bluuebunny/crossref_metadata_2025 huggingface dataset:
Optimization of the stochastic response of a bridge isolation system with hysteretic dampers
Authors: Xiaoming Li
Published: April 2007

A bridge structure with a seismic isolation system consisting of rubber bearings and hysteretic dissipators is considered. The non‐linear equations of motion are derived for the first mode vibration and the stochastic response to a white noise or a filtered white noise ground acceleration is determined by using the method of equivalent linearization. The sensitivity of the stochastic response to principal pàrameters for the bridge is investigated. Results of optimum design of the isolation system are presented.
Scattering of plane harmonic SH, SV, P and rayleigh waves by non‐axisymmetric three‐dimensional canyons: A wave function expansion approach
Authors: Eshraghi Hossein , Dravinski Marijan
Published: April 2007

Scattering of elastic waves by three‐dimensional canyons embedded within an elastic half‐space is investigated by using a wave function expansion technique. The geometry of the canyon is assumed to be non‐axisymmetric. The canyon is subjected to incident plane Rayleigh waves and oblique incident SH, SV and P waves. The unknown scattered wavefield is expressed in terms of spherical wave functions which satisfy the equations of motion and radiation conditions at infinity, but they do not satisfy stress‐free boundary conditions at the half‐space surface. The boundary conditions are imposed locally in the least‐squares sense at several points on the surface of the canyon and the half‐space.

Through a comparative study the validity and limitations of two‐dimensional approximations (antiplane strain and plane strain models) have been examined. It is shown that scattering of waves by three‐dimensional canyons may cause substantial change in the surface displacement patterns in comparison to the two‐dimensional models. These results emphasize the need for three‐dimensional modelling of realistic problems of interest in strong ground motion seismology and earthquake engineering.
Coupling of boundary and finite elements for soil‐structure interaction problems
Authors: von Estorff Otto , Kausel Eduardo
Published: April 2007

The investigation of complex soil‐structure interaction problems is usually carried out with numerical solution procedures such as the finite element or the boundary element method. It must be noted, however, that the choice of one or the other of these approaches is not just a matter of preferences; depending on the type of the problem under consideration, either boundary or finite elements may be more advantageous. A considerable expansion in the computational power can be obtained, on the other hand, if one resorts to hybrid schemes which retain the main advantages of the two methods and eliminate their respective disadvantages.

This paper presents results obtained with a boundary element‐finite element coupling procedure, and discusses its applicability to some representative soil‐structure interaction problems. The structures considered are elastic systems, such as foundations, tunnels and filled trenches (modelled by finite elements), which are coupled with homogeneous elastic halfspaces (modelled by boundary elements). The examples demonstrate the importance of using a model that includes wave radiation effects.

The coupling approach is formulated entirely in the time domain so that an extension of the algorithm to non‐linear analyses seems to present no further difficulties.
Dynamic parameter identification for non‐linear isolation systems in response spectrum analysis
Authors: Tsai Hsiang‐Chuan , Kelly James M.
Published: April 2007

The response spectrum method has been widely used in earthquake engineering design, but cannot be directly applied to non‐linear systems such as the lead‐filled rubber bearing used in base isolation systems. An appraoch to determine the equivalent linearized stiffness and damping coefficient of the lead‐filled rubber bearing by use of the results of shaking table tests is developed. Comparisons of time histories for the equivalent linear systems and the actual model show the method gives accurate maxima for displacement and acceleration and at the appropriate times. It is found that the identified parameters vary with the maximum deformation and the simplified formulae that can optimally describe the variations are derived. Using these formulae, an iterative algorithm using the response spectrum method to calculate the dynamic response of buildings isolated by lead‐filled rubber bearings is also presented.
Seismic demand in medium‐ and long‐period structures
Authors: Fajfar Peter , Vidic Tomaž , Fischinger Matej
Published: April 2007

