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1.
A new formulation is proposed to model pounding between two adjacent structures, with natural periods T1 and T2 and damping ratios ζ1 and ζ2 under harmonic earthquake excitation, as non‐linear Hertzian impact between two single‐degree‐of‐freedom oscillators. For the case of rigid impacts, a special case of our analytical solution has been given by Davis (‘Pounding of buildings modelled by an impact oscillator’ Earthquake Engineering and Structural Dynamics, 1992; 21 :253–274) for an oscillator pounding on a stationary barrier. Our analytical predictions for rigid impacts agree qualitatively with our numerical simulations for non‐rigid impacts. When the difference in natural periods between the two oscillators increases, the impact velocity also increases drastically. The impact velocity spectrum is, however, relatively insensitive to the standoff distance. The maximum relative impact velocity of the coupled system can occur at an excitation period Tn* which is either between those of the two oscillators or less than both of them, depending on the ratios T1/T2 and ζ1/ζ2. Although the pounding force between two oscillators has been primarily modelled by the Hertz contact law, parametric studies show that the maximum relative impact velocity is not very sensitive to changes in the contact parameters. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
2.
Kazuhiko Yamada 《地震工程与结构动力学》2000,29(8):1199-1217
A control strategy is proposed for variable damping elements (VDEs) used together with auxiliary stiffness elements (ASEs) that compose a time‐varying non‐linear Maxwell (NMW) element, considering near‐future excitation influence. The strategy first composes a state equation for the structural dynamics and the mechanical balance in the NMW elements. Next, it establishes a cost function for estimating future responses by the weighted quadratic norms of the state vector, the controlled force and the VDEs' damping coefficients. Then, the Euler equations for the optimum values are introduced, and also approximated by the first‐order terms under the autoregressive (AR) model of excitation information. Thus, at each moment tk, the strategy conducts the following steps: (1) identify the obtained seismic excitation information to an AR model, and convert it to a state equation; and (2) determine VDEs' damping coefficients under the initial conditions at tk and the final state at tk+L, using the first‐order approximation of the Euler equations. The control effects are examined by numerical experiments. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
3.
Seismic imaging is an important step for imaging the subsurface structures of the Earth. One of the attractive domains for seismic imaging is explicit frequency–space (f – x) prestack depth migration. So far, this domain focused on migrating seismic data in acoustic media, but very little work assumed visco‐acoustic media. In reality, seismic exploration data amplitudes suffer from attenuation. To tackle the problem of attenuation, new operators are required, which compensates for it. We propose the weighted L 1 ‐error minimisation technique to design visco‐acoustic f – x wavefield extrapolators. The L 1 ‐error wavenumber responses provide superior extrapolator designs as compared with the previously designed equiripple L 4 ‐norm and L∞‐norm extrapolation wavenumber responses. To verify the new compensating designs, prestack depth migration is performed on the challenging Marmousi model dataset. A reference migrated section is obtained using non‐compensating f – x extrapolators on an acoustic dataset. Then, both compensating and non‐compensating extrapolators are applied to a visco‐acoustic dataset, and both migrated sections are then compared. The final images show that the proposed weighted L 1 ‐error method enhances the resolution and results in practically stable images. 相似文献
4.
A new semiactive independently variable damper, SAIVD, is developed and shown to be effective in achieving response reductions in smart base isolated buildings in near fault earthquakes. The semiactive device consists of four linear visco‐elastic elements, commonly known as Kelvin–Voigt elements, arranged in a rhombus configuration. The magnitude of force in the semiactive device can be adjusted smoothly in real‐time by varying the angle of the visco‐elastic elements of the device or the aspect ratio of the rhombus configuration. Such a device is essentially linear, simple to construct, and does not present the difficulties commonly associated with modelling and analysing nonlinear devices (e.g. friction devices). The smooth semiactive force variation eliminates the disadvantages associated with rapid switching devices. Experimental results are presented to verify the proposed analytical model of the device. A H∞ control algorithm is implemented in order to reduce the response of base isolated buildings with variable damping semiactive control systems in near fault earthquakes. The central idea of the control algorithm is to design a H∞ controller for the structural system that serves as an aid in the determination of the optimum control force in the semiactive device. The relative performance of the SAIVD device is compared to a variable friction device, recently developed by the authors in a separate study, and several key aspects of performance are discussed regarding the use of the two devices for reducing the responses of smart base isolated buildings in near fault earthquakes. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
5.
