设置黏滞阻尼器的钢结构实用减震设计方法

黏滞阻尼器作为一种有效的消能减震装置,已在钢结构建筑中得到了大量应用.然而由于钢结构的延性和阻尼特征,实用的钢结构附加黏滞阻尼器设计方法仍需深度探讨.文中提出一种基于黏滞阻尼器延性需求的减震设计方法.首先,根据钢结构需求量化层间位移角性能目标及目标附加阻尼比,计算黏滞阻尼器延性需求,并确定黏滞阻尼器布置数量、进行控制效...     

Seismic performance of buildings retrofitted with nonlinear viscous dampers and adjacent reaction towers

An effective strategy of seismic retrofitting consists of installing nonlinear viscous dampers between the existing building, with insufficient lateral resistance, and some auxiliary towers, specially designed and erected as reaction structures. This allows improving the seismic performance of the existing building without any major alteration to its structural and nonstructural elements, which makes this approach particularly appealing for buildings with heritage value. In this paper, the nonlinear governing equations of the coupled lateral‐torsional seismic motion are derived from first principles for the general case of a multistory building connected at various locations in plan and in elevation to an arbitrary number of multistory towers. This formulation is then used to assess the performance of the proposed retrofitting strategy for a real case study, namely, a 5‐story student hall of residence in the city of Messina, Italy. The results of extensive time‐history analyses highlight the key design considerations associated with the stiffness of the reaction towers and the mechanical parameters of the nonlinear viscous dampers, confirming the validity of this approach.     

Simultaneous topology and sizing optimization of viscous dampers in seismic retrofitting of 3D irregular frame structures

A new methodology for performance‐based optimal seismic retrofitting using a limited number of size groups of viscous dampers is presented. The damping coefficient of each size group of dampers is taken as a continuous variable and is determined by the optimization algorithm. Furthermore, for each potential location, a damper of a single size group is optimally assigned, if any. Hence, the formulation presents a large step forward towards practical optimal design of dampers. The key for achieving an efficient optimization scheme is the incorporation of material interpolation techniques that were successfully applied in other structural optimization problems of discrete nature. This results in a very effective optimization methodology that is expected to be very efficient for large‐scale structures. The proposed approach is demonstrated on several example problems of 3D irregular frame structures. Copyright © 2014 John Wiley & Sons, Ltd.     

Fail-safe optimization of viscous dampers for seismic retrofitting

This paper presents a new optimization approach for designing minimum-cost fail-safe distributions of fluid viscous dampers for seismic retrofitting. Failure is modeled as either complete damage of the dampers or partial degradation of the dampers' properties. In general, this leads to optimization problems with large number of constraints. This may result in high computational costs if all the constraints are simultaneously considered during the optimization analysis. Thus, to reduce the computational effort, the use of a working-set optimization algorithm is proposed in this paper. The main idea is to solve a sequence of relaxed optimization subproblems with a small subset of all constraints. The algorithm terminates once a solution of a subproblem is found that satisfies all the constraints of the problem. The retrofitting cost is minimized with constraints on the interstory drifts at the peripheries of frame structures. The structures considered are subjected to a realistic ensemble of ground motions, and their response is evaluated with time-history analyses. The transient optimization problem is efficiently solved with a gradient-based sequential linear programming algorithm. The gradients of the response functions are calculated with a consistent adjoint sensitivity analysis procedure. Promising results attained for 3-D irregular frames are presented and discussed. The numerical results highlight the fact that the optimized layout and size of the dampers can change significantly even for moderate levels of damage.     

非线性黏滞阻尼减震结构基于位移的设计方法

结合我国抗震设计规范,提出非线性黏滞阻尼减震结构基于位移的设计方法.根据减震结构的特点,将其性能划分为使用良好、人身安全和防止倒塌3个水平,并用层间位移角限值予以量化;以简化的方法计算非线性黏滞阻尼器的等效阻尼比.在此基础上将结构转化为等效单自由度体系,利用基于位移的设计方法对非线性黏滞阻尼减震结构进行设计,通过算例,介绍用该方法对框架结构进行非线性黏滞阻尼减震设计的设计过程.实例分析表明,提出的非线性黏滞阻尼减震结构基于位移的设计方法是可行的,并且与时程分析得出的平均结果吻合较好,而且该方法简单实用,便于操作,能够控制减震结构在不同强度水准地震作用下的性能.     

