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1.
For a proper response spectrum analysis of a secondary system with multiple supports, the seismic inputs are required to be defined in terms of the auto and cross floor response spectra. If no feed-back or interaction effect from the secondary system to its supporting primary structure is suspected, these inputs can be developed by a direct analysis of the supporting structure alone. However, sometimes the effect of the interaction on the secondary system response can be quite significant. Herein, a method is developed to incorporate the feed-back effect, through proper modification of the interaction-free floor spectrum inputs. The interaction coefficients are used to effect such modifications in different floor spectral quantities. A procedure for the calculation of the interaction coefficients is proposed. The modified floor spectra when used as inputs to the secondary system do introduce the interaction effect in the secondary system response. A successful application of this method is demonstrated by numerical examples of secondary systems with three different secondary-to-primary system mass ratios. 相似文献
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A method is presented for generating floor response spectra for aseismic design of equipment attached to primary structures. The method accurately accounts for tuning, interaction and non-classical damping, which are inherent characteristics of composite oscillator-structure systems. Modal synthesis and perturbation techniques are used to derive the modal properties of the composite system in terms of the known properties of the structure and the oscillator. Floor spectra are generated directly in terms of these derived properties and the input ground response spectrum using modal combination rules that account for modal correlations and non-classical damping. The computed spectra, in general, are considerably lower than conventional floor response spectra due to the effect of interaction. They provide more realistic and economical criteria for design of equipment. The method is accurate to the order of perturbation and is computationally efficient, as it avoids time-history analysis and does not require numerical eigenvalue evaluation of the composite oscillator-structure system. The results of a parametric study demonstrate the accuracy of the method and illustrate several key features of floor response spectra. 相似文献
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A mode‐acceleration approach has been proposed for estimating the seismic response of a linear, classically‐damped, multiply‐supported secondary system within the framework of a power spectral density function (PSDF)‐based stochastic approach, while the primary system is linear and classically‐damped. Response transfer functions have been formulated in terms of chosen numbers of fixed‐base modes of the primary and secondary systems. The proposed approach does not involve the determination of combined system properties, and is applicable to the secondary systems with high mass ratios also. Through a few example primary–secondary systems and an example band‐limited white noise excitation, it has been shown that this approach leads to reasonably accurate results when only a few primary and secondary modes are to be considered. The proposed formulation has been used to obtain input data for a decoupled response spectrum analysis of secondary systems. This data accurately accounts for the effects of interaction between the primary and secondary systems. It is shown to lead to substantial reductions in the errors associated with the envelope spectrum method in the case of moderately heavy to heavy secondary systems and when the spatial coupling does not play a major role. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
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Response parameters used to estimate nonstructural damage differ depending on whether deformation‐sensitive or acceleration‐sensitive components are considered. In the latter case, seismic demand is usually represented through floor spectra, that is response spectra in terms of pseudo‐acceleration, which are calculated at the floor levels of the structure where the nonstructural components are attached to. Objective of this paper is to present a new spectrum‐to‐spectrum method for calculating floor acceleration spectra, which is able to explicitly account for epistemic uncertainties in the modal properties of the supporting structure. By using this method, effects on the spectra of possible variations from nominal values of the periods of vibration of the structure can be estimated. The method derives from the extension of closed‐form equations recently proposed by the authors to predict uniform hazard floor acceleration spectra. These equations are built to rigorously account for the input ground motion uncertainty, that is the record‐to‐record variability of the nonstructural response. In order to evaluate the proposed method, comparisons with exact spectra obtained from a standard probabilistic seismic demand analysis, as well as spectra calculated using the Eurocode 8 equation, are finally shown. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
