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1.
2.
The determination of displacement demands for masonry buildings subjected to seismic action is a key issue in the performance-based assessment and design of such structures. A technique for the definition of single-degree-of-freedom (SDOF) nonlinear systems that approximates the global behaviour of multi-degree-of-freedom (MDOF) 3D structural models has been developed in order to provide useful information on the dependency of displacement demand on different seismic intensity measures. The definition of SDOF system properties is based on the dynamic equivalence of the elastic properties (vibration period and viscous damping) and on the comparability with nonlinear hysteretic behaviour obtained by cyclic pushover analysis on MDOF models. The MDOF systems are based on a nonlinear macroelement model that is able to reproduce the in-plane shear and flexural cyclic behaviour of pier and spandrel elements. For the complete MDOF models an equivalent frame modelling technique was used. The equivalent SDOF system was modelled using a suitable nonlinear spring comprised of two macroelements in parallel. This allows for a simple calibration of the hysteretic response of the SDOF by suitably proportioning the contributions of flexure-dominated and shear-dominated responses. The comparison of results in terms of maximum displacements obtained for the SDOF and MDOF systems demonstrates the feasibility and reliability of the proposed approach. The comparisons between MDOF and equivalent SDOF systems, carried out for several building prototypes, were based on the results of time-history analyses performed with a large database of natural records covering a wide range of magnitude, distance and local soil conditions. The use of unscaled natural accelerograms allowed the displacement demand to be expressed as a function of different ground motion parameters allowing for the study of their relative influence on the displacement demand for masonry structures. 相似文献
3.
In the complex mode superposition method, the equations of motion for non-classically damped multiple-degree-of-freedom （MDOF） discrete systems can be transferred into a combination of some generalized SDOF complex oscillators. Based on the state space theory, a precise recurrence relationship for these complex oscillators is set up; then a delicate general solution of non-classically damped MDOF systems, completely in real value form, is presented in this paper. In the proposed method, no calculation of the matrix exponential function is needed and the algorithm is unconditionally stable. A numerical example is given to demonstrate the validity and efficiency of the proposed method. 相似文献
4.
Non-linear seismic behavior of structures with limited hysteretic energy dissipation capacity 总被引：1，自引：0，他引：1
Pierino Lestuzzi Youssef Belmouden Martin Trueb 《Bulletin of Earthquake Engineering》2007,5(4):549-569
This paper investigates the non-linear seismic behavior of structures such as slender unreinforced masonry shear walls or
precast post-tensioned reinforced concrete elements, which have little hysteretic energy dissipation capacity. Even if this
type of seismic response may be associated with significant deformation capacity, it is usually not considered as an efficient
mechanism to withstand strong earthquakes. The objective of the investigations is to propose values of strength reduction
factors for seismic analysis of such structures. The first part of the study is focused on non-linear single-degree-of-freedom
(SDOF) systems. A parametric study is performed by computing the displacement ductility demand of non-linear SDOF systems
for a set of 164 recorded ground motions selected from the European Strong Motion Database. The parameters investigated are
the natural frequency, the strength reduction factor, the post-yield stiffness ratio, the hysteretic energy dissipation capacity
and the hysteretic behavior model (four different hysteretic models: bilinear self-centring, with limited or without energy
dissipation capacity, modified Takeda and Elastoplastic). Results confirm that the natural frequency has little influence
on the displacement ductility demand if it is below a frequency limit and vice versa. The frequency limit is found to be around
2 Hz for all hysteretic models. Moreover, they show that the other parameters, especially the hysteretic behavior model, have
little influence on the displacement ductility demand. New relationships between the displacement ductility demand and the
strength reduction factor for structures having little hysteretic energy dissipation capacity are proposed. These relationships
are an improvement of the equal displacement rule for the considered hysteretic models. In the second part of the investigation,
the parametric study is extended to multi-degree-of-freedom (MDOF) systems. The investigation shows that the results obtained
for SDOF systems are also valid for MDOF systems. However, the SDOF system overestimates the displacement ductility demand
in comparison to the corresponding MDOF system by approximately 15%. 相似文献
5.
