Critical damping of structures with elastically supported visco‐elastic dampers

This paper presents a new formulation for critical damping of structures with elastically supported visco‐elastic dampers.Owing to the great dependence of damper performance on the support stiffness, this model is inevitable for reliable modelling of structures with visco‐elastic dampers. It is shown that the governing equation of free vibration of this model is reduced to a third‐order differential equation and the conventional method for defining the critical damping for second‐order differential equations cannot be applied to the present model. It is demonstrated that the region of overdamped vibration is finite in contrast to that (semi‐infinite) for second‐order differential equations and multiple critical damping coefficients exist. However, it turns out that the smaller one is practically meaningful. Copyright © 2001 John Wiley & Sons, Ltd.     

结构抗震设计中的强度折减系数研究

借助于单自由度弹塑性动力时程分析程序，对延性结构的强度折减系数进行了研究，在统计平均和回归分析的基础上，建立了平均强度折系数的函数形式，本文所建立的平强度折减系数函数，从理论上明确了结构具有延性对弹性地震力的折减关系，研究成果可供结构抗震设计规范采纳应用。     

Effect of viscous,viscoplastic and friction damping on the response of seismic isolated structures

In this paper the efficiency of various dissipative mechanisms to protect structures from pulse‐type and near‐source ground motions is examined. Physically realizable cycloidal pulses are introduced, and their resemblance to recorded near‐source ground motions is illustrated. The study uncovers the coherent component of some near‐source acceleration records, and the shaking potential of these records is examined. It is found that the response of structures with relatively low isolation periods is substantially affected by the high‐frequency fluctuations that override the long duration pulse. Therefore, the concept of seismic isolation is beneficial even for motions that contain a long duration pulse which generates most of the unusually large recorded displacements and velocities. Dissipation forces of the plastic (friction) type are very efficient in reducing displacement demands although occasionally they are responsible for substantial permanent displacements. It is found that the benefits by hysteretic dissipation are nearly indifferent to the level of the yield displacement of the hysteretic mechanism and that they depend primarily on the level of the plastic (friction) force. The study concludes that a combination of relatively low friction and viscous forces is attractive since base displacements are substantially reduced without appreciably increasing base shears and superstructure accelerations. Copyright © 2000 John Wiley & Sons, Ltd.     

A two‐step direct method for estimating the seismic response of nonlinear structures equipped with nonlinear viscous dampers

The insertion of fluid viscous dampers in building structures is an innovative technology that can improve significantly the seismic response. These devices could be very useful also in the retrofit of existing buildings. The effect of this typology of damping system is usually identified with an equivalent supplemental damping ratio, which depends on the maximum displacement of the structure, so that iterative procedures are required. In this paper, a simplified direct assessment method for nonlinear structures equipped with nonlinear fluid viscous dampers is proposed. The method proposed in this study is composed by two steps. The first one yields the direct estimate of the supplemental damping ratio provided by nonlinear viscous dampers in presence of a linear elastic structural response. The second step extends the procedure to structures with nonlinear behavior. Both graphical and analytical approaches have been developed. The proposed method has then been verified through several applications and comparisons with nonlinear dynamic analyses. Moreover, an investigation has been performed with regard to the influence of the relations that define the damping reduction factor and the hysteretic damping. Copyright © 2014 John Wiley & Sons, Ltd.     

Evaluation of reduction factors for high-damping design response spectra

High-damping response spectra are essential tools for the assessment and design methods based on the equivalent elastic structure concept. They are also often used for the analysis and design of structures with seismic isolation or energy dissipation systems. Many formulations of the reduction factors have been proposed and included in seismic codes to estimate high-damping response spectra from their 5% damping representation. They are reviewed in the present paper. The accuracy of each of them in estimating the maximum elastic response of structures with viscous damping ratios greater than 5% is assessed by comparing exact and approximate displacement response spectra for three different damping levels, namely 10, 20 and 30%, respectively. The comparison is referred to more than 120 ground motion records, relevant to earthquakes with magnitude between 6 and 8, epicentral distance ranging from 1 to 100 km and Peak Ground Accelerations (PGA’s) greater than 0.1 g. The comparison between exact and approximate response spectra is carried out for both single earthquakes and groups of earthquakes with similar magnitude and epicentral distance. The drawbacks of using the same damping reduction factor to estimate both maximum displacement response and design seismic forces are also addressed.     