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A new neural‐network‐based methodology for generating artificial earthquake spectrum compatible accelerograms from response spectra was proposed in 1997, in which, the learning capabilities of neural networks were used to develop the knowledge of the inverse mapping from the response spectra to earthquake accelerograms. Recently, this methodology has been further extended and enhanced. This paper presents a new stochastic neural network that is capable of generating multiple earthquake accelerograms from a single‐response spectrum. A new stochastic feature to the neural network has been combined with a new scheme for data compression using the replicator neural networks developed in the original method. A benefit of this extended methodology is gaining efficiency in compressing the earthquake accelerograms and extracting their characteristics. The proposed method produces a stochastic ensemble of earthquake accelerograms from any response spectra or design spectra. An example is presented that used 100 recorded accelerograms to train the neural network and several design spectra and response spectra to test this improved methodology. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
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A response spectrum procedure is developed for seismic analysis of multiply supported secondary systems. The formulation is based on the random vibration analysis of structural systems subjected to correlated inputs applied at several supports. For a proper response spectrum analysis of a multiple support system, the support inputs are required to be defined in terms of the auto and cross pseudo-acceleration and relative velocity floor response spectra. Also information about the floor displacements and velocities as well as their correlations is required. The response of the secondary system is expressed as a combination of the dynamic and pseudo-static response components. The dynamic component is associated with the inertial effects of the support accelerations, whereas the pseudo-static component is due to the displacement of the supports relative to each other. Herein, the correlation between these two parts of the response is included through a term called the cross response component. Each of these components of the response can be calculated by a response spectrum method. The application of the proposed method is demonstrated by numerical examples. 相似文献
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A method is proposed for the deterministic and stochastic non-stationary analysis of linear composite systems with cascaded secondary subsystems subjected to a seismic input. This method makes it possible to evaluate, by means of a unitary formulation, the deterministic and non-stationary stochastic response of both classically and non-classically damped subsystems and of secondary subsystems multiply supported on the primary one, as well as the ground. The proposed procedure is very efficient from a computational point of view, because of the Kronecker algebra systematically employed. Indeed, by using this algebra, it is possible to obtain in a very compact and elegant form the eigenproperties of the composite system as a function of the eigenproperties of the two subsystems taken separately. Moreover, it is possible to write the first order differential equations governing the evolution of the second order moments of the response and to solve them in a simple way. 相似文献
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Stavros Kasinos Mariateresa Lombardo Nicos Makris Alessandro Palmeri 《地震工程与结构动力学》2020,49(14):1473-1495
The paper deals with the seismic response analysis of nonlinear secondary oscillators. Bilinear, sliding and rocking single-degree-of-freedom dynamic systems are analysed as representative of a wide spectrum of secondary structures and nonstructural components. In the first stage, the equations governing their full dynamic interaction with linear multi-degree-of-freedom primary structures are formulated, and then conveniently simplified using primary-secondary two-degree-of-freedom systems and dimensionless coefficients. In the second stage, the cascade approximation is applied, whereby the feedback action of the secondary oscillator on the primary structure is neglected. Owing to the piecewise linearity of the secondary systems being considered, efficient semi-analytical and step-by-step numerical solutions are presented. The semi-analytical solutions allow the direct evaluation of the seismic response under pulse-type ground excitations and are also used to validate step-by-step numerical schemes, which in turn can be used for general-type seismic excitations. In the third stage, a set of decoupling criteria are proposed for the pulse-type base excitations, identifying the conditions under which a cascade analysis is admissible from an engineering standpoint. Finally, the influence and relative dependencies between the input parameters of the ground motion and the primary-secondary assembly are quantified on the response of the secondary systems through nonlinear floor response spectra, and general trends are identified and discussed. 相似文献
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Extended MSRS rule for seismic analysis of bridges subjected to differential support motions 总被引：1，自引：0，他引：1
