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1.
A procedure is presented to determine new modal combination rules (both CQC and SRSS) for non‐classically damped structures. The procedure presented in this paper does not need the solution of any complex eigenvalue problem, in contrast to other methods found in the literature. Thus, the modal combination rules presented here are easily applicable, even by those engineers who are unaccustomed to using complex algebra. Moreover, these formulations show the further advantage of requiring the response spectra only for the target damping ratio value. So the use of approximated formulae, necessary for passing from the response spectrum with the target damping ratio value to other ones, is avoided. Copyright © 2004 John Wiley & Sons, Ltd.  相似文献   

2.
A new response spectrum method, which is named complex multiple-support response spectrum (CMSRS) method in this article, is developed for seismic analysis of non-classically damped linear system subjected to spatially varying multiple-supported ground motion. The CMSRS method is based on fundamental principles of random vibration theory and properly accounts for the effect of correlation between the support motions as well as between the modal displacement and velocity responses of structure, and provides an reasonable and acceptable estimate of the peak response in term of peak seismic ground motions and response spectra at the support points and the coherency function. Meanwhile, three new cross-correlation coefficients or cross covariance especially for the non-classically damped linear structures with multiple-supports excitations are derived under the same assumptions of the MSRS method of classically damped system. The CMSRS method is examined and compared to the results of time history analyses in two numerical examples of non-classically damped structures in consideration of the coherences of spatially variable ground motion. The results show that for non-classically damped structure, the cross terms representing the cross covariance between the pseudo-static and dynamic component are also quite small just as same as classically damped system. In addition, it is found that the usual way of neglecting all the off-diagonal elements in transformed damping matrix in modal coordinates in order to make the concerned non-classically damped structure to become remaining proportional damping property will bring some errors in the case of subjected to spatially excited inhomogeneous ground motion.  相似文献   

3.
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   

4.
Civil engineering structures are often subjected to multidirectional actions such as earthquake ground motion, which lead to complex structural responses. The contributions from the latter multidirectional actions to the response are highly coupled, leading to a MIMO system identification problem. Compared with single‐input, multiple‐output (SIMO) system identification, MIMO problems are more computationally complex and error prone. In this paper, a new system identification strategy is proposed for civil engineering structures with multiple inputs that induce strong coupling in the response. The proposed solution comprises converting the MIMO problem into separate SIMO problems, decoupling the outputs by extracting the contribution from the respective input signals to the outputs. To this end, a QR factorization‐based decoupling method is employed, and its performance is examined. Three factors, which affect the accuracy of the decoupling result, including memory length, input correlation, and system damping, are investigated. Additionally, a system identification method that combines the autoregressive model with exogenous input (ARX) and the Eigensystem Realization Algorithm (ERA) is proposed. The associated extended modal amplitude coherence and modal phase collinearity are used to delineate the structural and noise modes in the fitted ARX model. The efficacy of the ARX‐ERA method is then demonstrated through identification of the modal properties of a highway overcrossing bridge. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

5.
Dynamic characteristics of structures — viz. natural frequencies, damping ratios, and mode shapes — are central to earthquake‐resistant design. These values identified from field measurements are useful for model validation and health‐monitoring. Most system identification methods require input excitations motions to be measured and the structural response; however, the true input motions are seldom recordable. For example, when soil–structure interaction effects are non‐negligible, neither the free‐field motions nor the recorded responses of the foundations may be assumed as ‘input’. Even in the absence of soil–structure interaction, in many instances, the foundation responses are not recorded (or are recorded with a low signal‐to‐noise ratio). Unfortunately, existing output‐only methods are limited to free vibration data, or weak stationary ambient excitations. However, it is well‐known that the dynamic characteristics of most civil structures are amplitude‐dependent; thus, parameters identified from low‐amplitude responses do not match well with those from strong excitations, which arguably are more pertinent to seismic design. In this study, we present a new identification method through which a structure's dynamic characteristics can be extracted using only seismic response (output) signals. In this method, first, the response signals’ spatial time‐frequency distributions are used for blindly identifying the classical mode shapes and the modal coordinate signals. Second, cross‐relations among the modal coordinates are employed to determine the system's natural frequencies and damping ratios on the premise of linear behavior for the system. We use simulated (but realistic) data to verify the method, and also apply it to a real‐life data set to demonstrate its utility. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