S. T. Mau 《地震工程与结构动力学》1988,16(6):931-942
For structures with non-proportional damping, complex eigenvectors or mode shapes must be used in order to decoe the equations of motion. The resulting equations can then be solved in a systematic way. The necessity of solvie complex eigenvalue problem of a large system remains an obstacle for the practical application of the method. This stres utilizes the fact that in practice only a small number of the complex modes are needed. Therefore, these complex modes be approximated by a linear combination of a small number of the undamped modes, which can be obtained by established methods with less cost. An additional eigenvalue problem is then solved in a subspace with a much sm dimension to provide the best combination coefficient for each complex mode. The method of solution for the decoue equations is then carried over, using the approximate complex modes expressed in undamped mode shapes, to resue simple formulas for the time- and frequency-domain solution. Thus, an efficient modal superposition method is develoe for non-proportionally damped systems. The accuracy of this approximate method is studied through an example. Comparing the frequency response result using the approximate method with that using the exact complex modes, found that the error is negligible. 相似文献
6.
Spectral analysis of systems with non-classical damping using classical mode superposition technique
A spectral method for random vibration analysis of a structural system with non-proportional damping is presented using classical (undamped) mode superposition technique. The method obtains the frequency response function of the system by solving the dynamic equilibrium equations in generalized co-ordinates through an iterative process. The iterative solution is written in closed form and the proof for convergence of the iterative process is given. Numerical examples show the convergence characteristics of the process and an excellent accuracy of the obtained results. The method turns out to be computationally more efficient than the conventional methods of spectral analysis using damped mode shapes and frequencies. 相似文献
7.
Quantification of ground-motion parameters and response spectra in the near-fault region 总被引：2，自引：1，他引：1
R. Rupakhety S. U. Sigurdsson A. S. Papageorgiou R. Sigbj?rnsson 《Bulletin of Earthquake Engineering》2011,9(4):893-930
This study focuses on the characteristics of near-fault ground motions in the forward-direction and structural response associated
with them. These ground motions are narrow-banded in nature and are characterized by a predominant period at which structures
excited by them are severely affected. In this work, predominant period is defined as the undamped natural period of a single-degree-of-freedom
(SDOF) oscillator at which its 5% damped linear elastic pseudo-spectral velocity (PSV) contains a clear and dominant peak. It is found that a linear relationship exists between predominant period and seismic
moment. An empirical equation describing this relationship is presented by using a large set of accelerograms. Attenuation
equations are developed to estimate peak ground velocity (PGV) as a function of earthquake magnitude and source-to-site distance. In addition, a predictive equation for spectral shapes
of PSV (i.e., PSV normalized by PGV) is presented as a continuous function of the undamped natural period of SDOF oscillators. The model is independent of PGV, and can be used in conjunction with any available PGV attenuation relation applicable to near-fault ground motion exhibiting forward-directivity effects. Furthermore, viscous
damping of the SDOF is included in the model as a continuous parameter, eliminating the use of so-called damping correction
factors. Finally, simple equations relating force reduction factors and displacement ductility of elasto-plastic SDOF systems
are presented. 相似文献
8.
本文提出了圆球减振装置对风力发电高塔振动控制的工作原理和计算方法,并对其控制效果进行了理论研究。首先利用拉格朗日方程推导得到圆球减振装置的自振频率及其对单自由度系统的被动控制力,并推广至多自由度系统。进而将风力发电高塔等效为集中质点模型,建立了风塔-减振装置体系的运动微分方程。用谐波叠加法模拟得到脉动风速时程,分析比较了风力发电高塔在无控及有控状态下的动力响应及疲劳寿命。计算结果表明,圆球减振装置是一种简单、经济和实用的减振装置,能够有效减小风塔的动力响应,延长其疲劳寿命。 相似文献
9.
The dynamic behaviour of two adjacent single‐degree‐of‐freedom (SDOF) structures connected with a viscous damper is studied under base acceleration. The base acceleration is modelled as harmonic excitation as well as stationary white‐noise random process. The governing equations of motion of the connected system are derived and solved for relative displacement and absolute acceleration responses of connected structures. The response of structures is found to be reduced by connecting with a viscous damper having appropriate damping. For undamped SDOF structures, the closed‐form expressions for optimum damping of viscous damper for minimum steady state as well as minimum mean square relative displacement and absolute acceleration of either of the connected SDOF structures are derived. The optimum damper damping is found to be functions of mass and frequency ratio of two connected structures. Further, numerical results had indicated that the damping of the connected structures does not have noticeable effects on the optimum damper damping and the corresponding optimized response. This implies that the derived closed‐form expressions for optimum damper damping of undamped structures can also be used in practical applications for damped structures. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
10.
