Damped resonant appendages to increase inherent damping in buildings

It is demonstrated that the addition of a tuned mass-spring-dashpot system with a relatively small mass and a high damping ratio can be an effective way to increase the inherent damping characteristics of buildings and reduce, thus, their response to earthquake excitations. The demonstration is based on a theoretical formulation and on numerical and experimental studies that confirm this formulation. In the theoretical formulation, it is shown first that, if certain conditions are satisfied, the damping ratios in two of the modes of the system that is formed by a building and an appendage in resonance are approximately equal to the average of the corresponding damping ratios of the building and the appendage. Based on this finding, it is then shown that an attached appendage with a high damping ratio and tuned to the fundamental frequency of a building may increase the damping ratio in the fundamental mode of the building to a value close to half the damping ratio of the appendage. In the numerical study, the response of a ten-storey shear building is analysed under two different earthquake ground motions with and without the proposed resonant appendages. Appendages with damping ratios of 20 and 30 per cent are considered. In this study, it is found that under one of the ground motions the maximum displacement of the building's roof is reduced 30 per cent with the appendage with 20 per cent damping and 39 per cent with the one with 30 per cent damping. Similarly, with these two appendages the building's base shear is reduced 31 and 41 per cent, respectively. In the experimental study, a wooden three-storey structural model is tested in a shaking table with and without an appendage designed and constructed to have a damping ratio of 53-5 per cent. The test is conducted under random and sinusoidal base excitations. In the shaking table test under random excitation, the attached appendage reduces the response of the model 38-6 per cent, while in that under sinusoidal vibration 45-2 per cent.     

规则型隔震房屋的自振特性和地震反应分析方法

文中根据规则型隔震房屋的刚度、质量和阻尼分布的特点，改进了阻尼比的简化计算表达式。此外还归纳给出了自振周期、振型和地震反应计算公式。文中还将我们提出的隔震结构振型阻尼比公式与Kelly的相应公式进行了数值比较，两式的复杂程度虽几无差异，但文中的公式更为精确。文中提出的简化计算公式可以方便地在一般房屋结构隔震方案设计和地震反应的振型叠加分析中应用。     

地震作用下智能相邻建筑的主动锚索控制

研究了应用主动锚索控制装置控制相邻建筑地震响应的有效性。首先，建立了主动锚索－相邻建筑系统的运动方程；然后应用广义振型分析方法，寻求了主动锚索联结的相邻建筑的力学特性，特别是振型阻尼比；最后，在频率域内应用广义振型分析与虚拟激励相结合的方法，建立了主动锚索控制装置联结相邻建筑的随机地震响应的分析方法。应用本文建立的公式，我们编制了计算机程序，进行了广泛的参数研究，以评价控制装置的有效性，并确定最优传感器类型及控制装置参数。研究表明，如果应用速度传感器，并能适当地选择主动锚索控制器的参数，则可以显著地提高系统的振型阻尼比，减小两个结构的地震响应。     

Passive seismic control of cable-stayed bridges with damped resonant appendages

A study is conducted to investigate the effectiveness of attaching to cable-stayed bridges resonant appendages with a relatively small mass and a high damping ratio as a means to reduce their response to earthquake excitations. The study is based on a previously developed formulation that shows that the use of these appendages may increase the inherent damping of building structures and, as a result, may reduce their response to seismic disturbances. It includes numerical and experimental tests that are conducted to assess the validity of such a formulation for the case of cable-stayed bridges and the extent to which such appendages can reduce their seismic response. In the numerical study, an actual cable-stayed bridge is modelled with finite elements and analysed with and without the proposed appendages under different earthquake ground motions. Appendages with damping ratios of 10, 15, 20 and 30 per cent and masses that, respectively, represent 0.67, 1.5, 2.7 and 6.0 per cent of the total mass of the bridge are considered. In the experimental test, a 3.7 m long cable-stayed bridge and an appendage consisting of a small mass, a small spring and a small viscous damper are built and the bridge tested, without and with the appendage, on a pair of shaking tables which are set to reproduce ground acceleration records from past earthquakes. The damping ratio of the appendage in this test is 32 per cent and its mass represents about 8 per cent of the total mass of the bridge model. In the numerical test, it is found that the appendages reduce the longitudinal response of the bridge deck up to 88 per cent. Similarly, in the experimental test it is found that the appendage reduces the longitudinal bridge deck response by about 41 per cent. From these studies, it is concluded that the suggested appendages may indeed be effective in reducing the seismic response of cable-stayed bridges as they are for building structures.     

