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1.
The objective of this note is to assess the accuracy of the half-power bandwidth method for the estimation of damping ratios in single- and multi-degree-of-freedom structures with linear viscous damping including those that do not possess classical normal modes. This is done by performing some numerical experiments involving single- and multi-degree-of-freedom structures. It is found that the use of the half-power bandwidth method in its classical form may lead to significant errors, while a third order correction to this classical form provides conservative and more reliable results. It is also found in conjunction with this correction that application of the half-power bandwidth method should be performed to the acceleration frequency response transfer function of the structure on a mode-to-mode basis and that its damping ratio estimates for higher modes should always be viewed with caution. 相似文献
2.
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. 相似文献
3.
In order to account for the non‐linear behavior of structures via non‐linear static procedure, the capacity spectrum method has been adopted by ATC‐40 for evaluation and retrofit of reinforced concrete buildings. For elastic‐perfectly‐plastic SDOF systems, the accuracy of the capacity spectrum method depends only on the acceleration response spectrum chosen to form the demand spectrum and the adopted model for calculating the equivalent viscous damping ratios. According to this method, the pseudo‐acceleration response spectrum (PSa) is used to create the demand diagram. It is found that the ATC‐40 procedure, using its Type A hysteretic model, may be inaccurate especially for systems with damping ratios greater than 10% and periods longer than 0.15sec. In order to improve the accuracy of the capacity spectrum method, this study proposes to use the real absolute acceleration response spectrum (S0.a) instead of the PSa to establish the demand diagram. The step‐by‐step procedure of the improved method and examples are implemented in this paper to illustrate the calculations of earthquake‐induced deformations. In addition, three selected models of equivalent viscous damping are also compared in this paper to assess the accuracy of the model used in the ATC‐40 procedure. Results show that the WJE damping model may be used by the capacity spectrum method to reasonably predict the inelastic displacements when the ductility demand (μ) of the structures is less than 4, whereas the damping model proposed by Kowalsky can be implemented when μ>4.0. Alternatively, the damping model proposed by Kowalsky may be used to calculate the equivalent viscous damping for the entire range of ductility. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
4.
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. 相似文献
5.
对一维剪切条计算模型进行改进,提出了土石坝非线性地震反应的简化计算方法。首先将坝体沿坝高离散为一系列的具有不同剪切刚度与阻尼比等参数特性的层状体系,建立了各层的振动控制方程及其边值条件,进而采用数学物理方程方法进行了求解,确定了体系的振动特性,并根据振型叠加原理和Duhamel积分确定了坝体地震反应的线弹性解。采用等价线性化方法考虑坝料的动力非线性性质,通过对线弹性地震响应的反复迭代计算,使得各层土的模量和阻尼比与其相应的剪应变水平相协调,确定出与非线性坝体系统相等效的线性解答,并将所得到的地震响应作为非线性地震响应的近似解。最后,以均质坝和心墙坝作为算例进行了具体的数值计算,将所得结果与有限元数值解进行对比分析,论证了所提方法的适用性和合理性。 相似文献
6.
The system damping, the system frequency, the relative building response and the base rocking response peak amplitudes are studied, as those depend on the building mass and height, the flexibility of the soil, the structural damping, the type of incident waves and their angle of incidence. A linear two-dimensional model is used, which assumes the soil to be a homogeneous isotropic half-space, the foundation supporting the building to be a rigid embedded cylinder, and in which the building model is an equivalent single-degree-of-freedom oscillator. The system frequency and the system damping ratio are determined by measuring the width and the frequency of the peak in the transfer function of the oscillator relative response, using the analogy with the half-power method for a single-degree-of-freedom fixed-base oscillator. Previous similar studies are for dynamic soil-structure interaction only, and for simplified models in which the stiffness of the soil and the damping due to radiation are represented by springs and dashpots. The study in this paper differs from the previous studies in that the wave passage effects (or the kinematic interaction) are also included, and that no additional simplifications of the model are made. Results are shown for excitation by plane P- and SV-waves. 相似文献
7.