Based on the results of an extensive parametric study of elastic and inelastic response of SDOF systems, in which the most important structural parameters were varied and ground motions of very different characteristics were taken into account, simple formulae for determining the seismic demand in SDOF systems with natural periods in the medium‐ and long‐period range are proposed. Seismic demand is expressed in terms of the mean values of maximum relative displacements and maximum input energy. These results can be used to provide rough estimates of structural behaviour when different damage models are applied. As well as this, the proposed formulae can be used to construct design spectra of the Newmark‐Hall type.
Centrifugal modelling of dynamic soil‐structure interaction
Authors: Weissman Karen , Prevost Jean H.
Published: April 2007

This paper presents a centrifuge model that is capable of realistically representing soil‐structure systems subjected to earthquake‐like excitation. The model is validated by performing (i) free field soil tests, (ii) dynamic soil‐structure interaction tests and (iii) a numerical analysis of the experimental results. The free field experiments show that the simulated earthquake, which is generated by the hammer‐exciter plate method, is similar in amplitude and frequency content to a real earthquake. The experiments also demonstrate that a confined soil sample can satisfactorily model a horizontal soil stratum of infinite lateral extent when the containment walls are lined with an absorptive material to attenuate wave reflections that would otherwise occur. Measurements of the acceleration at different locations on the free soil surface indicate that the surface motion is fairly uniform over a relatively large area. This is further confirmed by a comparison made between the measured free and scattered field motions for a surface foundation. Next, a series of soil‐structure interaction tests are performed which examine the dependence of radiation damping on the natural frequencies of the structure relative to the fundamental frequency of the soil stratum. The experimental results are shown to be consistent with established theories. Finally, the experimental results are used to compute the stiffness and damping parameters of a two degree of freedom numerical model of the soil‐structure system. The experimental parameters are shown to be in good agreement with calssical text book formulae. This study demonstrates that the centrifuge model consistently behaves as expected for simple, but realistic, dynamic soil and soil‐structure systems, and can, therefore, be used with confidence to examine more complicated systems that are not yet fully understood.
Evaluation of seismic energy in structures
Authors: Uang Chia‐Ming , Bertero Vitelmo V.
Published: April 2007

Research engineers use two types of energy equations to study single‐degree‐of‐freedom (SDOF) systems subject to earthquake induced ground motions. The first method uses an absolute energy formulation; the second method uses a relative energy formulation. While the relative energy formulation has been used in the majority of previous investigations, this study shows that the absolute energy equation is physically more meaningful. For a given ductility ratio, the input energy demands calculated by both methods are significantly different for both the short and long period ranges although the results are similar in the intermediate period range. A comparison between the analytically predicted absolute input energy of a SDOF system with the experimentally measured input energy of a six‐storey braced steel frame shows good correlation.
Seismic response of simple structures using spring‐assisted sliding slabs with coulomb damping
Authors: Singh M. P. , Malushte S. R.
Published: April 2007

Coulomb damping can be utilized effectively to reduce the dynamic response of structures subjected to seismic ground motions. To activate this damping, some parts of a vibrating structure are allowed to slide at rough interfaces. The dynamic response of structures provided with sliding interfaces at the base, between a floor slab and frame and in the cross bracings of a frame has been examined recently. In this paper, a simple slab sliding system provided with a spring to introduce a recovery mechanism and to reduce the sliding displacement requirement for low frequency structures has been examined. The equations of motion for this system are developed. An approach is presented to solve these coupled equations for earthquake induced ground motions. Structures with varying frequency and friction characterisics are considered and the numerical results are presented in response spectrum form. It is observed that, in low frequency structures, provision of a rather weak spring can reduce the sliding displacement requirements without significantly increasing the forces in the supporting frame and the acceleration input to supported secondary systems.
Transverse response of offshore pipelines to random ground motion
Authors: Datta T. K. , Mashaly E. A.
Published: April 2007