Minimum‐cost optimization of nonlinear fluid viscous dampers and their supporting members for seismic retrofitting

This paper presents an effective approach for achieving minimum‐cost designs for seismic retrofitting using nonlinear fluid viscous dampers. The damping coefficients of the dampers and the stiffness coefficients of the supporting braces are designed by an optimization algorithm. A realistic retrofitting cost function is minimized subject to constraints on inter‐story drifts at the peripheries of frame structures. The cost function accounts for costs related to both the topology and the sizes of the dampers. The behavior of each damper‐brace element is defined by the Maxwell model, where the force–velocity relation of the nonlinear dampers is formulated with a fractional power law. The optimization problem is first posed and solved as a mixed integer problem. For the reduction of the computational effort required in the optimization, the problem is then reformulated with continuous variables only and solved with a gradient‐based algorithm. Material interpolation techniques, which have been successfully applied in topology optimization and in multi‐material optimization, play a key role in achieving practical final design solutions with a reasonable computational effort. Promising results attained for 3‐D irregular frames are presented and discussed. Copyright © 2017 John Wiley & Sons, Ltd.     

黏滞阻尼器连接相邻结构减震优化分析

阻尼器参数的确定是利用阻尼器连接相邻结构进行减震设计的关键.根据随机地震反应理论,以相邻结构的频率比和质量比为参数,推导了结构位移反应均方差与连接阻尼比的关系式,得到了相邻结构的地震反应与频率比、质量比以及连接阻尼比的影响规律,从而得到了连接阻尼器的优化设计参数.根据自振频率相等的原则,探讨了将多自由度体系简化为单自由度体系的分析方法.最后在El Centro波、Taft 波及人工波激励下,对比分析了某相邻10层建筑结构有连接和无连接时的地震反应,表明黏滞阻尼器连接相邻结构具有较好的减震效果.本分析方法可供相邻结构减震设计参考.     

非线性粘滞阻尼器消能结构设计方法探讨

在建立非线形粘滞阻尼器消能结构性能曲线的基础上，建议了依据减震性能目标确定阻尼器参数的概略设计方法。提出了多自由度非线性粘滞阻尼器消能结构的等效阻尼比计算公式。在此基础上建议了适用于多自由度非线性粘滞阻尼器消能结构地震反应预测的模态叠加法，方法与时程分析结果对比吻合良好。为使各层阻尼器参数更好地满足减震性能要求，提出了将概略设计得到的层阻尼器参数依据减振性能目标进行调整的方法。     

On tuned mass dampers for reducing the seismic response of structures

This paper presents an energy‐based theoretical model for a two degree‐of‐freedom mechanical system. After a general formulation in Appendix A, the model is specialized to study tuned mass dampers as a means to substantially increase modal damping in order to induce a consequential decrease of the seismic response of the structures thus provided. Although approximate since it neglects coupling due to damping, it is shown that the model yields a first‐order approximation to the exact frequencies, providing values of optimum damping that closely match exact results proposed by others. In view of this, it is proposed that the model be applied through an iterative numerical procedure that identifies the pertinent optimum parameters. It is also shown that for certain particular benchmark cases the model provides closed‐form equations for the parameters defining the dynamic states related to these special conditions. Despite its approximate nature the model presented in this paper is rational, and due to its explicit consideration of energy balance and overall simplicity, it provides a convenient platform for the study of tuned mass dampers, as well as for other methods of structural passive control. Copyright © 2005 John Wiley & Sons, Ltd.     

非线性粘滞阻尼器消能结构减振效果分析

应用并完善了非线性粘滞阻尼器消能结构地震反应预测的反应谱方法,通过与时程分析计算结果对比证明了方法的可行性。利用本方法研究了支撑刚度及阻尼器参数对非线性粘滞阻尼器减振效果的影响。通过数值分析,给出了位移降低率达到最佳时支撑刚度取值的建议式。提出了为保证剪力降低率不大于1时非线性粘滞阻尼器参数的控制方法。     

On the efficiency of viscous dampers in reducing various seismic responses of wall structures

This paper rigorously assesses the efficiency of viscous dampers connecting two walls to result in “viscously coupled shear walls”. This assessment also holds for viscous dampers in wall structures as they are mounted on frames parallel to the walls leading to “wall-viscous frame” systems. A continuum approach is adopted to model the structure so as to enable non-dimensional formulation of the governing equations. Those equations reveal that, under the approximations considered, the system damping ratio (defined here by 0.5 sqrt(c^2/(m*EI))) is a convenient compact single parameter controlling the response reduction w.r.t. the response of the corresponding undamped system. In contrast to coupled shear walls, this controlling parameter does not depend on the height of the building; therefore, the viscously damped system is efficient for low-rise buildings as well. The continuum approach also allows a semi-analytical solution of the eigenproblem in the complex domain followed by a complex modal spectral analysis. Those solutions reveal the efficiency of the added damping in reducing not only the displacements, inter-story drifts, and wall moments but also the absolute accelerations, wall shear, total shear, and total overturning moments. The results of the analyses and the non-dimensional tables and graphs developed for important response parameters lead to a simple method that could easily be implemented in practice for the purpose of initial design. Copyright © 2012 John Wiley & Sons, Ltd.     

