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1.
The dynamic analysis of sliding structures is complicated due to the presence of friction. Synchronization of the kinematics of all the isolation bearings is often granted to simplify the task. This, however, may lead to inaccurate prediction of the structural responses under certain circumstances. Stepped structures or continuous bridges with seismic isolation are notable examples where unsynchronized bearing motions are expected. In this paper, a logically simple and numerically efficient procedure is proposed to solve the dynamic problem of sliding systems with unsynchronized support motions. The motion equations for the sliding and non‐sliding modes of the isolated structure are unified into a single equation that is represented as a difference equation in a discrete‐time state‐space form and the base shear forces between the sliding interfaces can be determined through simple matrix algebraic analysis. The responses of the sliding structure can be obtained recursively from the discrete‐time version of the motion equation with constant integration time step even during the transitions between the non‐sliding and sliding phases. Therefore, both accuracy and efficiency in the dynamic analysis of the highly non‐linear system can be enhanced to a large extent. Rigorous assessment of seismic structures with unsynchronized support motions has been carried out for both a stepped structure and a continuous bridge. Effectiveness of friction pendulum bearings for earthquake protection of such structures has been verified. Moreover, evident unsynchronized sliding motions of the friction bearings have been observed, confirming the necessity to deal with each of the bearings independently in the analytical model. Copyright © 2000 John Wiley & Sons, Ltd.  相似文献   

2.
The response of a rigid block supported on a horizontally moving foundation through a dry‐friction contact is investigated to near‐fault ground motions. Such motions can be thought of as consisting of a coherent component (‘pulse’) and an incoherent component, which can be described as a band‐limited ‘random noise’. The equation of motion of this strongly nonlinear system is reduced to a normalized form that reveals important parameters of the problem such as the critical acceleration ratio. The response of the sliding block to a set of uniformly processed near‐fault motions, covering a sufficiently wide range of magnitudes, is evaluated numerically for selected discrete values of the acceleration ratio. For each value of the critical acceleration ratio, the numerically computed residual slips are fitted with a Weibull (Gumbel type III) extreme value probability distribution. This allows the establishment of regression equations that describe accurately design sliding curves corresponding to various levels of non‐exceedance probability. The analysis reveals that the coherent component of motion contributes significantly to the response of the sliding block. Furthermore, the relevant acceleration in specifying the critical acceleration ratio is the (normalized) amplitude, αH_pulse, of the pulse and not the (normalized) amplitude of the incoherent component αH. Finally, the incoherent component is described quantitatively in terms of the root‐mean‐square acceleration aRMS, and an attempt is made to understand its influence on the response of the sliding block. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

3.
The problem of response of a single degree of freedom structure supported on a sliding foundation and subjected to harmonic support motions is considered. The non-linear governing equations of motion are derived. It turns out that these equations are linear in each sliding and non-sliding phase and can be solved in closed forms in each phase. The equations for evaluation of the beginning and ending times of different phases are also formulated and solved numerically. The response for different coefficients of friction and various levels of excitation is evaluated and presented graphically. It is concluded that sliding supports can be quite effective in isolating structures from support excitations.  相似文献   

4.
The pseudodynamic (PSD) test method imposes command displacements to a test structure for a given time step. The measured restoring forces and displaced position achieved in the test structure are then used to integrate the equations of motion to determine the command displacements for the next time step. Multi‐directional displacements of the test structure can introduce error in the measured restoring forces and displaced position. The subsequently determined command displacements will not be correct unless the effects of the multi‐directional displacements are considered. This paper presents two approaches for correcting kinematic errors in planar multi‐directional PSD testing, where the test structure is loaded through a rigid loading block. The first approach, referred to as the incremental kinematic transformation method, employs linear displacement transformations within each time step. The second method, referred to as the total kinematic transformation method, is based on accurate nonlinear displacement transformations. Using three displacement sensors and the trigonometric law of cosines, this second method enables the simultaneous nonlinear equations that express the motion of the loading block to be solved without using iteration. The formulation and example applications for each method are given. Results from numerical simulations and laboratory experiments show that the total transformation method maintains accuracy, while the incremental transformation method may accumulate error if the incremental rotation of the loading block is not small over the time step. A procedure for estimating the incremental error in the incremental kinematic transformation method is presented as a means to predict and possibly control the error. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