相邻结构的高效阻尼控制

提出了相邻结构高效阻尼控制的概念,并基于双液缸的放大原理提出了一处相应的装置,该装置通过放大相邻结构间的振动差别,使阻尼器具有更大的变形和速度,从而更高效地工作,文章阐明了该装置的工作原理,建立了两相邻结构高效阻尼控制体系的运动方程,并对此进行了计算机仿真分析,结果表明,高效阻尼控制的概念是正常的,本文提出的控制装置是有效的,可取得远优于普通阻尼控制的效果。     

Nonlinear elastic and inelastic spectra with inherent and supplemental damping

During severe seismic events, structures designed according to current standards yield and develop inelastic deformations. While the acceleration responses are limited by the yielding strength, these structures develop permanent deformations (and possible damage) due to such yielding. Spectra developed for inelastic structures can help in determining the desired yield levels and the associated inelastic deformations. Some structures made of special materials or equipped with innovative structural systems may yield, but can recover the deformation upon unloading and, thus, may avoid permanent deformations. These structures are known as nonlinear elastic. Often the post yielding excursions are very large and may exceed their toughness (or deformability). By introducing damping in form of supplemental devices, it is possible to control such deformations and keep them within acceptable limits. Spectra for such nonlinear elastic structures and inelastic structures are developed herein, by considering both inherent and supplemental damping. The difference between the two types of damping is addressed both theoretically and numerically. Design examples of several simple structures using the newly developed spectra are presented, which illustrate the importance of lower strength and damping in these nonlinear elastic or inelastic systems. Copyright © 2013 John Wiley & Sons, Ltd.     

Deterministic sliding block methods for estimating seismic displacements of earth structures

A review and quantitative comparison of existing deterministic sliding block methods for predicting permanent displacements of earth structures subjected to seismic loading is presented. The reviewed sliding block methods are divided into two main groups based on the characteristic earthquake parameters referenced in each method. One group uses the maximum horizontal ground acceleration and velocity, and the other uses the maximum horizontal ground acceleration and the predominant period of the acceleration spectrum. Displacement functions published by previous authors are reformulated to give common non-dimensionalized displacement functions of the critical acceleration ratio which are then used to compare the different methods for the estimate of permanent seismic displacement of soil structures. The results show that despite the fact that the different methods were formulated using a wide range of earthquake records and different characteristic seismic parameters, permanent displacement values predicted using these methods fall within a reasonably narrow band. Selected acceleration data from three recent earthquakes that occurred in California are used to evaluate and compare the accuracy of the reviewed displacement methods for practical applications.     

An advanced analytical model for high damping rubber bearings

Base‐isolation technologies have been developed over the years in attempts to mitigate the effects of earthquakes on structures and potentially vulnerable contents in earthquake prone areas of the world. The high damping rubber bearing (HDRB) is a relatively recent and evolving technology of this kind. The isolator shifts the fundamental period of the base‐isolated structure to a value beyond the range of the plentiful energy‐containing periods of earthquake motions and supplies significant damping to dissipate energy caused by motions. Nevertheless, the highly non‐linear mechanical behaviour of the HDRB is so complex, especially at large strains, that it is difficult to model it analytically. In this paper, an extensive study of experimental tests for identifying the mechanical characteristics of the HDRB is presented. By modifying the Wen's model to include the rate‐dependent effects, an advanced analytical model in an incremental form for the HDRB is also proposed. A very good agreement between the analytical and experimental results has been obtained. It is illustrated that the proposed mathematical model can predict well the mechanical behaviour of HDRB bearings, even at large shear strain. Copyright © 2003 John Wiley & Sons, Ltd.     