A method is presented for the determination of the transverse response of the idealized suspended span of an offshore pipeline to random seismic input. The method is based on spatial discretization of the pipe with nodal lumped masses. The earthquake is assumed to be a stationary random process characterized by a power spectral density function. The cross spectral density function between two random seismic excitations along the pipe length is defined with the help of a local earthquake power special density function, which is assumed to be the same for the two end supports of the pipeline, and a frequency dependent weighted function which decays exponentially with distance from the pipe supports. The solution is obtained in the frequency domain using the spectral approach and is presented in terms of r.m.s. displacements and stresses. The formulation adequately includes the pressure drag effect which tends to dampen the pipe motions. Utilizing this method of analysis, several idealized pipe sea bed configurations, in which the pipe is anchored between two end blocks and subjected to horizontal ground excitations normal to the pipe axis, have been analysed to predict the influence of certain important parameters on the response.
Application of fractional derivatives to seismic analysis of base‐isolated models
Authors: Koh Chan Ghee , Kelly James M.
Published: April 2007

The concept of fractional derivatives is employed in the formulation of a stress‐strain relationship for elastomers. An oscillator consisting of a mass and a ‘fractional’ Kelvin element is used to model elastomeric bearings used in base isolation systems. Efficient numerical multi‐step schemes are developed for the dynamic analysis of a single‐degree‐of‐freedom ‘fractional oscillator’ in the time domain. Numerical examples show that these multi‐step schemes are in good agreement with the Laplace and Fourier solutions. When applied to shaking table tests of a base‐isolated bridge deck, the fractional derivative model is found to agree well with the experimental results.
Analytical predictions of the seismic response of friction damped timber shear walls
Authors: Filiatrault A.
Published: April 2007

A new concept for the earthquake resistant design of timber shear wall structures is proposed. By providing friction devices in the corners of the framing system of the shear wall, its earthquake resistance and damage control potential can be enhanced considerably. During severe earthquake excitations, the friction devices slip and a large portion of the seismic energy input is dissipated by friction rather than by inelastic deformation of the sheathing‐to‐framing connectors. A simple numerical model is developed and results of inelastic time‐history dynamic analyses show the superior performance of the friction damped timber shear walls compared to conventional shear wall systems. The proposed friction devices act both as safety valves by limiting the inertia forces transmitted to the structure, and as structural dampers by dissipating a significant portion of the seismic energy input. The devices can be used in any configuration of the framing system to accommodate architectural or construction requirements. The damping system may also be conveniently incorporated in existing timber shear wall buildings to upgrade significantly their earthquake resistance.
Non‐stationary structural response with evolutionary spectra using seismological input model
Authors: Quek Ser‐Tong , Teo Yen‐Peng , Balendra Thambirajah
Published: April 2007

A recently developed seismological model of ground motion is incorporated into the non‐stationary random vibration theory making use of Priestley's evolutionary power spectral density. A general method of computing the input power spectrum is proposed and shown to reduce to the classical method when the input and the output are taken as stationary. Based on the concepts of Yang's non‐stationary envelopes and first‐passage reliability estimates via extreme point process, a statistical response spectrum for the pseudo‐velocity is developed. Comparisons made among the results of non‐stationary analysis with different modulating functions, and that of the stationary approximation, on SDOF linear structures with 5 per cent damping show that the type ofmodulating function chosen has little effect on the magnitudes of mean pseudo‐velocities, provided the input power spectrum is properly scaled, and that the stationary approximation produces conservative results for structures with natural periods greater than 0.5 sec.
Optimum design of actively controlled structures
Authors: Pantelides C. P.
Published: April 2007

The optimum design of seismic structures equipped with active controls is presented. The design variables are structural parameters, such as structural stiffness or moment of inertia. The optimization procedure is carried out in two stages. First, the optimal control forces are expressed in closed form, as implicit functions of the design variables. In the second stage, the structural parameters are varied in order to minimize a structural weight objective function. The algorithm is applied to structural systems under earthquake excitations, for displacement, frequency and control force constraints.
Response of piles and pile groups to travelling SH‐waves
Authors: Mamoon S. M. , Banerjee P. K.
Published: April 2007

