic protection for storage tanks. However, the vibration control-oriented mechanism of inerter-based seismic isolation systems on the seismic response of liquid storage tanks remains unclear, with designs limited to rigid base assumptions. Moreover, the objective existence of the soil-structure interaction (SSI) is overlooked. This study contributes to a discovered advantage of the inerter-based isolation system, including the reduction of input energy and precise control of specific or multiple modes of sloshing heights. Furthermore, an advantageous feature-oriented optimal design for storage tanks with an inerter-based isolation system and with the incorporation of soil conditions is proposed in this study. Initially, an analytical model is developed, considering a storage tank with multi-mode sloshing responses and representing SSIs with frequency-dependent stiffness and damping coefficients. Stochastic response analysis is performed, leading to a novel formulation of multi-mode control and an empirical power equation that quantifies the input energy reduction effect. An advantageous feature-oriented optimal design framework, in which the SSI effect, tank geometric parameters, and inerter-based isolation system parameters are implemented, is established through comprehensive parametric analysis. The results demonstrate that the inerter-based isolation system can be intentionally designed to mitigate specific modes of sloshing height, with the inerter effectively reducing the input power of the entire tank. This study emphasizes the importance of incorporating the SSI effect in the seismic analysis and optimal design of inerter-based tanks. Particularly, the inerter-based isolation system designed assuming a rigid base cannot perform as expected due to the SSI effect, significantly resulting in larger seismic responses and energy dissipation burdens. The developed optimal design method guarantees a target base shear force and sloshing height regarding the considered soil condition. [ABSTRACT FROM AUTHOR]

• Energy working principle of inerter system (IS) with grounded or ungrounded inerter. • A closed-form equation quantifies energy responses of structure-IS system. • IS with grounded inerter reduces the input power and energy of the entire structure. • IS with ungrounded inerter exhibits enhanced energy dissipation effect. • Design strategy and analytical equation to minimize energy dissipated by structure. Inerter systems have been proven to be effective vibration control devices. The energy-input-dissipation flow offers an alternative perspective to reveal the working mechanism of inerter-based systems for vibration control. In this study, the energy-based method is used to analytically explain the discovered benefits of inerter systems including the reduction in input energy and the enhancement of energy dissipation, which further yields optimal design for the inerter systems. Closed-form energy equations are derived for structures equipped with a basic inerter system composed of a grounded or ungrounded inerter. These energy equations theoretically establish the quantified relationship between the powers of input and dissipation and the key parameters of the inerter system in an analytical form. Furthermore, the differences in working mechanisms between inerter systems composed of grounded or ungrounded inerters are characterized via comparative analysis in terms of the displacement control, enhanced energy dissipation efficiency, and input energy reduction. Based on the revealed energy working basis, a unified energy-dissipation-based optimization strategy is developed to simultaneously control the displacement and energy responses. Finally, numerical examples are presented to validate the derived energy equations and the proposed optimization strategy. The findings of this study show that the energy equation supplies an analytical measurement for evaluating the input power of inerter-based structures and quantifies the energy dissipation effect of the inerter system. In particular, the derived energy equation explicitly reveals the dual benefits of an inerter system with a grounded inerter, which reduces the input power of the entire inerter-based structure and simultaneously dissipates the vibrational energy. Following the energy-dissipation-based optimal design strategy, which directly applies the grounded inerter to reduce input power or potentially uses the ungrounded inerter to enhance the energy dissipation effect, the target displacement can be quantitively achieved by the optimized inerter systems. Image, graphical abstract [ABSTRACT FROM AUTHOR]