Damping solvent extraction is a finite element method for the analysis of unbounded (visco-)elastic media which was suggested by Wolf and Song in 1994. It was originally recommended that the method should be employed with a variable domain size depending on excitation frequency. Furthermore, other researchers who have utilized this method in the context of constant domain size, have often imposed strict conditions on the mesh size for the whole domain, which reduces the effectiveness of the approach. Considering the effect of artificial damping on mesh density selection, the present study introduces damping solvent as a method in which one can relax typical mesh density requirements to a large extent by utilizing a large value of artificial damping. Therefore, it makes the finite element mesh to benefit from a large domain size which improves the results for low frequency range. Moreover, good results are simultaneously obtained for high frequency range due to employing a large value of artificial damping. To illustrate the point, a rigid strip foundation with a cross section of rectangle embedded in half plane is considered. According to some comparison between the results obtained from several finite element meshes, the best one which takes full advantages of a large value of artificial damping for dynamic stiffness coefficients of strip foundation is introduced. These comparisons are carried out on domain size, mesh density and artificial damping. 相似文献
6.
This paper presents a new formulation for critical damping of structures with elastically supported visco‐elastic dampers.Owing to the great dependence of damper performance on the support stiffness, this model is inevitable for reliable modelling of structures with visco‐elastic dampers. It is shown that the governing equation of free vibration of this model is reduced to a third‐order differential equation and the conventional method for defining the critical damping for second‐order differential equations cannot be applied to the present model. It is demonstrated that the region of overdamped vibration is finite in contrast to that (semi‐infinite) for second‐order differential equations and multiple critical damping coefficients exist. However, it turns out that the smaller one is practically meaningful. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
7.
A modified domain reduction method for numerical simulation of wave propagation in localized regions
A modified domain reduction method(MDRM) that introduces damping terms to the original DRM is presented in this paper. To verify the proposed MDRM and compare the computational accuracy of these two methods, a numerical test is designed. The numerical results of the MDRM and DRM are compared using an extended meshed model. The results show that the MDRM significantly improved the computational accuracy of the DRM. Then, the MDRM is compared with two existing conventional methods, namely Liao's transmitting boundary and viscous-spring boundary with Liu's method. The MDRM shows its great advancement in computational accuracy, stability and range of applications. This paper also discusses the influence of boundary location on computational accuracy. It can be concluded that smaller models tend to have larger errors. By introducing two dimensionless parameters, φ_1 and φ_2, the rational distance between the observation point and the MDRM boundary is suggested. When φ_1 2 or φ_213, the relative PGA error can be limited to 5%. In practice, the appropriate model size can be chosen based on these two parameters to achieve desired computational accuracy. 相似文献
8.
The effect of the long‐period filter cut‐off, Tc, on elastic spectral displacements is investigated using a strong ground‐motion database from Europe and the Middle East. The relation between the filter and oscillator responses is considered to observe the influence of Tc for both analogue and digital records, and the variations with site classification, magnitude, filter order and viscous damping. Robust statistics are derived using the re‐processed European data to generalize the effects of the long‐period filter cut‐off on maximum oscillator deformation demands as a function of these seismological and structural features. Statistics with a 95% confidence interval are derived to suggest usable period ranges for spectral displacement computations as a function of Tc. The results indicate that the maximum period at which spectral displacements can be confidently calculated depend strongly on the site class, magnitude and filter order. The period range where reliable long‐period information can be extracted from digital accelerograms is twice that of analogue records. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
9.
Based on the dynamic theory for saturated porous media by Biot (Journal of the Acoustical Society of America 1956; 28 : 168–178), a numerical model is presented to analyse the reflection behaviours of reservoir sediment and compared with those from the visco‐elastic model. It is concluded that the two models give very similar results of reflection coefficient α within the frequency range of interest. Then, using the two models, the change of the reflection coefficients α with various sedimentation parameters and excitation frequencies are studied in detail. The results are further used in the analysis of response functions of hydro‐dynamic pressures on, and structural displacements of the Xiang Hong Dian arch dam, for which some results from a field vibration test are available. It appears that effects of water compressibility with sediment reflection on hydro‐dynamic pressures and structural response are not significant for this specific case. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
10.