The response of single piles and pile groups under vertically and obliquely incident seismic waves is obtained using the hybrid boundary element (BEM) formulation. The piles are represented by compressible beam‐column elements and the soil as a hysteretic viscoelastic half‐space. A recently developed Green function corresponding to the dynamic Mindlin problem is implemented in the numerical formulation. Exact analytical solutions for the differential equations for the piles under distributed harmonic excitations are used. Treating the half‐space as a three‐dimensional elastic continuum, the interaction problem is formulated by satisfying equilibrium and displacement compatibility along the pile‐soil interface. Solutions adopted for the seismic waves are obtained by direct integration of the differential equations in terms of amplitudes. Salient features of the seismic response are identified in several non‐dimensional plots. Results of the analyses compare favourably with the limited data available in the literature.
Amplification of elastic waves by a three dimensional valley. Part 2: Transient response
Authors: Mossessian Tomi K. , Dravinski Marijan
Published: April 2007

Transient response of three dimensional dipping layers of different shapes subjected to incident P, SV, SH and Rayleigh waves is investigated. The time domain response is constructed from steady state solutions through the Fourier synthesis. An indirect boundary integral equation method is applied to calculate the required steady state solutions. The material of the half‐space and the layer is assumed to be linear, weakly inelastic, homogeneous and isotropic.

Numerical results show that the maximum amplification of motion is strongly dependent upon the type of incident wave, the shape of the basin and signal frequency. The change in the shape of the valley from hemispherical to semi‐prolate causes a significant increase in the amplitude of surface waves near the edges; however, the maximum amplification of motion near the centre of the valley decreases. This phenomenon is especially apparent for the case of an incident P wave. In comparison to the corresponding two dimensional responses, the amplitude of motion near the centre of the valley is in general higher for three dimensional models.
Effective time‐domain soil‐structure interaction analysis based on FFT algorithm with causality condition
Authors: Hayashi Yasuhiro , Katukura Hiroshi
Published: April 2007

We propose an effective and reliable time‐domain substructure technique which takes soil‐structure interaction effects into account and uses the flexibility coefficients of unbounded soil obtained in the frequency domain. Compared with previous methods, the frequency points to calculate flexibility coefficients, and computational loads in the calculation of time‐domain interaction forces, are reduced.

In the formulation, we have assumed the flexibility coefficient to be a periodic function, obtained within the bandlimited frequency range, which also includes the predominant frequencies of the structure and incident wave. Then we simulate the periodic flexibility coefficients using discrete impulse responses in the time‐domain analyses. However, the real and imaginary parts of the bandlimited flexibility coefficients do not form a Hilbert transform pair; the discrete impulse responses should be modified to be causal for the time‐domain analyses. We present various discrete impulse responses which have been obtained from only the real part, only the imaginary part and from both the real and imaginary parts of the frequency‐domain flexibility coefficients by FFT with causality conditions. Through a numerical example the relationship between the modified discrete impulse responses and the validity of the time‐domain substructure method is presented.
Response of multi‐degree‐of‐freedom structures with sliding supports
Authors: Yang Yeong‐Bin , Lee Tzu‐Ying , Tsai I.‐Chau
Published: April 2007

The response of multi‐degree‐of‐freedom (MDOF) structures with sliding supports is studied. The problem of sliding structures is a discontinuous one in that different numbers of equations of motion with varying forcing functions are required for the sliding and non‐sliding phases. The numerical difficulties involved in this regard in an incremental finite element analysis can be circumvented through the introduction of a fictitious spring for the sliding support. Such a treatment enables one to study the higher mode effects on MDOF sliding structures under the excitation of harmonic or earthquake motions. The dynamic characteristics of MDOF sliding structures will be highlighted in the analysis of a four‐storey shear building with sliding support.
Response of multi‐span beams to spatially incoherent seismic ground motions
Authors: Zerva Aspasia
Published: April 2007

The response of continuous two‐ and three‐span beams of various lengths subjected to spatially varying seismic ground motions is evaluated. Stochastic representations of the seismic ground motions are used as input at the supports of the structures, and sensitivity analyses of the response with respect to the degree of correlation between the support motions are performed. The validity of the commonly used assumption of equal support motion is examined. Square‐roots of mean‐square values of total displacements, bending moments and shear forces are outputs of the analyses. The results indicate that fully correlated motions may produce higher or lower response than partially correlated motions, depending on the dynamic characteristics of the structure, the response quantity (bending moment or shear force) that is evaluated, the position along the axis of the beam where the response quantity is evaluated, the separation between the natural frequencies of the structure and the dominant frequencies of the input motions, and on the degree of partial correlation between the support motions.
Diagonal brace with ductile knee anchor for aseismic steel frame
Authors: Balendra Thambirajah , Sam Ming‐Tuck , Liaw Chih‐Young
Published: April 2007