Predominant period and equivalent viscous damping ratio identification for a full‐scale building shake table test

The predominant period and corresponding equivalent viscous damping ratio, also known in various loading codes as effective period and effective damping coefficient, are two important parameters employed in the seismic design of base‐isolated and conventional building structures. Accurate determination of these two parameters can reduce the uncertainty in the computation of lateral displacement demands and interstory drifts for a given seismic design spectrum. This paper estimates these two parameters from data sets recorded from a full‐scale five‐story reinforced concrete building subjected to seismic base excitations of various intensities in base‐isolated and fixed‐base configurations on the outdoor shake table at the University of California, San Diego. The scope of this paper includes all test motions in which the yielding of the reinforcement has not occurred and the response can still be considered ‘elastic’. The data sets are used with three system identification methods to determine the predominant period of response for each of the test configurations. One of the methods also determines the equivalent viscous damping ratio corresponding to the predominant period. It was found that the predominant period of the fixed‐base building lengthened from 0.52 to 1.30 s. This corresponded to a significant reduction in effective system stiffness to about 16% of the original stiffness. The paper then establishes a correlation between predominant period and peak ground velocity. Finally, the predominant periods and equivalent viscous damping ratios recommended by the ASCE 7‐10 loading standard are compared with those determined from the test building. Copyright © 2017 John Wiley & Sons, Ltd.     

Evaluation of damping reduction factors for estimating elastic response of structures with high damping

The damping reduction factors are used in a few building codes in order to estimate the elastic response spectrum with high damping ratios from its 5%‐damped counterpart. At present, much research regarding this factor has been published. The purpose of this paper is to evaluate the accuracy of five different models of damping reduction factors. In addition, the damping reduction factors adopted in the recent U.S.A. seismic codes are also evaluated. Statistical studies are carried out according to a total of 216 earthquake ground motions recorded on firm sites in California. Considered here are elastic single‐degree‐of‐freedom (SDOF) systems with natural vibrating periods between 0.1 and 6.0 s. Mean ratios and dispersion of approximate to exact maximum elastic displacement demands corresponding to various damping reduction factors are computed as functions of the natural vibrating period and the viscous damping ratio. Copyright © 2005 John Wiley & Sons, Ltd.     

水平分层土层系统等效阻尼比的简化计算方法

在实际工程场地中,很多土层可视为水平分层,各层土的物理和力学性质存在差异,其中包括土的振动阻尼比。本文讨论水平分层土层系统的等效阻尼比的近似计算方法,基于5个不同的加权函数推导了10种等效阻尼比的计算公式。通过2个算例,分别以等效阻尼比为参数计算水平分层土层的地震反应,并与准确解相比较,分析了不同等效阻尼比近似计算方法的计算精度。数值结果表明,若等效阻尼比计算方法选择不恰当,会导致土层地震反应的计算结果出现较大误差。针对2种不同类型的水平分层土层,建议采用基于三角形分布的加权函数来计算土层系统的等效阻尼比。     

Dynamic properties analysis of a stay cable-damper system in consideration of design and construction factors

A numerical solution based on the Steffensen stable point iterative method is proposed to resolve the transcendental frequency equation of a stay cable-damper system. The frequency equation, which considers clamped supports and fl exural rigidity of the cable, is intended to investigate the infl uence of the parameters of the cable damper system on its dynamic characteristics. Two factors involved in the design and construction phases, the damping coeffi cient induced by external dampers and the cable tension, are the focus of this study. Their impact on modal frequencies and damping ratios in these two phases of cable-damper systems are investigated by resolving the equation with the proposed solution. It is shown that the damping coeffi cient and cable tension exert more noticeable effects on the modal damping ratios than on the modal frequencies of stay cable-damper systems, and the two factors can serve as design variables in the design phase and as adjustment factors in the construction phase. On the basis of the results, a roadmap for system-level optimal design of stay cable-damper systems that can achieve global optimal vibration suppression for the entire bridge is proposed and discussed.     

On a modal damping identification model for non-classically damped linear building structures subjected to earthquakes

A simple modal damping identification model developed by the present authors for classically damped linear building frames is extended here to the non-classically damped case. The modal damping values are obtained with the aid of the frequency domain modulus of the roof-to-basement transfer function and the resonant frequencies of the structure (peaks of the transfer function) as well as the modal participation factors and mode shapes of the undamped structure. The assumption is made that the modulus of the transfer function of the non-classically damped structure matches the one of the classically damped structure in a discrete manner, i.e., at the resonant frequencies of that function modulus. This proposed approximate identification method is applied to a number of plane building frames with and without pronounced non-classical damping under different with respect to their frequency content earthquakes and its limitations and range of applicability are assessed with respect to the accuracy of both the identified damping ratios and that of the seismic structural response obtained by classical mode superposition and use of those identified modal damping ratios.     