It has been shown that the use of base isolation not only attenuates the response of a primary structural system but also reduces the response of a secondary system mounted on or within the main structure. The isolation system, superstructure and equipment may be made of different materials with significantly different energy dissipation characteristics such that the damping matrix for the combined system is non-classical and can only be approximately expressed by modal damping ratios if the classical mode method is used for analysis. The object of this paper is to evaluate the accuracy of this procedure in approximating the responses of base-isolated structures and internal equipment. The complex mode method can provide exact solutions to problems with non-classical damping and is used here to find the exact response of the isolation-superstructure-equipment system. The entire system is assumed to be linear elastic with viscous damping and the superstructure is assumed to be proportionally damped so that the deformation of the superstructure can be expressed in terms of its classical modes. Recognizing that the ratio of the equipment mass to the structural mass and the ratio of the stiffness of the isolation system to the superstructural stiffness are both small, perturbation methods are used to find the response. This study shows that the response of base-isolated structures can be determined by the classical mode method to some degree of accuracy, but the higher frequency content is distorted. The equipment response derived by the classical mode method is much smaller than the exact solution so that the complex mode method should be applied to find equipment response. 相似文献
8.
Based on the Hilbert–Huang spectral analysis, a method is proposed to identify multi‐degree‐of‐freedom (MDOF) linear systems using measured free vibration time histories. For MDOF systems, the normal modes have been assumed to exist. In this method, the measured response data, which are polluted by noises, are first decomposed into modal responses using the empirical mode decomposition (EMD) approach with intermittency criteria. Then, the Hilbert transform is applied to each modal response to obtain the instantaneous amplitude and phase angle time histories. A linear least‐square fit procedure is proposed to identify the natural frequency and damping ratio from the instantaneous amplitude and phase angle for each modal response. Based on a single measurement of the free vibration time history at one appropriate location, natural frequencies and damping ratios can be identified. When the responses at all degrees of freedom are measured, the mode shapes and the physical mass, damping and stiffness matrices of the structure can be determined. The applications of the proposed method are illustrated using three linear systems with different dynamic characteristics. Numerical simulation results demonstrate that the proposed system identification method yields quite accurate results, and it offers a new and effective tool for the system identification of linear structures in which normal modes exist. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
9.
It is widely known that the seismic response characteristics of a soil site depends heavily on several key dynamic properties
of the soil stratum, such as predominant frequency and damping ratio. A widely used method for estimating the predominant
frequency of a soil site by using microtremor records, proposed by Nakamura, is investigated to determine its effectiveness
in estimating the damping ratio. The authors conducted some microtremor measurements of soil sites in Hong Kong and found
that Nakamura’s method might also be used to estimate the damping ratio of a soil site. Damping ratio data from several typical
soil sites were obtained from both Nakamura’s ratio curves using the half power point method and resonant column tests. Regression
analysis indicates that there is a strong correlation between the damping ratios derived from these two different approaches.
Supported by: Research project (PolyU 5076/97E), of the Department of Civil and Structural Engineering, The Hong Kong Polytechnic University 相似文献
10.
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。 相似文献
11.
This paper explores the influence of linear hysteretic damping on the performance of passive tuned-inerter devices. An inerter is a device that produces a force proportional to the relative acceleration across its two terminals; devices incorporating inerters have received widespread attention in the earthquake engineering community, because they offer the ability to improve the seismic response of structures. However, the majority of this research has assumed that the damping components within the tuned-inerter device exhibit viscous, rather than hysteretic, damping. This restriction imposes an essential question on how the hysteretic damping model will change the performance of the device compared with the viscous damping model. It is shown that the response of viscous and hysteretic inerter systems have significant differences in displacement amplitude due to the frequency dependency of the damping. Therefore, a new formulation for obtaining the optimum loss factor of the hysteretic damping in the inerter system is proposed. Next, the challenges associated with accurately predicting the time-response of a hysteretically damped system are discussed. A numerical time-integration method is extended to address these challenges, using a new formulation that has the benefit of being broadly applicable to multidegree-of-freedom hysteretic linear systems and nonstationary random signals. The results show that the earthquake responses from the hysteretic damping model can differ significantly from the ones obtained via the viscous model. 相似文献
12.
A new direct performance‐based design method utilizing design tools called performance‐spectra (P‐Spectra) for low‐rise to medium‐rise frame structures incorporating supplemental damping devices is presented. P‐Spectra are graphic tools that relate the responses of nonlinear SDOF systems with supplemental dampers to various damping parameters and dynamic system properties that structural designers can control. These tools integrate multiple response quantities that are important to the performance of a structure into a single compact graphical format to facilitate direct comparison of different potential solutions that satisfy a set of predetermined performance objectives under various levels of seismic hazard. An SDOF to MDOF transformation procedure that defines the required supplemental damping properties for the MDOF structure to achieve the response defined by the target SDOF system is also presented for hysteretic, linear viscous and viscoelastic damping devices. Using nonlinear time‐history analyses of idealized shear structures, the accuracy of the transformation procedure is verified. A seismic performance upgrade design example is presented to demonstrate the usefulness of the proposed method for achieving design performance goals using supplemental damping devices. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
13.