A new structural system for earthquake resistant steel structures is investigated in this paper. This new framing system, called the knee‐brace‐frame (KBF), is a braced frame with diagonal braces connected to ductile knee members. The diagonal braces provide the lateral stiffness, whereas the knee anchors yield in flexure to dissipate energy during severe seismic excitation. To assess the inelastic characteristics of the KBF, a large scale model of a KBF was tested using the pseudodynamic test procedure. The experimental results are compared with analytical results obtained from a DRAIN‐2D model. It is found that, with an appropriate design of knee anchors, the KBF can be made to be ductile to dissipate energy during severe seismic excitation.
Seismic testing of large panel precast walls: Comparison of pseudostatic and shaking table tests
Authors: Oliva Michael , Gavrilovic Predrag , Clough Ray W.
Published: April 2007

Urban housing has been provided economically in many parts of the world by large panel precast building systems; in seismic regions, however, special attention must be given to the connections between panels in order to achieve the necessary earthquake resistance. In this paper a comprehensive seismic test programme of concrete panel assemblages done as part of a U.S.‐Yugoslavia cooperative research plan in earthquake engineering is described. The test structures were three‐storey assemblages of 1/3 scale concrete panels supplied by a Yugoslavian construction company; the models were about 12 ft high and 6 ft long, with the panels interconnected by various types of joint systems along their tops, bottoms and sides.

Cyclic pseudostatic testing of the models was done at the IZIIS Laboratories in Skopje, Yugoslavia. A second set of models was assembled at the University of California, Berkeley from identical panels that had been shipped from the Belgrade factory; these models were tested on the 20 ft square EERC shaking table. The purpose of this paper is to compare the earthquake response represented by the two different types of test procedures.

A major conclusion was that the response mechanisms in both cases were similar, with the principal deformation being opening of the panel joint at the base of the model due to overturning moments. As the rocking response continued, tension and compression failure occurred alternately at the two ends of the joint. The principal difference between the results was that pseudostatic testing imposed an increasing sequence of symmetric deformation that was independent of the damage being developed in the model, while the shaking table response was greatly influenced by the damage as it occurred—leading to significant unsymmetry. Moreover, the damage occurred in a concentrated region with the shaking table test. This difference emphasizes the fact that pseudostatic test results must be interpreted with caution because they do not fully simulate an actual earthquake response.
Ritz method for dynamic analysis of large discrete linear systems with non‐proportional damping
Authors: Ibrahimbegovic Adnan , Chen Harn C. , Wilson Edward L. , Taylor Robert L.
Published: April 2007

Real and complex Ritz vector bases for dynamic analysis of large linear systems with non‐proportional damping are presented and compared. Both vector bases are generated utilizing load dependent vector algorithms that employ recurrence equations analogous to the Lanczos algorithm. The choice of static response to fixed spatial loading distribution, as a starting vector in recurrence equations, is motivated by the static correction concept. Different phases of dynamic response analysis are compared with respect to computational efficiency and accuracy. It is concluded that the real vector basis approach is approximately eight times more efficient than the complex vector basis approach. The complex vector basis has some advantages with respect to accuracy, if the excitation is of piecewise linear form, since the exact solution can be utilized. In addition, it is demonstrated that both Ritz vector bases, real and complex, possess superior accuracy over the adequate eigenvector bases.
Regional seismic slope failure probability matrices
Authors: Lin Jeen‐Shang
Published: April 2007