Abstract The traditional design method of the elastic response reduction curve (ERRC) was used to design the parameters of the viscoelastic damper (VED), where the plastic behavior of the primary structure is neglected. Considering the structural plastic behavior, in this study, a direct design method is proposed to obtain the parameters of VEDs based on the elastic-plastic response reduction curve (EPRRC), which can illustrate the relationship between damper parameters and the response reduction effect in the elastic-plastic stage. First, the ERRC is developed to the EPRRC, and the differences between them are compared using the displacement and acceleration response difference ratios, which demonstrate an overestimated response reduction effect of VEDs in the elastic-plastic stage using the ERRC. Then, the corresponding design procedures are given based on the EPRRC by referring to the direct displacement-based design theory. Finally, a benchmark model is used to illustrate the effectiveness of this proposed design method by conducting a time history analysis. The analysis results indicate that the target story drift of the structure can be satisfied under different earthquake intensities using VEDs. Thus, based on this study, the development of the EPRRC can be considered worthwhile, and the proposed design method of VED parameters is easy to implement and is effective. Highlights • EPRRC based elastoplastic design is developed for structure with viscoelastic damper. • Response control effect can be overestimated by traditional ERRC method. • Parameters of viscoelastic dampers can be obtained directly using the proposed method. [ABSTRACT FROM AUTHOR]

• Energy dissipation enhancement of negative stiffness amplifying damper (NSAD). • Closed form enhanced energy dissipation formula for theoretical basic. • Enhanced-energy-dissipation-oriented design for NSAD with significant enhancement. • Analytical design formulae to facilitate the new design framework. Negative-stiffness devices are of rapidly increasing interest for high-performance vibration control. With a tuning spring in series, the negative-stiffness device forms an enhancement mechanism for the dashpot, named the negative stiffness amplifying damper (NSAD), which is much more efficient in dissipating energy than the viscous damper alone. Based on the observed enhancement phenomenon, this study reveals the theoretical basis of the energy dissipation enhancement benefit by deriving the analytical enhanced energy dissipation formula. The basic concept and physical realization methods for the negative-stiffness device are introduced, based on which the mechanical models of NSAD and NSAD-equipped structures are established for dimensionless response analysis. Following a stochastic framework, the stochastic responses of the NSAD-equipped structure are solved in closed form. Correspondingly, simple and easy-to-understand equations are derived and denoted as the "enhanced energy dissipation formula" to quantify each component's contribution in the NSAD explicitly. Inspired by the formula, a design framework with two strategies is proposed for NSADs with a synthetic consideration of the energy dissipation enhancement mechanism and target control performance. Following the design principle, detailed design formulae are derived in a simple form. Finally, a design procedure is provided and applied to a series of design cases for illustration. The results show that the energy dissipation enhancement mechanism enables NSADs to offer improved energy dissipation efficiency over conventional dampers without sacrificing the vibration isolation effect or the excessive damping force. The analytical formula clearly explains the theoretical basis by quantifying the NSAD components' contribution to the vibration control and energy dissipation enhancement effects. Based on this newly explained benefit, the design framework successively provides a high-efficiency energy dissipation device that fulfills its intended control performance. In addition, the easy-to-use design formulae are derived for the new design strategy to allow the direct design of NSADs. [Display omitted] [ABSTRACT FROM AUTHOR]

A simple design procedure is proposed for seismic retrofitting of existing structures using viscoelastic dampers (VEDs) based on the uniform damping ratio (UDR) concept to make full use of each damper. The UDR concept states that the equivalent damping ratios, which represent the energy dissipation capacities of the dampers, are the same for each installed VED. The stiffness and damping characteristic parameters of the damped structure can be formally decoupled using UDR-based derivations, which simplify the determination of the VEDs' parameters. The generalized single-degree-of-freedom method and pushover analysis are adopted for a fast estimation of the seismic response of the damped elastoplastic structure. Taking the response reduction ratio as the design target, a seismic retrofit design procedure is proposed based on the UDR concept to meet the performance demand. Finally, a six-story frame is adopted to illustrate the proposed design method. The dynamic analysis results show that the seismic responses of the structure are well-controlled, as expected, and that the installed VEDs are used effectively. The conclusion can be drawn that the UDR-based design method for retrofitting an existing structure using VEDs is rational and effective. • UDR concept is raised for a structural seismic retrofit design with viscoelastic damper. • Stiffness and damping parameters of the damped structure are decoupled using the UDR concept. • Stiffness of the damper is proportionally distributed to retrofit the existing structure. • Response reduction ratio is applied in the seismic retrofit design procedure. • Both elastoplastic behavior and safety redundancy of the structure are considered. [ABSTRACT FROM AUTHOR]