6.
A new complex modal analysis‐based method is developed in the frequency domain for efficient computation of the earthquake input energy to a highly damped linear elastic passive control structure. The input energy to the structure during an earthquake is an important measure of seismic demand. Because of generality and applicability to non‐linear structures, the earthquake input energy has usually been computed in the time domain. It is shown here that the formulation of the earthquake input energy in the frequency domain is essential for deriving a bound on the earthquake input energy for a class of ground motions and for understanding the robustness of passively controlled structures to disturbances with various frequency contents. From the viewpoint of computational efficiency, a modal analysis‐based method is developed. The importance of overdamped modes in the energy computation of specific non‐proportionally damped models is demonstrated by comparing the energy transfer functions and the displacement transfer functions. Through numerical examinations for four recorded ground motions, it is shown that the modal analysis‐based method in the frequency domain is very efficient in the computation of the earthquake input energy. Copyright © 2004 John Wiley & Sons, Ltd.  相似文献   

7.
This paper presents the application of system identification (SI) to long‐span cable‐supported bridges using seismic records. The SI method is based on the System Realization using Information Matrix (SRIM) that utilizes correlations between base motions and bridge accelerations to identify coefficient matrices of a state‐space model. Numerical simulations using a benchmark cable‐stayed bridge demonstrate the advantages of this method in dealing with multiple‐input multiple‐output (MIMO) data from relatively short seismic records. Important issues related to the effects of sensor arrangement, measurement noise, input inclusion, and the types of input with respect to identification results are also investigated. The method is applied to identify modal parameters of the Yokohama Bay Bridge, Rainbow Bridge, and Tsurumi Fairway Bridge using the records from the 2004 Chuetsu‐Niigata earthquake. Comparison of modal parameters with the results of ambient vibration tests, forced vibration tests, and analytical models are presented together with discussions regarding the effects of earthquake excitation amplitude on global and local structural modes. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

8.
In many parts of the world, the repetition of medium–strong intensity earthquake ground motions at brief intervals of time has been observed. The new design philosophies for buildings in seismic areas are based on multi‐level design approaches, which take into account more than a single damageability limit state. According to these approaches, a sequence of seismic actions may produce important consequences on the structural safety. In this paper, the effects of repeated earthquake ground motions on the response of single‐degree‐of‐freedom systems (SDOF) with non‐linear behaviour are analysed. A comparison is performed with the effect of a single seismic event on the originally non‐damaged system for different hysteretic models in terms of pseudo‐acceleration response spectra, behaviour factor q and damage parameters. The elastic–perfect plastic system is the most vulnerable one under repeated earthquake ground motions and is characterized by a strong reduction of the q‐factor. A moment resisting steel frame is analysed as well, showing a reduction of the q‐factor under repeated earthquake ground motions even larger than that of an equivalent SDOF system. Copyright © 2002 John Wiley & Sons, Ltd.  相似文献   

9.
The Vincent Thomas Bridge in the Los Angeles metropolitan area, is a critical artery for commercial traffic flow in and out of the Los Angeles Harbor, and is at risk in the seismically active Southern California region, particularly because it straddles the Palos Verdes fault zone. A combination of linear and non‐linear system identification techniques is employed to obtain a complete reduced‐order, multi‐input–multi‐output (MIMO) dynamic model of the Vincent Thomas Bridge based on the dynamic response of the structure to the 1987 Whittier and 1994 Northridge earthquakes. Starting with the available acceleration measurements (which consists of 15 accelerometers on the bridge structure and 10 accelerometers at various locations on its base), an efficient least‐squares‐based time‐domain identification procedure is applied to the data set to develop a reduced‐order, equivalent linear, multi‐degree‐of‐freedom model. Although not the main focus of this study, the linear system identification method is also combined with a non‐parametric identification technique, to generate a reduced‐order non‐linear mathematical model suitable for use in subsequent studies to predict, with good fidelity, the total response of the bridge under arbitrary dynamic environments. Results of this study yield measurements of the equivalent linear modal properties (frequencies, mode shapes and non‐proportional damping) as well as quantitative measures of the extent and nature of non‐linear interaction forces arising from strong ground shaking. It is shown that, for the particular subset of observations used in the identification procedure, the apparent non‐linearities in the system restoring forces are quite significant, and they contribute substantially to the improved fidelity of the model. Also shown is the potential of the identification technique under discussion to detect slight changes in the structure's influence coefficients, which may be indicators of damage and degradation in the structure being monitored. Difficulties associated with accurately estimating damping for lightly damped long‐span structures from their earthquake response are discussed. The technical issues raised in this paper indicate the need for added spatial resolution in sensor instrumentation to obtain identified mathematical models of structural systems with the broadest range of validity. Copyright © 2003 John Wiley & Sons, Ltd.  相似文献   