This paper has two objectives: to connect directly radiation damping and 1D elastic wave propagation, and to create a simple teaching tool to introduce the subject to students and engineers trained in Structural Dynamics. The first objective is achieved by obtaining the equivalent radiation modal damping using time domain solutions for the fundamental mode in shear of an elastic layer (soil) on flexible rock, for the case in which the rock–soil Impedance Ratio in shear, I=(ρrVr)/(ρsVs)>1, where ρ=mass density and V=shear wave velocity. These time domain solutions are developed for the case of steady-state input sinusoidal shear waves propagating vertically in the rock as well as for horizontal free vibration of the layer. Both derivations result in the same approximate expression for the modal radiation damping in the first mode, ζr1≈2/(πI), which is in turn identical to the approximate equation obtained by Roesset and Whitman [11] using a frequency domain approach. This expression for ζr1 is linked to the fact that, during free vibration, the ratio between two successive positive displacement peaks uso and us1 at the ground surface is us0/us1=[(1+I)/(1−I)]2, associated with two wave reflections at the soil–rock interface. From this ratio, and after applying the standard expression to obtain modal damping from damped free vibration, the same expression for ζr1 is reached again, ζr1≈[1/(2π)] ln(us0/us1)≈[1/(2π)] ln[(1+I)/(1−I)]2≈2/(πI). This finding allows development of the simple teaching tool proposed at the end of the paper. While only a crude approximation lacking in rigor, this teaching tool is physically intuitive, links directly wave propagation and modal damping in a simple way and gives the correct result. 相似文献
11.
Experimental and analytical studies were conducted to determine dynamic soil–structure interaction characteristics of a single-span, prestressed-concrete bridge with monolithic abutments supported by spread footings. The experimental programme, consisting of harmonic forced vibration excitation of the bridge in the transverse and longitudinal directions, revealed the presence of four modes in the frequency band, 0 to 11 Hz, and the onset of a fifth mode at 14 Hz, the highest frequency attained during the tests. The fundamental mode at 4.7 Hz was the primary longitudinal bending mode of the deck and had a relatively low damping ratio (ζ1), that was approximately 0.025 of critical. The second and third modes at 6.4 Hz and 8.2 Hz were the primary twisting modes of the deck which involved substantial transverse rocking, transverse translation and torsion of the footings. As expected, the damping ratios associated with these two modes, ζ2 = 0.035 and ζ3 = 0.15, were directly related to the relative amounts of deck and footing motion. The fourth mode at 10.6 Hz was the second twisting mode of the deck and involved relatively little motion of the footings and abutment walls, which was consistent with the low damping, ζ4 = 0.02, observed in this mode. The response data at 14 Hz suggested that the fifth mode beyond this frequency was the second longitudinal bending mode of the deck involving longitudinal translation and bending of the abutment walls. A three-dimensional finite element model of the bridge, with Winkler springs attached to the footings and abutment walls to represent the soil–structure interaction, was able to reproduce the experimental data (natural frequencies, mode shapes and bridge response) reasonably well. Although the stiffnesses assigned to the Winkler springs were based largely on the application of a form of Rayleigh's principle to the experimental data, these stiffnesses were similar to theoretical foundation stiffnesses of the same size footings on a linearly elastic half space and theoretical lateral stiffnesses of a rigid retaining wall against a linearly elastic backfill. 相似文献
12.
It is important to include the viscous effect in seismic numerical modelling and seismic migration due to the ubiquitous viscosity in an actual subsurface medium. Prestack reverse‐time migration (RTM) is currently one of the most accurate methods for seismic imaging. One of the key steps of RTM is wavefield forward and backward extrapolation and how to solve the wave equation fast and accurately is the essence of this process. In this paper, we apply the time‐space domain dispersion‐relation‐based finite‐difference (FD) method for visco‐acoustic wave numerical modelling. Dispersion analysis and numerical modelling results demonstrate that the time‐space domain FD method has great accuracy and can effectively suppress numerical dispersion. Also, we use the time‐space domain FD method to solve the visco‐acoustic wave equation in wavefield extrapolation of RTM and apply the source‐normalized cross‐correlation imaging condition in migration. Improved imaging has been obtained in both synthetic and real data tests. The migration result of the visco‐acoustic wave RTM is clearer and more accurate than that of acoustic wave RTM. In addition, in the process of wavefield forward and backward extrapolation, we adopt adaptive variable‐length spatial operators to compute spatial derivatives to significantly decrease computing costs without reducing the accuracy of the numerical solution. 相似文献
13.