Optimal design of supplemental viscous dampers for irregular shear‐frames in the presence of yielding

A methodology for the optimal design of supplemental viscous dampers for regular as well as irregular yielding shear‐frames is presented. It addresses the problem of minimizing the added damping subject to a constraint on an energy‐based global damage index (GDI) for an ensemble of realistic ground motion records. The applicability of the methodology for irregular structures is achieved by choosing an appropriate GDI. For a particular choice of the parameters comprising the GDI, a design for the elastic behavior of the frame or equal damage for all stories is achieved. The use of a gradient‐based optimization algorithm for the solution of the optimization problem is enabled by first deriving an expression for the gradient of the constraint. The optimization process is started for one ‘active’ ground motion record which is efficiently selected from the given ensemble. If the resulting optimal design fails to satisfy the constraints for other records from the original ensemble, additional ground motions (loading conditions) are added one by one to the ‘active’ set until the optimum is reached. Two examples for the optimal designs of supplemental dampers are given: a 2‐story shear frame with varying strength distribution and a 10‐story shear frame. The 2‐story shear frame is designed for one given ground motion whereas the 10‐story frame is designed for an ensemble of twenty ground motions. Copyright © 2005 John Wiley & Sons, Ltd.     

黏滞阻尼器在单层网壳结构中的优化布置

目前采用黏滞阻尼器对单层网壳结构进行减振控制时,阻尼器最优布置位置通过试算确定。针对此问题,推导了地震作用下黏滞阻尼器耗能公式,提出了以能量比例系数为评价指标的阻尼器优化布置准则。以单层球面网壳和单层柱面网壳为例,对比分析了地震作用下分别采用优化布置准则与现有布置方式布置阻尼器时结构最大节点位移减振系数,验证了所提出优化布置准则的正确性及在单层球面网壳和单层柱面网壳中的适用性。     

Asymmetric one‐storey elastic systems with non‐linear viscous and viscoelastic dampers: Simplified analysis and supplemental damping system design

Investigated is the accuracy in estimating the response of asymmetric one‐storey systems with non‐linear viscoelastic (VE) dampers by analysing the corresponding linear viscous system wherein all non‐linear VE dampers are replaced by their energy‐equivalent linear viscous dampers. The response of the corresponding linear viscous system is determined by response history analysis (RHA) and by response spectrum analysis (RSA) extended for non‐classically damped systems. The flexible and stiff edge deformations and plan rotation of the corresponding linear viscous system determined by the extended RSA procedure is shown to be sufficiently accurate for design applications with errors generally between 10 and 20%. Although similar accuracy is also shown for the ‘pseudo‐velocity’ of non‐linear VE dampers, the peak force of the non‐linear VE damper cannot be estimated directly from the peak damper force of the corresponding linear viscous system. A simple correction for damper force is proposed and shown to be accurate (with errors not exceeding 15%). For practical applications, an iterative linear analysis procedure is developed for determining the amplitude‐ and frequency‐dependent supplemental damping properties of the corresponding linear viscous system and for estimating the response of asymmetric one‐storey systems with non‐linear VE dampers from the earthquake design (or response) spectrum. Finally, a procedure is developed for designing non‐linear supplemental damping systems that satisfy given design criteria for a given design spectrum. Copyright © 2003 John Wiley & Sons, Ltd.     

A method for tuning tuned mass dampers for seismic applications

This paper studies tuned mass dampers (TMDs) resulting in high modal damping for mechanical systems incorporating such devices for the purpose of seismic response reduction. Focusing on the determination of damping and tuning, the proposed methodology identifies a point of multiplicity of complex eigenvalues and eigenvectors, resulting in different parameters for TMDs according to their location with respect to such multiplicity condition. It is shown that significant equal modal damping and average modal damping can be induced by properly tuning highly damped TMDs, obtaining parameters intrinsic to the mechanical systems, and excitation independent. Further, it is shown that the methodology yields, as particular cases, two proposals by others using TMDs for the same purpose of seismic response abatement. Copyright © 2012 John Wiley & Sons, Ltd.     