This paper introduces a generalized formulation of the multiple support response spectrum (MSRS) method (Earthquake Engng Struct. Dyn. 1992; 21 :713–740) and extends it by accounting for the quasi‐static contributions of truncated modes. The generalized formulation allows consideration of response quantities that involve support degrees of freedom (DOF). This situation arises for many response quantities of interest when rotational DOF are condensed out. New cross‐correlation coefficients are introduced in the extended rule and a parametric study is performed to gain insight and identify cases of ground motion spatial variability in which these terms are significant. An efficient computer implementation of the extended MSRS method is described and used for comprehensive analysis of two real bridge models with vastly different structural characteristics. The specified input is in accordance with standards used in engineering practice. The effects of differential support motions, including the influence of spatially varying soil conditions, on the pseudo‐static and dynamic components and the total response are examined and the improvement achieved with the extended MSRS method is assessed. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
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Estimation of design forces in ductility‐based earthquake‐resistant design continues to be carried out with the application of response modification factors on elastic design spectra, and it remains interesting to explore how best to estimate strength reduction factors (SRFs) for a design situation. This paper considers the relatively less explored alternative of modelling SRF spectrum via a given response spectrum. A new model is proposed to estimate the SRF spectrum in terms of a pseudo‐spectral acceleration (PSA) spectrum and ductility demand ratio with the help of two coefficients. The proposed model is illustrated for an elasto‐plastic oscillator, in case of 10 recorded accelerograms and three ductility ratios. The proposed model is convenient and is able to predict SRF spectrum reasonably well, particularly at periods up to 1.0 s. Coefficients of the proposed model may also be determined in case of a given design spectrum when there is uncertainty in SRF spectrum due to uncertainty in temporal characteristics of the ground motion. This is illustrated with the help of 474 accelerograms recorded in western U.S.A. and different scaled PSA spectra. It is shown that probabilistic estimates may be obtained in this situation for SRF spectrum by assuming the error residuals to be log normally distributed with period‐dependent parameters. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
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Nakamura's method, which uses a horizontal-to-vertical Fourier spectrum ratio of microtremor, has become popular to determine the predominant period and amplification of a site. In this study, this method is extended for earthquake ground motion recordings using new strong motion data recorded by JMA-87-type accelerometers. From the analysis of these accelerograms, horizontal-to-vertical Fourier spectrum ratios of a site for different earthquakes are also found to be stable irrespective of magnitude, distance and depth. To establish this fact, attenuation relations of velocity response spectra for horizontal and vertical components are derived for three damping ratios (0, 2 and 5 per cent) using the JMA data. Then the horizontal-to-vertical ratios of the velocity response spectra are obtained. The results show that the horizontal and vertical velocity response spectra are dependent on magnitude, distance and depth, but that their ratios are almost independent of magnitude, distance and depth. However, since the current data set consists of mostly intermediate to far field data, this observation should be limited to records of these distance ranges. Introducing station coefficients, representing site amplification, to this relation yields the value comparable to the horizontal-to-vertical Fourier spectrum ratio at a specific site. The stability of the spectrum ratio is explained by the transfer function between the ground surface and stiff-soil outcrop due to S-wave propagation. These results suggest that site amplification characteristics can be evaluated by one-point two-component surface recordings of earthquake ground motion, in a similar manner as proposed by Nakamura for microtremor. © 1997 by John Wiley & Sons, Ltd. 相似文献
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An important aspect of earthquake loads exerted on extended structures, or structures founded on several foundations, is the spatial variability of the seismic motion. Hence, a rigorous earthquake resistant design of lifeline structures should account for the spatial character of the seismic input, at least in an approximate way. A procedure is proposed which enables addressing the problem of multiply supported structures, subjected to imperfectly correlated seismic excitations, by means of an extension to the response spectrum method. A modified response spectrum model is developed for the design of extended facilities subjected to single and multicomponent ground motion. The modification procedure is based on adjusting each spectral value of the given design response spectrum by means of a correction factor, which depends on the structural properties and on the characteristics of the wave propagation phenomenon. Finally, the theoretical model is validated through digital simulation of seismic ground motion, whereby model predictions are found to be in good agreement with exact results. 相似文献