延性需求谱在基于性能的抗震设计中的应用 总被引：23，自引：4，他引：19
基于性能的抗震设计理论涉及如何简便而合理地确定结构在指定强度地震下的弹塑性位移需求。本文给出了利用延性需求谱求解结构位移需求的一般步骤:借助模态Pushover分析将多自由度体系分解为几个非线性单自由度体系,以考虑各阶振型的影响;利用延性需求谱计算对应模态的等效单自由度体系的延性及位移需求,并以一定方式组合转化为多自由度体系位移需求。最后,通过算例分析表明:利用延性需求谱求解结构位移需求是一种具有一定精度可为工程接受的简便方法,在基于性能的抗震设计中具有较好的应用前景。 相似文献
11.
A probabilistic approach to estimate maximum inelastic displacement demands of single‐degree‐of‐freedom (SDOF) systems is presented. By making use of the probability of exceedance of maximum inelastic displacement demands for given maximum elastic spectral displacement and the mean annual frequency of exceedance of elastic spectral ordinates, a simplified procedure is proposed to estimate mean annual frequencies of exceedance of maximum inelastic displacement demands. Simplifying assumptions are thoroughly examined and discussed. Using readily available elastic seismic hazard curves the procedure can be used to compute maximum inelastic displacement seismic hazard curves and uniform hazard spectra of maximum inelastic displacement demands. The resulting maximum inelastic displacement demand spectra provide a more rational way of establishing seismic demands for new and existing structures when performance‐based approaches are used. The proposed procedure is illustrated for elastoplastic SDOF systems having known‐lateral strength located in a region of high seismicity in California. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
12.
A relatively simple and straightforward procedure is given for representing analytically defined or data-based covariance kernels of arbitrary random processes in a compact form that allows its convenient use in later analytical random vibration response studies. The method is based on the spectral decomposition of the random process by the orthogonal Karhunen-Loeve expansion and the subsequent use of least-squares approaches to develop an approximating analytical fit for the data-based eigenvectors of the underlying random process. The resulting compact analytical representation of the random process is then used to derive a closed-form solution for the non-stationary response of a damped SDOF harmonic oscillator. The utility of the method for representing the excitation and calculating the mean-square response is illustrated by the use of an ensemble of acceleration records from the 1971 San Fernando earthquake. 相似文献
13.
In this paper, the effects of pulse period associated with near‐field ground motions on the seismic demands of soil–MDOF structure systems are investigated by using mathematical pulse models. Three non‐dimensional parameters are employed as the crucial parameters, which govern the responses of soil–structure systems: (1) non‐dimensional frequency as the structure‐to‐soil stiffness ratio; (2) aspect ratio of the superstructure; and (3) structural target ductility ratio. The soil beneath the superstructure is simulated on the basis of the Cone model concept. The superstructure is modeled as a nonlinear shear building. Interstory drift ratio is selected as the main engineering demand parameter for soil–structure systems. It is demonstrated that the contribution of higher modes to the response of soil–structure system depends on the pulse‐to‐interacting system period ratio instead of pulse‐to‐fixed‐base structure period ratio. Furthermore, results of the MDOF superstructures demonstrate that increasing structural target ductility ratio results in the first‐mode domination for both fixed‐base structure and soil–structure system. Additionally, increasing non‐dimensional frequency and aspect ratio of the superstructure respectively decrease and increase the structural responses. Moreover, comparison of the equivalent soil–SDOF structure system and the soil–MDOF structure system elucidates that higher‐mode effects are more significant, when soil–structure interaction is taken into account. In general, the effects of fling step and forward directivity pulses on activating higher modes of the superstructure are more sever in soil–structure systems, and in addition, the influences of forward directivity pulses are more considerable than fling step ones. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
14.