Design formulations for supplemental viscous dampers to highway bridges

Design formulas for supplemental viscous dampers to building structures are readily available in FEMA provisions and MCEER research reports. However, for the design of supplemental viscous dampers corresponding to a desired system damping ratio of highway bridges, there exist, if any, few design guidelines. This is particularly true if the bridge components such as elastomeric bearings, piers and abutment possess different damping ratios, stiffnesses, and lumped masses. In this paper, the design formulas for supplemental viscous dampers to highway bridges have been derived based on the concept of ‘composite damping ratio’. The design formulas can be used to determine the damping coefficients of the dampers corresponding to a desired system damping ratio of the bridge in which different component damping ratios may be assumed for the elastomeric bearings, piers and abutments. The proposed design formulas are numerically validated by comparing the seismic responses of a three‐span bridge equipped with viscous dampers with those of the same bridge without viscous dampers but with an assigned inherent system damping ratio equal to the target system damping ratio. Copyright © 2005 John Wiley & Sons, Ltd.     

Optimal placement of dampers for passive response control

The effectiveness of viscous and viscoelastic dampers for seismic response reduction of structures is quite well known in the earthquake engineering community. This paper deals with the optimal utilization of these dampers in a structure to achieve a desired performance under earthquake‐induced ground excitations. Frequency‐dependent and ‐independent viscous dampers and viscoelastic dampers have been considered as the devices of choice. To determine the optimal size and location of these dampers in the structure, a genetic algorithm is used. The desired performance is defined in terms of several different forms of performance functions. The use of the genetic approach is not limited to any particular form of performance function as long as it can be calculated numerically. For illustration, numerical examples for different building structures are presented showing the distribution and size of different dampers required to achieve a desired level of reduction in the response or a performance index. Copyright © 2002 John Wiley & Sons, Ltd.     

Probabilistic seismic response assessment of linear systems equipped with nonlinear viscous dampers

The paper aims at evaluating the influence of damper properties on the probabilistic seismic response of structural systems equipped with nonlinear viscous dampers. For this purpose, a linear single‐degree‐of‐freedom system with an added linear or nonlinear viscous damper is considered, and the response statistics are evaluated for a set of natural records describing the ground motion uncertainty. A dimensional analysis of the seismic problem is carried out first to identify the minimum set of characteristic parameters describing the system and controlling the seismic response. An extensive parametric study is then performed to estimate the influence of the damper properties on the statistics of the main response quantities of interest (i.e. maximum displacements, accelerations and damper forces), for a wide range of values of the characteristic parameters. Finally, a set of case studies is investigated to show some interesting issues concerning the influence of the damper nonlinear behaviour on the evaluation of the system reliability and to highlight some limitations of current deterministic approaches neglecting the probabilistic properties of the response. Copyright © 2014 John Wiley & Sons, Ltd.     

Optimal design of viscoelastic dampers using eigenvalue assignment

In this study a procedure for determining the optimum size and location of viscoelastic dampers is proposed using the eigenvalue assignment technique. Natural frequencies and modal damping ratios, required to realize a given target response, are determined first by the convex model. Then the desired dynamic structural properties are realized by optimally distributing the damping and stiffness coefficients of viscoelastic dampers using non‐linear programming based on the gradient of eigenvalues. This optimization method provides information on the optimal location as well as the magnitude of the damper parameters. The proposed procedure is applied to the retrofit of a 10‐story shear frame, and to a three‐dimensional structure with an asymmetric plan. The analysis results confirm that the responses of model structures retrofitted by the proposed method correspond well with the given target response. Copyright © 2003 John Wiley & Sons, Ltd.     

Optimal design of added viscoelastic dampers and supporting braces

This paper presents a simultaneous optimization procedure for both viscoelastic dampers (VEDs) and supporting braces installed in a structure. The effect of supporting braces on the control efficiency of VEDs is also investigated. To apply a general gradient‐based optimization algorithm, closed‐form expressions for the gradients of objective function and constraints are derived. Also, the constraint on the dynamic behavior of a structure is embedded in the gradient computation procedure to reduce the number of variables in the optimization. From numerical analysis of an example structure, it was found that when sufficient stiffness cannot be provided for the supporting braces, the flexibility of the brace should be taken into account in the design of the VED to achieve the desired performance of the structure. It was also observed that, as a result of the proposed optimization process, the size of the supporting brace could be reduced while the additional VED size (to compensate for the loss of the control effect) was insignificant. Copyright © 2003 John Wiley & Sons, Ltd.