等位移理论估计高层建筑结构非弹性地震反应的进一步研究

为进一步研究用等位移理论估计高层建筑结构非弹性地震反应,选用五个钢筋混凝土高层结构实例,输入二十条不同场地条件的地震波,采用结构弹性和非弹性地震时程反应分析方法,研究了结构弹性和非弹性最大顶点位移以及最大层间位移角之间的关系。提出可以直接用弹性最大顶点位移估计非弹性最大顶点位移。对于非弹性层间位移角反应,在中、弱非线陛阶段宜可直接用弹性反应结果估计,而在强非线性阶段则需进行一定修正。     

高阻尼混凝土框架的动力特性与抗震试验

在混凝土中加入高阻尼掺料,从而有效地提高钢筋混凝土结构自身的阻尼比,这是从材料角度出发的一种新的结构振动控制方法。本文利用聚合物的高阻尼特性和材料的表面改性技术,在普通钢筋混凝土柱中掺加一定数量的苯丙乳液和改性的硅粉,制作了3组单层两榀混凝土框架;然后对其进行了试验研究,测定了框架结构的阻尼比和频率等动力特性;并且研究和比较了不同地震动下高阻尼混凝土框架的相对位移和绝对加速度反应。试验结果表明:改性硅粉和苯丙乳液的加入均可以提高混凝土框架结构破坏前后的阻尼比,分别提高52.4%、82.3%和27.5%、42.5%;改性硅粉可以有效地提高混凝土框架结构破坏前后的刚度,分别提高5%和15%~50%;虽然苯丙乳液的加入降低了混凝土框架结构的初始刚度,大约降低17%,但却提高了混凝土框架结构破坏后的残余刚度,提高大约10%~20%。改性硅粉和苯丙乳液的加入对于混凝土框架结构地震反应的减振控制起到了很好的作用。     

Seismic performance of bridges with novel SMA cable-restrained high damping rubber bearings against near-fault ground motions

This study presents a novel type of shape memory alloy (SMA) cable-restrained high damping rubber (SMA-HDR) bearing, which is particularly suited to near-fault (NF) regions where the pulsing effect potentially exists in the ground motions. The working mechanism of the bearing is first described, followed by an experimental investigation on a full-scale SMA-HDR bearing specimen. The test results confirm the efficient restraining effect offered by the SMA cables, which contribute to 65% and 24.4% of the lateral load resistance and total energy dissipation, respectively, prior to the initial fracture of the SMA cables. The failure of the cables is initiated near the end grip where moderate stress concentration exists at this region. Following the experimental study, the numerical modeling strategy for the bearing is discussed, and a case study is then presented, demonstrating the application of the SMA-HDR bearings in the Datianba #2 highway bridge, a real project that first adopts the proposed bearings in the world. A simplified design process is introduced for the bridge with novel SMA-HDR bearings to mitigate the potential damage during strong earthquakes especially the NF ones. The system-level analysis on the prototype bridge shows that the novel SMA-HDR bearings equipped with ten 7×7×1.2 SMA cables in each bearing could reduce the average maximum bearing displacement (MBD) by nearly 30% compared with the conventional bridge with HDR bearings. The application of the novel SMA-HDR bearing can significantly alleviate the pounding effect, especially under the NF earthquakes. The presence of the SMA cables tends to increase the maximum force response of the piers, but this effect is minor and under control.     