Accuracy of the half-power bandwidth method with a third-order correction for estimating damping in multi-DOF systems

A third-order correction was recently suggested to improve the accuracy of the half-power bandwidth method in estimating the damping of single DOF systems.This paper analyzes the accuracy of the half-power bandwidth method with the third-order correction in damping estimation for multi-DOF linear systems.Damping ratios in a two-DOF linear system are estimated using its displacement and acceleration frequency response curves,respectively.A wide range of important parameters that characterize the shape of these response curves are taken into account.Results show that the third-order correction may greatly improve the accuracy of the half-power bandwidth method in estimating damping in a two-DOF system.In spite of this,the half-power bandwidth method may significantly overestimate the damping ratios of two-DOF systems in some cases.     

A method for the transfer function matrix of combined primary–secondary systems using classical modal decomposition

An iterative method is presented to compute the transfer function matrix of combined primary–secondary systems for seismic response analysis. It accounts for non‐proportional damping and dynamic interaction of the combined system. A closed form sequence is developed for the iterative computation of the transfer function matrix. Such sequence is assembled using independently the real classical mode frequencies, shapes and damping ratios of the primary system, and the natural frequency and critical damping ratio of the SDOF secondary system. The necessary and sufficient condition for convergence of the sequence is given in the paper. The method is illustrated through a couple of examples, including one of an appendix connected to a multi‐storey shear building. Convergence of the method is thoroughly analysed and peak responses are obtained using a spectral density function approach. Copyright © 2005 John Wiley & Sons, Ltd.     

Equivalent uniform damping ratios for linear irregularly damped concrete/steel mixed structures

Structures consisting of two parts, a lower part made of concrete and an upper part made of steel are investigated. In code-based seismic design of such structures several practical difficulties are encountered, due to inherent differences in the nature of dynamic response of each part. The specific issue addressed here is the analysis complications due to the different damping ratios of the two parts. Such structures are irregularly damped and have complex modes of vibration, so that their analysis cannot be handled with readily available commercial software. This work aims at providing a simple yet sufficiently accurate methodology for handling the damping irregularity of such structures, by proposing an overall equivalent damping ratio that can be applied to the complete structure for obtaining its dynamic response. This is achieved by first transforming MDOF irregular structures into equivalent 2-DOF oscillators, using the first mode characteristics of each part, and then using equivalent uniform damping ratios that are derived by means of a semi-empirical error minimization procedure. Thus, available commercial software can be applied for seismic analysis and design and the provisions of existing seismic codes can be adhered to.     

Simplifications of CQC method and CCQC method

The response-spectrum mode superposition method is widely used for seismic response analyses of linear systems. In using this method, the complete quadratic combination （CQC） is adopted for classically damped linear systems and the complex complete quadratic combination （CCQC） formula is adopted for non-classically damped linear systems. However, in both cases, the calculation of seismic response analyses is very time consuming. In this paper, the variation of the modal correlation coefficients of displacement, velocity and displacement-velocity with frequency and damping ratios of two modes of interest are studied, Moreover, the calculation errors generated by using CQC and square-root-of-the-sum-of-thesquares （SRSS） methods （or CCQC and CSRSS methods） for different damping combinations are compared. In these analyses, some boundary lines for classically and non-classically damped systems are plotted to distinguish the allowed minimum frequency ratio at given geometric mean of the damping ratios of both modes if their relativity is neglected. Furthermore, the simplified method, which is a special mode quadratic combination method considering only relativity of adjacent modes in CQC method and named simplified CQC or partial quadratic combination （PQC） method for classically damped linear system, is proposed to improve computational efficiency, and the criterion for determination of how many correlated modes should be adopted is proposed. Similarly, the simplified CCQC or complex partial quadratic combination （CPQC） method for the non-classically damped linear system and the corresponding criterion are also deduced. Finally, a numerical example is given to illustrate the applicability, computational accuracy and efficiency of the PQC and CPQC methods.     