A method for constructing seismic slope failure probability matrices is presented. The core of the method is a probabilistic sliding block model which allows for systematic incorporation of the uncertainties associated with both the ground excitation and the strength of the slope materials. The extent of damage to a slope is defined in terms of the magnitude of the earthquake‐induced permanent displacement. The intensity of the ground shaking is characterized by a peak ground acceleration as well as an earthquake magnitude, and the possible scatter in the ground motion details is included through the use of an equivalent stationary motion model. After the effects of essential contributing factors are discussed, regional seismic slope failure probability matrices are presented for general applications.
A simple boundary element formulation and its application to wavefield excited soil‐structure interaction
Authors: Auersch L. , Schmid G.
Published: April 2007

A simple boundary element formulation which is based directly on the point load solutions for an elastic full‐space is presented. It is integrated in a finite element program to calculate dynamic soil‐structure interaction problems. The combined boundary and finite element method is applied to structures which are excited by horizontally propagating waves in the soil.

For three different types of flexible structure‐elastic beams, low and high (square) shear walls‐and the corresponding rigid structures the vibration modes and the soil‐structure transfer functions have been investigated. The flexible foundations display the same wave pattern as the exciting free‐field of the soil, but the amplitudes are reduced with increasing frequency, depending on the stiffness or wave resistance of the structure. Rigid structures show, in part, quite different behaviour, giving free‐field reductions caused by kinematic and inertial soil‐structure interaction.
A note on the fast computation of response spectra estimates
Authors: Reinoso Eduardo , Ordaz Mario , Sanchez‐Sesma Francisco J.
Published: April 2007

An algorithm is presented for fast computation of estimates of response spectra. It is based on the formalism of random vibration theory. Numerical results show that estimates are reliable and useful for practical applications.
Analysis of saturated dense sand‐structure system and comparison with results from shaking table test
Authors: Fukutake Kiyoshi , Ohtsuki Akira , Sato Masayoshi , Shamoto Yasuhiro
Published: April 2007

An effective stress method is presented for the analysis of liquefaction of ground including soil‐structure interaction, based on an explicit‐implicit finite element method. A simple constitutive model is developed to be incorporated in the effective stress method. The constitutive model consists of the Ramberg‐Osgood model extended to two‐dimensional problems and a new dilatancy model. The effectiveness of the constitutive model is examined with results of a simple shear test. Besides, the effective stress method is verified by comparing its numerical results with results of a shaking table test. It is found that the present method can simulate well the response of a saturated dense sand‐structure system. The difference of the response computed by the effective stress method and the total stress method is discussed. It is found that the total stress method can simulate the response of the saturated sand within an accumulating excess pore water pressure of less than 70 per cent of the initial overburden stress.
The many steady state responses of a rigid block under harmonic forcing
Authors: Hogan S. J.
Published: April 2007

Recent mathematical advances in the study of the response of a rigid block to horizontal simple harmonic forcing conclude that (i) all types of subharmonic response are possible, (ii) several types can occur at one point in parameter space, (iii) exact expressions are available for stability boundaries in parameter space, (iv) asymmetric solutions exist just outside the upper boundaries of symmetric solutions, (v) period‐ and impact‐doubling cascades occur as parameter values are varied even further outside the boundaries, (vi) aperiodic (or chaotic) responses are possible, (vii) periodic responses can occur which appear to violate West's formula and (viii) steady state responses of the forced system can be so large as to produce toppling of the block if the system were unforced.

These results are used to explain and extend recent computational work. Also we find quantitative agreement between our theoretical work and some recent experimental work of Tso and Wong.
A strong motion database for the chiba seismometer array and its engineering analysis
Authors: Katayama Tsuneo , Yamazaki Fumio , Nagata Shigeru , Lu Lin , Turker Turgay
Published: April 2007

A three‐dimensional seismometer array was installed in the Chiba Experiment Station of the Institute of Industrial Science, University of Tokyo in 1982. The array system consists of 44 three‐component accelerometers densely placed both on the ground surface and in boreholes. A complementary system for the measurement of ground and buried pipe strains was also installed at the same site. The array system has been successfully in operation, and more than 160 earthquakes have been recorded. Considering a wide use of these seismograms, the Chiba array database has recently been created comprising twenty‐seven major events. This paper describes the Chiba array system and its strong motion database. Results of engineering analysis using the selected records are also presented.
Attenuation models inferred from intraplate earthquake recordings
Authors: Dahle Anders , Bungum Hilmar , Kvamme Leif B.
Published: April 2007

Strong‐motion recordings at 87 sites from 56 different intraplate earthquakes from North America, Europe, China and Australia have been used through a two‐step regression analysis to develop new attenuation models for peak ground acceleration, and for pseudo‐relative velocity for frequencies of 0.25, 0.5, 1.0, 2.0, 5.0 and 10.0 Hz, all for 5 per cent of critical damping. The estimates are obtained along with an analysis of residuals and scatter.