5.
A combined structure is assumed to be composed of a rigid part and a flexible part. Each component structure would have a different period of natural vibration if it were built independently. When they are combined in one structure and subjected to an earthquake, there must be generated some interaction forces so that the component structures will have a common vibration. In this paper is an analytical method described to evaluate such interaction forces The general principle is as follows. For each of the component structures, equations of motion taking account of the unknown interaction forces are derived first. Then by eliminating the interaction forces, equations of motion of the combined structure are obtained. After solving these equations and substituting the solution into the equations of motion of the component structures, the unknown interaction forces are obtained directly In the present paper, two structures corresponding to two-degree elastic systems are considered; numerical examples also are included.  相似文献   

6.
This investigation deals with non‐linear seismic responses of free‐standing rectangular rigid bodies on horizontally and vertically accelerating rigid foundations. The responses are classified into two initial responses and four subsequent responses, accordingly the equations of motion governing the liftoff, slip and liftoff–slip interaction motions and boundary conditions corresponding to commencement and termination of the motions are defined. The time histories of responses presented herein show that the body is sensitive to small changes in the friction coefficient and slenderness, and to the wave properties and intensity of ground motions. Systematic trends are observed: the bodies on the low‐grip foundation avoid overturning while they are allowed to slip regardless of details of ground motions; the long period earthquakes tend to make the body overturn and slip largely. In contrast, the timing when liftoff and slip commences and terminates and their directions do not directly correspond with intensity of ground motions. Moreover, the vertical ground motion adds irregularities on the responses, since it excites or damps the responses. It is concluded that governing equations of motion and boundary conditions in view of discontinuous non‐linear systems are necessary to analyse actual motions of the rectangular rigid bodies subjected to horizontal and vertical ground motion. Copyright © 2002 John Wiley & Sons, Ltd.  相似文献   

7.
In structural mechanics there are several occasions where a linearized formulation of the original non‐linear problem reduces considerably the computational effort for the response analysis. In a broader sense, a linearized formulation can be viewed as a first‐order expansion of the dynamic equilibrium of the system about a ‘static’ configuration; yet caution should be exercised when identifying the ‘correct’ static configuration. This paper uses as a case study the rocking response of a rigid block stepping on viscoelastic supports, whose non‐linear dynamics is the subject of the companion paper, and elaborates on the challenge of identifying the most appropriate static configuration around which a first‐order expansion will produce the most dependable results in each regime of motion. For the regime when the heel of the block separates, a revised set of linearized equations is presented, which is an improvement to the unconservative equations published previously in the literature. The associated eigenvalues demonstrate that the characteristics of the foundation do not affect the rocking motion of the block once the heel separates. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

8.
The use of base isolation for enhancing seismic resistibility has been proven as an efficient method in experimental and theoretical studies. It is usual to insert a flexible device in the horizontal direction to permit the most of relative deformation of a structure at this level. Because the rigidity of the superstructure is much higher than that of the base isolator underneath the structure, the behavior of the superstructure can be idealized as a rigid body during earthquakes. In general, hundreds of degrees of freedom and a step‐by‐step time history analysis are the basic requirements for calculating the seismic response of a base‐isolated structure under earthquakes. In order to develop a simple tool which can be easily adopted for calculating the seismic responses of the spherical sliding type isolated structures, a piecewise exact solution for predicting the seismic responses of base‐isolated structures has been derived in this study. The comparison between the experimental results conducted at the National Center for Research on Earthquake Engineering (NCREE) in Taiwan and the analytical results obtained from the piecewise exact solution show that the formulation derived in this study can predict the seismic responses of the base‐isolated structure with a very high accuracy. Copyright © 2005 John Wiley & Sons, Ltd.  相似文献   