Understanding and predicting effects of supplemental viscous damping on seismic response of asymmetric one‐storey systems

Supplemental damping could mitigate the earthquake‐induced damage in buildings with asymmetric plan, known to be more vulnerable to damage than comparable symmetric‐plan buildings. This investigation aims to improve the understanding of how and why planwise distribution of fluid viscous dampers (FVDs) influences the response of linearly elastic, one‐storey, asymmetric‐plan systems. Starting with vibration mode shapes, we predict this influence on the modal damping ratios, and in turn on the individual modal responses and the total response. These predictions are confirmed by the computed responses, which demonstrated that the reduction in earthquake response of the system achieved by supplemental damping is strongly influenced by its planwise distribution, which is characterized by four parameters. Identified are asymmetric distributions of supplemental damping that are more effective in reducing the response compared to symmetric distribution. The percentage reduction achieved by a judiciously selected asymmetric distribution can be twice or even larger compared to symmetric distribution. Copyright © 2001 John Wiley & Sons, Ltd.     

Dynamic characteristics of a base isolated building from ambient vibration measurements and low level earthquake shaking

Ambient vibration tests were conducted on a base-isolated apartment building in Takamatsu, Japan, to determine the mode shapes and the associated natural frequencies and damping ratios at very low levels of excitation. The latest developments in signal analysis for modal decomposition are used to analyze the ambient response data. A finite element model of the building and isolators was calibrated and refined using the experimental results from the ambient vibration tests. This model was then used to simulate the recorded response of the building under excitation from a small earthquake. The finite element model, calibrated by ambient vibration data and the low level of earthquake shaking, provides the starting point for modelling the non-linear response of the building when subjected to strong shaking.     

Design approaches for active, semi-active and passive control systems based on analysis of characteristics of active control force

In this paper,the characteristics of forces in active control systems connected to adjacent levels of a building are analyzed.The following characteristics are observed:(1) active control can provide signifi cantly superior supplemental damping to a building,but causes a small frequency shift;(2) the linear quadratic regulator(LQR)-based control force is composed of an elastic restoring force component and a damping force component,where the damping force is almost identical to the total control force,howev...     

Forced vibration test of a building with semi‐active damper system

The authors developed a semi‐active hydraulic damper (SHD) and installed it in an actual building in 1998. This was the first application of a semi‐active structural control system that can control a building's response in a large earthquake by continuously changing the device's damping coefficient. A forced vibration test was carried out by an exciter with a maximum force of 100 kN to investigate the building's vibration characteristics and to determine the system's performance. As a result, the primary resonance frequency and the damping ratio of a building that the SHDs were not jointed to, decreased as the exciting force increased due to the influence of non‐linear members such as PC curtain walls. The equivalent damping ratio was estimated by approximating the resonance curves using the steady‐state response of the SDOF bilinear hysteretic system. After the eight SHDs were jointed to the building, the system's performance was identified by a response control test for steady‐state vibration. The elements that composed the semi‐active damper system demonstrated the specified performance and the whole system operated well. Copyright © 2000 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.     

Experimental investigation of adjacent buildings connected by fluid damper

Dynamic characteristic and harmonic response of adjacent buildings connected by fluid damper were experimentally investigated using model buildings and fluid damper. Two building models were constructed as two three-storey shear buildings of different natural frequencies. Model fluid damper connecting the two buildings was designed as linear viscous damper of which damping coefficient could be adjusted. The two buildings without fluid dampers connected were first tested to obtain their individual dynamic characteristics and responses to harmonic excitation. The tests were then carried out to determine modal damping ratios of the adjacent buildings connected by the fluid damper of different damping coefficients and at different locations. Optimal damper damping coefficient and location for achieving the maximum modal damping ratio were thus found. The measured modal damping ratios and harmonic responses of the building-fluid damper system were finally compared with those from the individual buildings. The comparison showed that the fluid damper of proper parameter could significantly increase the modal damping ratio and tremendously reduce the dynamic response of both buildings. Copyright © 1999 John Wiley & Sons, Ltd.     

结构附加粘滞阻尼器的抗震设计

本文结合抗震设计规范反应谱,给出了一个附加非线性流体粘滞阻尼器结构的抗震设计方法。研究了非线性阻尼器的力学特性,引入了非线性流体阻尼器的等效线性阻尼比,给出了计算最大加速度时刻附加非线性流体阻尼器结构反应的荷载组合系数,提出了按阻尼力的水平力分量与楼层剪力成正比的原则分配阻尼器阻尼系数的方法。同时给出了基于抗震规范设计反应谱附加非线性阻尼器结构的设计流程,通过一个算例说明了使用该方法设计附加非线性粘滞阻尼器结构的全过程。算例分析表明,这种设计方法适合于手算,便于设计人员掌握,在初步设计阶段可以快速、有效地设计满足给定性能水平的附加非线性流体阻尼器体系。