Scaling of spectral displacement ordinates with damping ratios

The next generation of seismic design codes, especially those adopting the framework of performance‐based design, will include the option of design based on displacements rather than forces. For direct displacement‐based design using the substitute structure approach, the spectral ordinates of displacement need to be specified for a wide range of response periods and for several levels of damping. The code displacement spectra for damping values higher than the nominal value of 5% of critical will generally be obtained, as is the case in Eurocode 8 and other design codes, by applying scaling factors to the 5% damped ordinates. These scaling factors are defined as functions of the damping ratio and, in some cases, the response period, but are independent of the nature of the expected ground shaking. Using both predictive equations for spectral ordinates at several damping levels and stochastic simulations, it is shown that the scaling factors for different damping levels vary with magnitude and distance, reflecting a dependence of the scaling on the duration of shaking that increases with the damping ratio. The options for incorporating the influence of this factor into design code specifications of displacement response spectra are discussed. Copyright © 2004 John Wiley & Sons, Ltd.     

Stability of average acceleration method for structures with nonlinear damping

The energy approach is used to theoretically verify that the average acceleration method （AAM）, which is unconditionally stable for linear dynamic systems, is also unconditionally stable for structures with typical nonlinear damping, including the special case of velocity power type damping with a bilinear restoring force model. Based on the energy approach, the stability of the AAM is proven for SDOF structures using the mathematical features of the velocity power function and for MDOF structures by applying the virtual displacement theorem. Finally, numerical examples are given to demonstrate the accuracy of the theoretical analysis.     

Active viscous damping system with amplifying braces for control of MDOF structures

The development and the applications of an active controlled viscous damping device with amplifying braces are described. The system of the dampers, defined as active viscous damping system (AVDS), connected to an amplifying brace (AB) is presented herein. Instantaneous control theory with velocity and acceleration feedback is used to obtain the control forces at each time step during an excitation. Control of the damping forces is possible due to the mechanical structure of the proposed AVDS, and the connection to the AB. The proposed system can be efficiently used to enhance the damping of a structure without modifying its stiffness. The added damping forces can be adjusted in a wide range. The efficiency of the presented system is demonstrated by a numerical simulation of a seven‐storey building subjected to earthquakes. The simulation shows a considerable reduction of control forces required for control to the AVDS with AB, compared to the same system without AB. Copyright © 2002 John Wiley & Sons, Ltd.     

Inelastic displacement ratios for evaluation of existing structures

Results of a detailed statistical study of constant relative strength inelastic displacement ratios to estimate maximum lateral inelastic displacement demands on existing structures from maximum lateral elastic displacement demands are presented. These ratios were computed for single‐degree‐of‐freedom systems with different levels of lateral strength normalized to the strength required to remain elastic when subjected to a relatively large ensemble of recorded earthquake ground motions. Three groups of soil conditions with shear wave velocities higher than 180m/s are considered. The influence of period of vibration, level of lateral yielding strength, site conditions, earthquake magnitude, distance to the source, and strain‐hardening ratio are evaluated and discussed. Mean inelastic displacement ratios and those associated with various percentiles are presented. A special emphasis is given to the dispersion of these ratios. It is concluded that distance to the source has a negligible influence on constant relative strength inelastic displacement ratios. However, for periods smaller than 1s earthquake magnitude and soil conditions have a moderate influence on these ratios. Strain hardening decreases maximum inelastic displacement at a fairly constant rate depending on the level of relative strength for periods of vibration longer than about 1.0s while it decreases maximum inelastic displacement non‐linearly as the period of vibration shortens and as the relative‐strength ratio increases for periods of vibration shorter than 1.0s. Finally, results from non‐linear regression analyses are presented that provide a simplified expression to be used to approximate mean inelastic displacement ratios during the evaluation of existing structures built on firm sites. Copyright © 2003 John Wiley & Sons, Ltd.     