10.
There is no consensus at the present time regarding an appropriate approach to model viscous damping in nonlinear time‐history analysis of base‐isolated buildings because of uncertainties associated with quantification of energy dissipation. Therefore, in this study, the effects of modeling viscous damping on the response of base‐isolated reinforced concrete buildings subjected to earthquake ground motions are investigated. The test results of a reduced‐scale three‐story building previously tested on a shaking table are compared with three‐dimensional finite element simulation results. The study is primarily focused on nonlinear direct‐integration time‐history analysis, where many different approaches of modeling viscous damping, developed within the framework of Rayleigh damping are considered. Nonlinear direct‐integration time‐history analysis results reveal that the damping ratio as well as the approach used to model damping has significant effects on the response, and quite importantly, a damping ratio of 1% is more appropriate in simulating the response than a damping ratio of 5%. It is shown that stiffness‐proportional damping, where the coefficient multiplying the stiffness matrix is calculated from the frequency of the base‐isolated building with the post‐elastic stiffness of the isolation system, provides reasonable estimates of the peak response indicators, in addition to being able to capture the frequency content of the response very well. Furthermore, nonlinear modal time‐history analyses using constant as well as frequency‐dependent modal damping are also performed for comparison purposes. It was found that for nonlinear modal time‐history analysis, frequency‐dependent damping, where zero damping is assigned to the frequencies below the fundamental frequency of the superstructure for a fixed‐base condition and 5% damping is assigned to all other frequencies, is more appropriate, than 5% constant damping. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

11.
This paper verifies the feasibility of the proposed system identification methods by utilizing shaking table tests of a full‐scale four‐story steel building at E‐Defense in Japan. The natural frequencies, damping ratios and modal shapes are evaluated by single‐input‐four‐output ARX models. These modal parameters are prepared to identify the mass, damping and stiffness matrices when the objective structure is modelled as a four degrees of freedom (4DOF) linear shear building in each horizontal direction. The nonlinearity in stiffness is expressed as a Bouc–Wen hysteretic system when it is modelled as a 4DOF nonlinear shear building. The identified hysteretic curves of all stories are compared to the corresponding experimental results. The simple damage detection is implemented using single‐input‐single‐output ARX models, which require only two measurements in each horizontal direction. The modal parameters are equivalent‐linearly evaluated by the recursive Least Squares Method with a forgetting factor. When the structure is damaged, its natural frequencies decrease, and the corresponding damping ratios increase. The fluctuation of the identified modal properties is the indirect information for damage detection of the structure. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

12.
A large number of high quality strong-motion records of building response are obtained from recent earthquake events in California. The accelerometers are typically deployed at several levels from the basement up. In order to learn as much as possible about the building behaviour from these records, a multiple input-multiple output (MIMO) system identification procedure is implemented to analyse these records in a systematic way. The procedure is an extension of the least-square-output-error method applied to a classically damped linear second order system. The time varying behaviour is modelled through a time window approach. The procedure includes (i) preliminary record analysis, (ii) input and model selection, (iii) parameter identification and (iv) drift analysis. The records of a 15-storey reinforced concrete building obtained during the Whittier earthquake are analysed. It is found that the fundamental period is much longer than that of a regular building. The torsional response is significant and is caused by both the translational and the torsional motions at the ground level. The maximum drift occurs at the ground storey. The second and the third translational modes in each direction are as important as the first modes in making up the ground storey drift. When the maximum drift occurs in one direction the corresponding drift in the orthogonal direction can be as high as 30 per cent of the maximum drift.  相似文献   