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A method is presented to obtain the exact complex-valued eigenproperties of a classically damped structure and equipment system. The non-classically damped character of the combined system as well as the effect of dynamic interaction between primary structure and equipment are properly included in the calculation of these eigenproperties. It is necessary only to know the classical modal properties of the structure and, of course, the equipment characteristics. The eigenvalues are obtained as the solution of a non-linear equation which can be easily solved by the Newton–Raphson algorithm. Once the eigenvalues are known, the corresponding eigenvectors are obtained from simple closed-form expressions. The method can be used equally effectively with light as well as heavy equipment. Numerical results demonstrating the effectiveness of the method are presented. A procedure which utilizes the complex-valued eigenproperties is developed for calculating the floor response spectra directly from the ground spectra. Numerical results of floor response spectra obtained from this procedure are presented. The floor spectra calculated by this approach include the structure–equipment interaction effect. 相似文献
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A good response spectrum method, used for calculating the seismic design response for design inputs defined in terms of response spectra, should be able to include the effect of the higher modes, even though they may be truncated and not explicitly considered in the analysis. It should also be able to include the intercorrelation of the retained modes as well as their correlation with truncated modes. Herein one such method based on a suitable combination of the mode displacement and mode acceleration formulations of structural dynamics is proposed. Several numerical examples are presented to demonstrate the efficiency of the proposed approach vis-a-vis some other commonly used response spectrum approaches. 相似文献
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Seismic risk analysis and mitigation of spatially extended structures require the synthesis of spatially varying ground motions in the response history analysis of these structures. These synthetic motions are usually desired to be spatially correlated, site reflected, nonstationary, and compatible with target design response spectra. In this paper, a method is presented for simulating spatially varying ground motions considering the nonstationarity, local site effects, and compatibility of response spectra. The scheme for generating spatially varying and response spectra compatible ground motions is first established for spatial locations on the ground surface with varying site conditions. The design response spectrum is introduced as the “power” spectrum at the base rock. The site amplification approach is then derived based on the deterministic wave propagation theory, by assuming that the base rock motions consist of out-of-plane SH wave or in-plane combined P and SV waves propagating into the site with assumed incident angles, from which tri-directional spatial ground motions can be generated. The phase difference spectrum is employed to model ground motions exhibiting nonstationarity in both frequency and time domains with different site conditions. The proposed scheme is demonstrated with numerical examples. 相似文献
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With the recent emergence of wavelet‐based procedures for stochastic analyses of linear and non‐linear structural systems subjected to earthquake ground motions, it has become necessary that seismic ground motion processes are characterized through statistical functionals of wavelet coefficients. While direct characterization in terms of earthquake and site parameters may have to wait for a few more years due to the complexity of the problem, this study attempts such characterization through commonly available Fourier and response spectra for design earthquake motions. Two approaches have been proposed for obtaining the spectrum‐compatible wavelet functionals, one for input Fourier spectrum and another for input response spectrum, such that the total number of input data points are 30–35% of those required for a time‐history analysis. The proposed methods provide for simulating ‘desired non‐stationary characteristics’ consistent with those in a recorded accelerogram. Numerical studies have been performed to illustrate the proposed approaches. Further, the wavelet functionals compatible with a USNRC spectrum in the case of 35 recorded motions of similar strong motion durations have been used to obtain the strength reduction factor spectra for elasto‐plastic oscillators and to show that about ±20% variation may be assumed from mean to 5 and 95% confidence levels due to uncertainty in the non‐stationary characteristics of the ground motion process. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
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To develop uniform and seismic environment-dependent design spectrum, common acceleration response spectral characteristics need to be identified. In this paper, a bi-normalized response spectrum (BNRS) is proposed, which is defined as a spectrum of peak response acceleration normalized with respect to peak acceleration of the excitation plotted vs. the natural period of the system normalized with respect to the spectrum predominant period, Tp. Based on a statistical analysis of records from the 1999 Chi-Chi earthquake, the conventionally normalized response spectrum(NRS) and the BNRS are examined to account for the effects of soil conditions, epicentral distance, hanging wall and damping. It is found that compared to the NRS, the BNRS is much less dependent on these factors. Finally, some simple relationships between the BNRS for a specified damping ratio and that for a damping ratio of 5%, and between the spectra predominant period and epicentral distance for different soil types are provided. 相似文献