In this paper, vertical peak floor acceleration (PFAv) demands on elastic multistory buildings are statistically evaluated using recorded ground motions. These demands are applicable to the assessment of nonstructural components that are rigid in the vertical direction and located at column lines or next to columns. Hence, PFAv demands of the floor system away from column lines and their effects on nonstructural components are not addressed. This study is motivated by the questionable general assumption that typical buildings are considered to be relatively flexible in the horizontal (lateral) direction but relatively rigid in the vertical (longitudinal) direction. Consequently, only few papers address the evaluation of vertical component acceleration demands throughout a building, and there is no consensus on the relevance of vertical accelerations in buildings. The results presented in this study show that the vertical ground acceleration demands are amplified throughout the column line of a steel frame structure. This amplification is in many cases significant, depending on the vertical stiffness of the load‐bearing system, damping ratio, and the location of the nonstructural component in the building. From these outcomes it can be concluded that the perception of a rigid‐body response of the column lines in the vertical direction is highly questionable, and further research on this topic is required. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
14.
In order to account for the non‐linear behavior of structures via non‐linear static procedure, the capacity spectrum method has been adopted by ATC‐40 for evaluation and retrofit of reinforced concrete buildings. For elastic‐perfectly‐plastic SDOF systems, the accuracy of the capacity spectrum method depends only on the acceleration response spectrum chosen to form the demand spectrum and the adopted model for calculating the equivalent viscous damping ratios. According to this method, the pseudo‐acceleration response spectrum (PSa) is used to create the demand diagram. It is found that the ATC‐40 procedure, using its Type A hysteretic model, may be inaccurate especially for systems with damping ratios greater than 10% and periods longer than 0.15sec. In order to improve the accuracy of the capacity spectrum method, this study proposes to use the real absolute acceleration response spectrum (S0.a) instead of the PSa to establish the demand diagram. The step‐by‐step procedure of the improved method and examples are implemented in this paper to illustrate the calculations of earthquake‐induced deformations. In addition, three selected models of equivalent viscous damping are also compared in this paper to assess the accuracy of the model used in the ATC‐40 procedure. Results show that the WJE damping model may be used by the capacity spectrum method to reasonably predict the inelastic displacements when the ductility demand (μ) of the structures is less than 4, whereas the damping model proposed by Kowalsky can be implemented when μ>4.0. Alternatively, the damping model proposed by Kowalsky may be used to calculate the equivalent viscous damping for the entire range of ductility. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
15.
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
16.
In this paper the influence of base isolation on the behaviour of a work of art has been analysed. To make things more realistic, the work of art has been modelled with a non‐symmetrical rigid body, sitting on a base that is connected to a visco‐elastic device, which represents the passive control system. To prevent the breaking of the isolation device, security stops have been introduced to limit the displacement of the oscillating base to a maximum safety value. All analyses have been carried out comparing the behaviour of the non‐isolated and the isolated non‐symmetric rigid body subject to impulsive and seismic excitations. The analysis is particularly focused on the effects of the eccentricity of the rigid body and on the presence of the security stops. Generally, base isolation improves the behaviour of the system while the presence of an eccentricity makes the performance of the system worse with respect to the symmetric rigid body. Moreover the security stops, although they preserve the isolator devices, cause a worsening in the performance of the systems. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
17.