Tetsuji Itoh 《地震工程与结构动力学》1973,2(1):47-57
In the dynamic response analysis of extremely complex structural systems in which the damping characteristics of each element are independent, the damping matrix is not always diagonalized by the use of undamped free vibration mode shapes. In the present paper, a mode-superposition method by the use of damped free vibration mode shapes is developed for such structural systems. It is also shown that the Fast Fourier Transform (FFT) procedures, that are available for the dynamic response analysis of linear structural systems, are used effectively in this mode-superposition method with good accuracy. 相似文献
14.
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. 相似文献
15.
Real and complex Ritz vector bases for dynamic analysis of large linear systems with non-proportional damping are presented and compared. Both vector bases are generated utilizing load dependent vector algorithms that employ recurrence equations analogous to the Lanczos algorithm. The choice of static response to fixed spatial loading distribution, as a starting vector in recurrence equations, is motivated by the static correction concept. Different phases of dynamic response analysis are compared with respect to computational efficiency and accuracy. It is concluded that the real vector basis approach is approximately eight times more efficient than the complex vector basis approach. The complex vector basis has some advantages with respect to accuracy, if the excitation is of piecewise linear form, since the exact solution can be utilized. In addition, it is demonstrated that both Ritz vector bases, real and complex, possess superior accuracy over the adequate eigenvector bases. 相似文献
16.
Correction factors for SSI effects predicted by simplified models: 2D versus 3D rectangular embedded foundations 
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下载免费PDF全文 The effects of soil‐structure interaction (SSI) are often studied using two‐dimensional (2D) or axisymmetric three‐dimensional (3D) models to avoid the high cost of the more realistic, fully 3D models, which require 2 to 3 orders of magnitude more computer time and storage. This paper analyzes the error and presents correction factors for system frequency, system damping, and peak amplitude of structural response computed using impedances for linear in‐plane 2D models with rectangular foundations, embedded in uniform or layered half‐space. They are computed by comparison with results for 3D rectangular foundations with the same vertical cross‐section and different aspect ratios. The structure is represented by a single degree‐of‐freedom oscillator. Correction factors are presented for a range of the model parameters. The results show that in‐plane 2D approximations overestimate the SSI effects, exaggerating the frequency shift, the radiation damping, and the reduction of the peak amplitude. The errors are larger for stiffer, taller, and heavier structures, deeper foundations, and deeper soil layer. For example, for a stiff structure like Millikan library (NS response; length‐to‐width ratio ≈ 1), the error is 6.5% in system frequency, 44% in system damping, and 140% in peak amplitude. The antiplane 2D approximation has an opposite effect on system frequency and the same effect on system damping and peak relative response. Linear response analysis of a case study shows that the NEHRP‐2015 provisions for reduction of base shear force due to SSI may be unsafe for some structures. The presented correction factor diagrams can be used in practical design and other applications. 相似文献
17.
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. 相似文献
18.
19.
Roberto Villaverde 《地震工程与结构动力学》1985,13(1):33-42
It is shown that two of the damping ratios of certain systems composed of a building and a small attachment in resonance are given by the average of the damping ratios of the two independent components. Based on this fact and the fact that the seismic response of a building can always be reduced by increasing its damping, it is demonstrated that the attachment of a small heavily-damped system in resonance can increase the damping of a building and reduce thus its response to earthquake excitations. Numerical solutions are presented to confirm the demonstration, and recommendations are given to calculate the parameters of such systems. 相似文献
20.
In this paper, an extensive parametric study was carried out to evaluate the dynamic response of single degree of freedom (SDOF) systems with elasto-plastic and flag-shape hysteretic behaviour for three different dissipation capacities. Three sets of natural accelerograms were used, each one composed by at least 7 records which are on average spectrum-consistent in pseudo-acceleration, spectral displacement or both of them. All sets were also employed to draw the inelastic spectra for different ductility values. Such rigorous spectra were then compared with the approximated curves calculated using the N2 method and the Equivalent Linearization Procedure (ELP) based on the use of overdamped elastic spectra.The analyses demonstrate a general accuracy of the N2 method, which is mostly based on the ductility of the system, even for the hysteretic behaviour characterised by reduced energy dissipation. Larger discrepancies were found for systems with lower damping ratios and reduced fundamental periods. The ELP, which mainly depends upon the dissipated energy, led instead to overall slightly larger discrepancies than the N2 method, particularly for not dissipative and ductile systems, whereas the approximation is generally acceptable for elasto-plastic systems. 相似文献