9.
In this paper the rocking response of slender/rigid structures stepping on a viscoelastic foundation is revisited. The study examines in depth the motion of the system with a non‐linear analysis that complements the linear analysis presented in the past by other investigators. The non‐linear formulation combines the fully non‐linear equations of motion together with the impulse‐momentum equations during impacts. The study shows that the response of the rocking block depends on the size, shape and slenderness of the block, the stiffness and damping of the foundation and the energy loss during impact. The effect of the stiffness and damping of the foundation system along with the influence of the coefficient of restitution during impact is presented in rocking spectra in which the peak values of the response are compared with those of the rigid block rocking on a monolithic base. Various trends of the response are identified. For instance, less slender and smaller blocks have a tendency to separate easier, whereas the smaller the angle of slenderness, the less sensitive the response to the flexibility, damping and coefficient of restitution of the foundation. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

10.
To verify the importance of the non‐stationary frequency characteristic of seismic ground motion, a joint time–frequency analysis technique of time signals, called chirplet‐based signal approximation, is developed to extract the non‐stationary frequency information from the recorded data. The chirplet‐based signal approximation is clear in concept, similar to Fourier Transform in mathematical expressions but with different base functions. Case studies show that the chirplet‐based signal approximation can represent the joint time–frequency variation of seismic ground motion quite well. Both the random models of uniform modulating process and evolutionary process are employed to generate artificial seismic waves. The joint time–frequency modulating function in the random model of evolutionary process is determined by chirplet‐based signal approximation. Finally, non‐linear response analysis of a SODF system and a frame structure is performed based on the generated artificial seismic waves. The results show that the non‐stationary frequency characteristic of seismic ground motion can significantly change the non‐linear response characteristics of structures, particularly when a structure goes into collapse phase under seismic action. It is concluded that non‐stationary frequency characteristic of seismic ground motion should be considered for the assessment of seismic capacity of structures. Copyright © 2002 John Wiley & Sons, Ltd.  相似文献   

11.
The dynamic response of equipment mounted on an isolated raised floor inside a building while the primary fixed base structure is subjected to harmonic and earthquake ground motions is numerically investigated. Sliding concave foundation (SCF) system is utilized for isolating the raised floor. The equations of motion for a MDOF shear building containing a SCF isolated raised floor with a mounted equipment are developed and the rigid link method is utilized to handle the non‐linearity of the system. The equipment, which can be modelled as a SDOF or MDOF system, may represent a critical computer unit or telecommunication processing system. SCF can be used easily to achieve the desired long period, necessary for protecting sensitive equipment. In this investigation, the ability of SCF in reducing the acceleration level experienced by the equipment inside a building is demonstrated while the lateral displacement is still within an acceptable range. The analysis considered the case of equipment housed in the upper floors of a building where the acceleration is amplified and the motion contains strong components at long periods. For this purpose, different excitations including both harmonic and real earthquake ground motions are employed and the performance of the system is evaluated. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

12.
Recently, several new ground‐motion prediction equations (GMPEs) have been developed in the U.S.A. (the NGA project) and elsewhere. Unfortunately, the predictions obtained by using different models still differ considerably, although starting from the same database. In this paper, a non‐parametric approach, called the Conditional Average Estimator (CAE) method, has been used for ground‐motion prediction. The comparison between the CAE results and the predictions obtained by five NGA and one European model suggest that the model predictions depend substantially on the selection of the effective database and on the adopted functional form. Both decisions rely to some extent on judgement, and their influence is especially important at short distances from the source. The differences between the results obtained from the European and NGA databases seem to be of the same or even smaller magnitude than the differences observed between different NGA models, at least at short and moderate distances. Aftershocks in the database generally decrease the median values and increase dispersion. The non‐parametric CAE method has proved to be a simple but powerful tool for ground‐motion prediction, especially in a research environment. It can be used for quick predictions with different databases and different input parameters within the range of available data. It is easy to add to or remove data from the database, and to check the influence of additional input parameters. With availability of high quality data, the non‐parametric approach will become more reliable and more attractive also for practical applications. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