Simplified analysis of asymmetric structures with supplemental damping

This study investigated the effects of neglecting off‐diagonal terms of the transformed damping matrix on the seismic response of non‐proportionally damped asymmetric‐plan systems with the specific aim of identifying the range of system parameters for which this simplification can be used without introducing significant errors in the response. For this purpose, a procedure is presented in which modal damping ratios computed by neglecting off‐diagonal terms of the transformed damping matrix are used in the traditional modal analysis. The effects of the simplification are evaluated first by comparing the aforementioned modal damping ratios with the apparent damping ratios obtained from the complex‐valued eigenanalysis. The variation of a parameter that was defined by Warburton and Soni as an indicator of the errors introduced by the simplification is examined next. Finally, edge deformations obtained from the simplified procedure are compared with those obtained from the direct integration of the equations of motion. It is found that the simplified procedure may be used without introducing significant errors in response for most practical values of the system parameters. Furthermore, estimates of the edge deformations, in general, tend to be on the conservative side. Copyright © 2001 John Wiley & Sons, Ltd.     

Spectral and fragility evaluations of retrofitted structures through strength reduction and enhanced damping

A retrofit procedure for existing buildings called the "weakening and damping technique" (WED) is presented in this paper. Weakening of structures can limit the maximum response accelerations during severe ground motions, but leads to an increase in the displacements or inter-story drifts. Added damping by using viscous dampers, on the other hand, reduces the inter-story drifts and has no significant effect on total accelerations, when structures behave inelastically. The weakening and damping technique addresses the two main causes for both structural and nonstructural damage in structures. The weakening retrofit is particularly suitable for structures that have overstressed components and weak brittle components. In this paper, the advantages of the WeD are verified by nonlinear dynamic analysis and simplified spectral approach that has been modified to fit structures with additional damping devices. A hospital structure located in the San Femando Valley in California is selected as a case study. The results from both analyses show that the retrofit solution is feasible to reduce both structural acceleration and displacement. A sensitivity analysis is also carried out to evaluate the effectiveness of the retrofitting method using different combinations of performance thresholds in accelerations and displacements through fragility analysis.     

Effect of viscous damping devices on the response of seismically isolated structures

Viscous and other damping devices are often used as elements of seismic isolation systems. Despite the widespread application of nonlinear viscous systems particularly in Japan (with fewer applications in the USA and Taiwan), the application of viscous damping devices in isolation systems in the USA progressed intentionally toward the use of supplementary linear viscous devices due to the advantages offered by these devices. This paper presents experimental results on the behavior of seismically isolated structures with low damping elastomeric (LDE) and single friction pendulum (SFP) bearings with and without linear and nonlinear viscous dampers. The isolation systems are tested within a six‐story structure configured as moment frame and then again as braced frame. Emphasis is placed both on the acquisition of data related to the structural system (drifts, story shear forces, and isolator displacements) and on non‐structural systems (floor accelerations, floor spectral accelerations, and floor velocities). Moreover, the accuracy of analytical prediction of response is investigated based on the results of a total of 227 experiments, using 14 historic ground motions of far‐fault and near‐fault characteristics, on flexible moment frame and stiff braced frame structures isolated with LDE or SFP bearings and linear or nonlinear viscous dampers. It is concluded that when damping is needed to reduce displacement demands in the isolation system, linear viscous damping results in the least detrimental effect on the isolated structure. Moreover, the study concludes that the analytical prediction of peak floor accelerations and floor response spectra may contain errors that need to be considered when designing secondary systems. Copyright © 2014 John Wiley & Sons, Ltd.     

A note on strength-reduction factors for design of structures near earthquake faults

Strength-reduction factors are analyzed for simplified near-fault, fault-normal and fault-parallel strong-motion displacements. It is shown that the common design rules for selection of the strength-reduction factors are conservative and properly describe the reduction amplitudes near faults of strong earthquakes, for fault-normal pulses. However, for fault-parallel displacements, the same reduction factors are not conservative and should be changed. It is recommended that for design close to active faults, the strength-reduction factors for all components of motion should be constant for all periods and equal to (2μ−1)^1/2, where μ is ductility.