It is shown that the method recommended by the Nuclear Regulatory Commission to be used to combine spectral response in the case of closely spaced modes is unnecessarily conservative for certain systems. Closely spaced modes arise in structures from symmetry and where there is a light appendage with a frequency close to one of the natural frequencies of the structure. In the former case, the closely spaced modes do not involve significant interaction between components of the system and the Nuclear Regulatory Commission Guide is reasonable. The latter case, that is when there are closely spaced modes where interaction of components occurs as in the examples of light appendages and torsionally unbalanced buildings, must be treated by consideration of the interacting components. The approach proposed here is that the modes that are not closely spaced be treated by modal analysis and the closely spaced modes, in the case of two closely spaced modes, be treated as a coupled two-degree-of-freedom system. If this is done, the beat phenomenon, the most important characteristic of the interaction, is evident, as is the associated result that the peak response of the coupled system is developed much later than the peak responses obtained in the individual modes. It is shown that the square root of the sum of the squares procedure underestimates, as expected, the response for undamped and very lightly damped systems, but for damped systems the square root of the sum of the squares method can be extremely conservative. It follows that the other methods specified by the Nuclear Regulatory Commission for closely spaced modes must be even more conservative. 相似文献
15.
The paper investigates the degree of accuracy achievable when some non‐linear static procedures based on a pushover analysis are used to evaluate the seismic performance. In order to assess the significance of different sources of errors, three types of structural systems are analysed: (i) single‐degree‐of‐freedom (SDOF) systems with different hysteretic behaviour; (ii) shear‐type multi‐degree‐of‐freedom (MDOF) systems with elastic–perfect plastic (EPP) shear force–interstorey drift relationships; (iii) a steel moment‐resisting frame with rigid joints and EPP moment–curvature relationship. In SDOF systems, the source of approximation comes only from the calibration of the demand spectrum, while in MDOF systems some further errors are introduced by the schematization with an equivalent SDOF system. The non‐linear static procedures are compared with rigorous time‐history analyses carried out by considering ten generated earthquake ground motions compatible with the Eurocode 8 elastic spectra. It was found that SDOF systems with longer periods satisfy the equal displacement approximation regardless of the hysteretic model, while hysteresis loops with smaller energy dissipated indicate lower response for shorter periods. This is the opposite of what predicted by the ATC‐40 capacity spectrum method, which underestimates and overestimates, respectively, the actual response of low‐ and high‐ductility systems. Conversely, the inelastic spectrum method proposed by Vidic, Fajfar and Fischinger leads to the most accurate results for all types of structural systems. The analyses carried out on EPP shear‐type frames point out a large concentration of the ductility demand on some storeys. However, such a concentration markedly reduces when some hardening is accounted for. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
16.
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
17.
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
18.
The use of uniform hazard spectra which have the same probability of exceedance at different frequencies has been proposed for the future version of the National Building Code of Canada. Commonly used combination rules to estimate the peak responses of multi‐degree‐of‐freedom (MDOF) systems are the square root of sum of squares rule and the complete quadratic combination rule. However, the probability that the peak response of a MDOF system exceeds the one estimated by using these rules with the peak modal responses from the uniform hazard spectra cannot be inferred directly. The assessment of the probability of exceedance of the peak response of MDOF systems is presented by considering that the uncertainty in seismic excitation due to all potential earthquakes can be lumped in the power spectral density function of the ground acceleration with uncertain model parameters. This probability is evaluated based on the random vibration of linear systems and the first‐order reliability method. It is found that the under‐ or over‐estimations are less than about 5 or 10% if the modal contributions are not within 10–90% of, or not within 20–80% of, the absolute sum of the effective modal peak responses, respectively. Otherwise, severe under‐ or over‐estimation could result. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
19.
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
20.
In this study, simplified numerical models are developed to analyze the soil-structure interaction (SSI) effect on frame structures equipped with viscoelastic dampers (VEDs) based on pile group foundation. First, a single degree-of-freedom (SDOF) oscillator is successfully utilized to replace the SDOF energy dissipated structure considering the SSI effect. The equivalent period and damping ratio of the system are obtained through analogical analysis using the frequency transfer function with adoption of the modal strain energy (MSE) technique. A parametric analysis is carried out to study the SSI effect on the performance of VEDs. Then the equilibrium equations of the multi degree-of-freedom (MDOF) structure with VEDs considering SSI effect are established in the frequency domain. Based on the assumption that the superstructure of the coupled system possesses the classical normal mode, the MDOF superstructure is decoupled to a set of individual SDOF systems resting on a rigid foundation with adoption of the MSE technique through formula derivation. Numerical results demonstrate that the proposed methods have the advantage of reducing computational cost, however, retaining the satisfactory accuracy. The numerical method proposed herein can provide a fast evaluation of the efficiency of VEDs considering the SSI effect. 相似文献