13.
In this paper, the effects of a mass damper on the rocking motion of a non‐symmetric rigid block‐like structure, subject to different seismic excitation, are investigated. The damper is modelled as a single degree of freedom oscillating mass, running at the top of the block and connected to it by a linear visco‐elastic device. The equations of rocking motion, the uplift and the impact conditions are derived. A nondimensionalisation of the governing equations is performed with the aim to obtain an extensive parametric analysis. The results are achieved by numerical integration of these equations. The slenderness and the base of the rigid block, and the eccentricity of the centre of mass are taken as variable parameters in the analyses. The main objective of the study is to check the performance of the damper versus the spectral characteristics of the seismic input. Three earthquake registrations with different frequency contents are used in the analyses. The results show that the presence of the mass damper leads to different levels of improvement of the response of the system, depending on the spectral characteristics of the seismic input. Curves providing the overturning slenderness of blocks of specific sizes versus the characteristics of the TMD are obtained. Copyright © 2017 John Wiley & Sons, Ltd.  相似文献   

14.
Predictors (or estimates) of seismic structural demands that are less computationally time‐consuming than non‐linear dynamic analysis can be useful for structural performance assessment and for design. In this paper, we evaluate the bias and precision of predictors that make use of, at most, (i) elastic modal vibration properties of the given structure, (ii) the results of a non‐linear static pushover analysis of the structure, and (iii) elastic and inelastic single‐degree‐of‐freedom time‐history analyses for the specified ground motion record. The main predictor of interest is an extension of first‐mode elastic spectral acceleration that additionally takes into account both the second‐mode contribution to (elastic) structural response and the effects of inelasticity. This predictor is evaluated with respect to non‐linear dynamic analysis results for ‘fishbone’ models of steel moment‐resisting frame (SMRF) buildings. The relatively small number of degrees of freedom for each fishbone model allows us to consider several short‐to‐long period buildings and numerous near‐ and far‐field earthquake ground motions of interest in both Japan and the U.S. Before doing so, though, we verify that estimates of the bias and precision of the predictor obtained using fishbone models are effectively equivalent to those based on typical ‘full‐frame’ models of the same buildings. Copyright © 2003 John Wiley & Sons, Ltd.  相似文献   

15.
Real‐time substructure testing is a novel method of testing structures under dynamic loading. The complete structure is separated into two substructures, one of which is tested physically at large scale and in real time, so that time‐dependent non‐linear behaviour of the substructure is realistically represented. The second substructure represents the surrounding structure, which is modelled numerically. In the current formulation this numerical substructure is assumed to remain linear. The two substructures interact in real‐time so that the response of the complete structure, incorporating the non‐linear behaviour of the physical substructure, is accurately represented. This paper presents several improvements to the linear numerical modelling of substructures for use in explicit time‐stepping routines for real‐time substructure testing. An extrapolation of a first‐order‐hold discretization is used which increases the accuracy of the numerical model over more direct explicit methods. Additionally, an integral form of the equation of motion is used in order to reduce the effects of noise and to take into account variations of the input over a time‐step. In order to take advantage of this integral form, interpolation of the model output is performed in order to smooth the output. The improvements are demonstrated using a series of substructure tests on a simple portal frame. While the testing approach is suitable for cases in which the physical substructure behaves non‐linearly, the results presented here are for fully linear systems. This enables comparisons to be made with analytical solutions, as well as with the results of tests based on the central difference method. Copyright © 2001 John Wiley & Sons, Ltd.  相似文献   