In spite of important differences in structural response to near‐fault and far‐fault ground motions, this paper aims at extending well‐known concepts and results, based on elastic and inelastic response spectra for far‐fault motions, to near‐fault motions. Compared are certain aspects of the response of elastic and inelastic SDF systems to the two types of motions in the context of the acceleration‐, velocity‐, and displacement‐sensitive regions of the response spectrum, leading to the following conclusions. (1) The velocity‐sensitive region for near‐fault motions is much narrower, and the acceleration‐sensitive and displacement‐sensitive regions are much wider, compared to far‐fault motions; the narrower velocity‐sensitive region is shifted to longer periods. (2) Although, for the same ductility factor, near‐fault ground motions impose a larger strength demand than far‐fault motions—both demands expressed as a fraction of their respective elastic demands—the strength reduction factors Ry for the two types of motions are similar over corresponding spectral regions. (3) Similarly, the ratio um/u0 of deformations of inelastic and elastic systems are similar for the two types of motions over corresponding spectral regions. (4) Design equations for Ry (and for um/u0) should explicitly recognize spectral regions so that the same equations apply to various classes of ground motions as long as the appropriate values of Ta, Tb and Tc are used. (5) The Veletsos–Newmark design equations with Ta=0.04 s, Tb=0.35 s, and Tc=0.79 s are equally valid for the fault‐normal component of near‐fault ground motions. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
18.
An eigenfunction solution is presented for the dynamic response of vertical circular cylinders to earthquake excitation in a compressible fluid of finite depth. This single eigenseries expansion eliminates the need for a double summation over both the eigenfunctions and the trial functions as required by Rayleigh-Ritz methods. Revised definitions for the added mass and hydrodynamic radiation damping coefficients per unit length are derived from the hydrodynamic fluid pressures. Based on comparisons between these newly defined coefficients, the compressibility of the fluid is found to be relatively more important at dimensionless frequencies greater than unity (ω > 1.0) when analysing both rigid and flexible cylinders having relatively large diameter to water depth ratios,r0/h > 0.25 (squatty type). This conclusion regarding the relative importance of the fluid compressibility is derived from a comparison between the relative magnitudes and the vertical distributions over depth of both the added mass and radiation damping coefficients per unit length for both rigid and flexible squatty cylinders. From additional comparisons with Rayleigh-Ritz solutions that require trial functions, the results for totally immersed flexible slender cylinders (r0/h< 0.10) are shown to be equivalent; but the results for totally immersed flexible squatty cylinders (r0/h > 0.25) are not. The reason for this difference appears to be in the truncation of the trial function series in the Rayleigh-Ritz methods, which excludes the higher mode shapes, and in the definitions of the added mass coefficients. Comparisons with laboratory data for both rigid and flexible cylinders confirm the accuracy of the solutions obtained by the eigenseries in the limited frequency interval above the highest frequency for surface gravity waves (f > 1.0 Hz) and below the first dimensionless cut-off frequency for acoustic waves (ω< 1.0). 相似文献
19.
A first-order formulation to analyze the dynamic response of layered soil profiles is presented as an alternative to the widely used second-order thin-layer method by the direct stiffness approach, including an efficient simulation of the underlaying elastic half-space. In contrast to the thin-layer method where response is expressed through a combination of second-order propagation modes, the proposed procedure uses first-order modal parameters that have the capacity to provide a good approximation in the complete wave number domain k, including the exact stiffness values for k=0 and k→∞, thus justifying its designation of doubly-asymptotic. This feature allows obtaining the exact soil profile response for static loads, while the proposed treatment of the elastic half-space reproduces naturally the radiation condition without a need of artificial damping. The capacity of the proposed formulation to solve elastodynamic problems is assessed by comparing its results with those of exact solutions available in the literature, and numerical solutions of rigid disks supported on the surface of different soil profiles. 相似文献
20.
One‐dimensional simulations of the unsteady saltation process show that the transport rate's response depends on the amplitude and frequency of the wind fluctuations. At frequencies higher than f ≈ 0·5 Hz the transport rate was found not to respond to the wind changes. The initial overshoot reported by previous investigators was found not to appear for simulation heights smaller than 50 to 60 cm. This is due to the fast propagation of the grains' influence upward in the flow and the immediate deceleration of the wind. Confirmation of these findings comes from reports of experiments conducted in wind tunnels of different sizes. Further test calculations show that the discretization time step size Δt has an influence on the model's temporal behaviour. The reason for this is the better coupling of the wind–sand system when a smaller Δt is used. The implications of bed area choice on the statistical accuracy of predicted transport rate is also demonstrated. In the one‐dimensional case the grain cloud's total forward momentum equals transport rate, which is independent of model geometry. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献