13.
An approximation approach of seismic analysis of two‐way asymmetric building systems under bi‐directional seismic ground motions is proposed. The procedures of uncoupled modal response history analysis (UMRHA) are extended to two‐way asymmetric buildings simultaneously excited by two horizontal components of ground motion. Constructing the relationships of two‐way base shears versus two‐way roof translations and base torque versus roof rotation in ADRS format for a two‐way asymmetric building, each modal pushover curve bifurcates into three curves in an inelastic state. A three‐degree‐of‐freedom (3DOF) modal stick is developed to simulate the modal pushover curve with the stated bifurcating characteristic. It requires the calculation of the synthetic earthquake and angle β. It is confirmed that the 3DOF modal stick is consistent with single‐degree‐of‐freedom modal stick in an elastic state. A two‐way asymmetric three‐story building was analyzed by UMRHA procedure incorporating the proposed 3DOF modal sticks. The analytical results are compared with those obtained from nonlinear response history analysis. It is shown that the 3DOF modal sticks are more rational and effective in dealing with the assessment of two‐way asymmetric building systems under two‐directional seismic ground motions. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

14.
This paper reviews the theoretical principles of subspace system identification as applied to the problem of estimating black‐box state‐space models of support‐excited structures (e.g., structures exposed to earthquakes). The work distinguishes itself from past studies by providing readers with a powerful geometric interpretation of subspace operations that relates directly to theoretical structural dynamics. To validate the performance of subspace system identification, a series of experiments are conducted on a multistory steel frame structure exposed to moderate seismic ground motions; structural response data is used off‐line to estimate black‐box state‐space models. Ground motions and structural response measurements are used by the subspace system identification method to derive a complete input–output state‐space model of the steel frame system. The modal parameters of the structure are extracted from the estimated input–output state‐space model. With the use of only structural response data, output‐only state‐space models of the system are also estimated by subspace system identification. The paper concludes with a comparison study of the modal parameters extracted from the input–output and output‐only state‐space models in order to quantify the uncertainties present in modal parameters extracted from output‐only models. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

15.
The probability that an earthquake occurs when a train is running over a bridge in earthquake‐prone regions is much higher than before, for high‐speed railway lines are rapidly developed to connect major cities worldwide. This paper presents a finite element method‐based framework for dynamic analysis of coupled bridge–train systems under non‐uniform seismic ground motion, in which rail–wheel interactions and possible separations between wheels and rails are taken into consideration. The governing equations of motion of the coupled bridge–train system are established in an absolute coordinate system. Without considering the decomposition of seismic responses into pseudo‐static and inertia‐dynamic components, the equations of motion of the coupled system are formed in terms of displacement seismic ground motions. The mode superposition method is applied to the bridge structure to make the problem manageable while the Newmark‐β method with an iterative computation scheme is used to find the best solution for the problem concerned. Eight high‐speed trains running over a multi‐span steel truss‐arch bridge subject to earthquakes are taken as a case study. The results from the case study demonstrate that the spatial variation of seismic ground motion affects dynamic responses of the bridge–train system. The ignorance of pseudo‐static component when using acceleration seismic ground motions as input may underestimate seismic responses of the bridge–train system. The probability of separation between wheels and rails becomes higher with increasing train speed. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

16.
Output‐only system identification is developed here towards assessing current modal dynamic properties of buildings under seismic excitation. Earthquake‐induced structural response signals are adopted as input channels for two different Operational Modal Analysis (OMA) techniques, namely, a refined Frequency Domain Decomposition (rFDD) algorithm and an improved Data‐Driven Stochastic Subspace Identification (SSI‐DATA) procedure. Despite that short‐duration, non‐stationary, earthquake‐induced structural response signals shall not fulfil traditional OMA assumptions, these implementations are specifically formulated to operate with seismic responses and simultaneous heavy damping (in terms of identification challenge), for a consistent estimation of natural frequencies, mode shapes, and modal damping ratios. A linear ten‐storey frame structure under a set of ten selected earthquake base‐excitation instances is numerically simulated, by comparing the results from the two identification methods. According to this study, best up‐to‐date, reinterpreted OMA techniques may effectively be used to characterize the current dynamic behaviour of buildings, thus allowing for potential Structural Health Monitoring approaches in the Earthquake Engineering range.  相似文献   