16.
This paper carries out a parametrical study of the pounding phenomenon associated with the seismic response of multi‐span simply supported bridges with base isolation devices. In particular, the analyses focus on the causal relationship between pounding and the properties of a spatially varying earthquake ground motion. In order to include the effect of the torsional component of pounding forces on the seismic response of the whole structure, a three‐dimensional (3D) finite element model has been defined and 3D non‐linear time‐history analyses have been performed. A parametrical study on the size of the gaps between adjacent bridge decks has highlighted that the pounding effects are amplified when the spatially varying ground motion time histories at each support are considered. Because of a spatially varying input, the pounding forces can assume values 3–4 times larger than those derived by a conventional seismic analysis with uniform input or with spatial input but considering ground motion wave passage effect only. The numerical results show that in order to achieve an acceptably safe structural performance during seismic events, a correct design of the isolation devices should take into account the relative displacements calculated by means of a non‐linear time‐history analysis with multi‐support excitation. Copyright © 2002 John Wiley & Sons, Ltd.  相似文献   

17.
This paper focuses on seismic vulnerability assessment of restrained block‐type non‐structural components under sliding response on the basis of seismic inputs specified by current seismic codes. The general representation of restrained equipment considered in this study consists of a rigid block restrained by four post‐tensioned, symmetrically arranged cables. Two sliding‐related failure modes are considered: restraint breakage and excessive absolute acceleration. Fragility analysis is proposed as an appropriate tool to evaluate these failure modes. Sample fragility curves developed through Monte‐Carlo simulations show that the restraint breakage limit state is sensitive to the parameters of the equation of motion. For instance, fragility estimates obtained without taking into account vertical base accelerations can be significantly unconservative for relatively large values of the coefficient of friction. In contrast, the excessive absolute acceleration limit state exhibits little sensitivity to the parameters of the equation of motion. Peak absolute acceleration response is almost always equal to or greater than the horizontal peak base acceleration. Representative results suggest that reasonable response estimates for blocks located at stories other than the ground in multistorey buildings can in general be obtained by simply scaling the ground acceleration to the peak acceleration at the corresponding storey. Copyright © 2002 John Wiley & Sons, Ltd.  相似文献   

18.
The seismic assessment of the local failure modes in existing masonry buildings is currently based on the identification of the so‐called local mechanisms, often associated with the out‐of‐plane wall behavior, whose stability is evaluated by static force‐based approaches and, more recently, by some displacement‐based proposals. Local mechanisms consist of kinematic chains of masonry portions, often regarded as rigid bodies, with geometric nonlinearity and concentrated nonlinearity in predefined contact regions (unilateral no‐tension behavior, possible sliding with friction). In this work, the dynamic behavior of local mechanisms is simulated through multi‐body dynamics, to obtain the nonlinear response with efficient time history analyses that directly take into account the characteristics of the ground motion. The amplification/filtering effects of the structure are considered within the input motion. The proposed approach is validated with experimental results of two full‐scale shaking‐table tests on stone masonry buildings: a sacco‐stone masonry façade tested at Laboratório Nacional de Engenharia Civil and a two‐storey double‐leaf masonry building tested at European Centre for Training and Research in Earthquake Engineering (EUCENTRE). Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

19.
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20.
Dynamic analysis of stacked rigid blocks   总被引：1，自引：0，他引：1  
The dynamic behavior of a structural model of two stacked rigid blocks subjected to ground excitation is examined. Assuming no sliding, the rocking response of the system standing free on a rigid foundation is investigated. The derivation of the equations of motion accounts for the consecutive transition from one pattern of motion to another, each being governed by a set of highly nonlinear differential equations. The system behavior is described in terms of four possible patterns of response and impact between either the two blocks or the base block and the ground. The equations governing the rocking response of the system to horizontal and vertical ground accelerations are derived for each pattern, and an impact model is developed by conservation of angular momentum considerations. Numerical results are obtained by developing an ad hoc computational scheme that is capable of determining the response of the system under an arbitrary base excitation. This feature is demonstrated by using accelerograms from the Northridge, CA, 1994, earthquake. It is hoped that the two-blocks model used herein can facilitate the development of more sophisticated multi-block structural models.  相似文献   

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