17.
A step‐by‐step approximate procedure taking into consideration high‐frequency modes, usually neglected in the modal analysis of both classically and non‐classically damped structures, is presented. This procedure can be considered as an extension of traditional modal correction methods, like the mode‐acceleration method and the dynamic correction method, which are very effective for structural systems subjected to forcing functions described by analytical laws. The proposed procedure, herein called improved dynamic correction method, requires two steps. In the first step, the number of differential equations of motion are reduced and consequently solved by using the first few undamped mode‐shapes. In the second step, the errors due to modal truncation are reduced by correcting the dynamic response and solving a new set of differential equations, formally similar to the original differential equations of motion. The difference between the two groups of differential equations lies in the forcing vector, which is evaluated in such a way as to correct the effects of modal truncation on applied loads. Copyright © 2001 John Wiley & Sons, Ltd.  相似文献   

18.
Output‐only modal identification is needed when only structural responses are available. As a powerful unsupervised learning algorithm, blind source separation (BSS) technique is able to recover the hidden sources and the unknown mixing process using only the observed mixtures. This paper proposes a new time‐domain output‐only modal identification method based on a novel BSS learning algorithm, complexity pursuit (CP). The proposed concept—independent ‘physical systems’ living on the modal coordinates—connects the targeted constituent sources (and their mixing process) targeted by the CP learning rule and the modal responses (and the mode matrix), which can then be directly extracted by the CP algorithm from the measured free or ambient system responses. Numerical simulation results show that the CP method realizes accurate and robust modal identification even in the closely spaced mode and the highly damped mode cases subject to non‐stationary ambient excitation and provides excellent approximation to the non‐diagonalizable highly damped (complex) modes. Experimental and real‐world seismic‐excited structure examples are also presented to demonstrate its capability of blindly extracting modal information from system responses. The proposed CP is shown to yield clear physical interpretation in modal identification; it is computational efficient, user‐friendly, and automatic, requiring little expertise interactions for implementations. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

19.
This paper focuses on the effects of long‐period pulse of near‐fault ground motions on the structural damage potential. Two sets of near‐fault ground motion records from Chi‐Chi, Taiwan earthquake and Northridge earthquake with and without distinct pulse are selected as the input, and the correlation analysis between 30 non‐structure‐specific intensity measure parameters and maximum inelastic displacements and energy responses (input energy and hysteretic energy) of bilinear single degree of freedom systems are conducted. Based on the frequency characteristic of near‐fault ground motions with remarkable long‐period components, two intensity indices are proposed, namely, the improved effective peak acceleration (IEPA) and improved effective peak velocity (IEPV). In addition a new characteristic period of these ground motions is defined based on IEPA and IEPV. Numerical results illustrate that the intensity measure parameters related to ground acceleration present the best correlation with the seismic responses for rigid systems; the velocity‐related and displacement‐related parameters are better for medium‐frequency systems and flexible systems, respectively. The correlation curves of near‐fault ground motions with velocity pulse differ from those of ground motions without pulse. Moreover, the improved parameters IEPA and IEPV of near‐fault impulsive ground motions enhance the performance of intensity measure of corresponding conventional parameters, i.e. EPA and EPV. The new characteristic period based on IEPA and IEPV can better reflect the frequency content of near‐fault ground motions. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

20.
A new method of stiffness‐damping simultaneous identification of building structures is proposed using limited earthquake records. It is shown that when horizontal accelerations are recorded at the floors just above and below a specific storey in a shear building model, the storey stiffness and the damping ratio can be identified uniquely. The viscous damping coefficient and the linear hysteretic damping ratio can also be identified simultaneously in a numerical model structure. The accuracy of the present identification method is investigated through the actual limited earthquake records in a base‐isolated building. It is further shown that an advanced identification technique for mechanical properties of a Maxwell‐type model can be developed by combining the present method with a perturbation technique. Copyright © 2000 John Wiley & Sons, Ltd.  相似文献   

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