A similar regression analysis has been performed also for Fourier spectra of acceleration, in which case the coefficient for the anelastic term has been interpreted in terms of a frequency dependent quality factor Q. The resulting Q‐model shows a strong frequency sensitivity with values around 600–700 at 1 Hz, around 2000 at 10 Hz and around 5200 at 25 Hz.

These PGA, PSV and Q results depend, however, on the underlying assumption for geometrical spreading, in particular for low frequencies.
Investigation of the dynamic interaction between a high‐pressure pipeline and the moving liquid inside under seismic loading
Authors: Kisliakov Dimiter
Published: April 2007

The response of an open high‐pressure pipeline containing moving liquid to horizontal seismic loading is investigated. The problem of the interaction between the pipe and the liquid inside it is solved after thorough kinematic analysis, involving two‐stage application of the Coriolis theorem. The basic axial loading on the pipeline is also taken into account. As a result, the equation of motion of an arbitrary one‐span part of the pipeline under seismic loading is obtained. The harmonic balance is used to find the solution. As an illustration to the theory a numerical example is given with the data of a real water power station pressure pipeline under a past earthquake record.
Consistent lumped‐parameter models for unbounded soil: Frequency‐independent stiffness, damping and mass matrices
Authors: Wolf John P.
Published: April 2007

A systematic procedure to develop consistent (symmetric) stiffness, damping and mass matrices with real coefficients to represent any unbounded soil is developed. These property matrices are based on the lumped‐parameter models of Reference 1. Either stiffness and damping matrices corresponding to first‐order differential equations involving the internal degrees of freedom and those on the structure‐soil interface result or, alternatively, in addition mass matrices are introduced, corresponding to second‐order differential equations, which reduce the number of internal degrees of freedom by a factor 2.

The stiffness, damping and mass matrices can easily be incorporated in a general‐purpose structural dynamics program working in the time domain, whereby the structure can even be non‐linear.
A method to estimate intensity occurrence probabilities in low seismic activity regions
Authors: Egozcue J. J. , Barbat A. , Canas J. A. , Miquel J. , Banda E.
Published: April 2007

The estimation of site intensity occurrence probabilities in low seismic activity regions has been studied from different points of view. However, no method has been definitively established because several problems arise when macroseismic historical data are incomplete and the active zones are not well determined. The purpose of this paper is to present a method that estimates site occurrence probabilities and at the same time measures the uncertainties inherent in these probabilities in low activity regions. The region to be studied is divided into very broad seismic zones. An exponential intensity probability law is adjusted for each zone and the degree of uncertainty in the assumed incompleteness of the catalogue is evaluated for each intensity. These probabilities are used to establish what may be termed ‘prior site occurrence models’. A Bayesian method is used to improve ‘prior models’ and to obtain the ‘posterior site occurrence models’. Epicentre locations are used to recover spatial information lost in the prior broad zoning. This Bayesian correction permits the use of specific attenuation for different events and may take into account, by means of conservative criteria, epicentre location errors. Following Bayesian methods, probabilities are assumed to be random variables and their distribution may be used to estimate the degree of uncertainty arising from (a) the statistical variance of estimators, (b) catalogue incompleteness and (c) mismatch of data to prior assumptions such as Poisson distribution for events and exponential distribution for intensities. The results are maps of probability and uncertainty for each intensity. These maps exhibit better spatial definition than those obtained by means of simple, broad zones. Some results for Catalonia (NE of Iberian Peninsula) are shown.
Inelastic seismic response of one‐storey, asymmetric‐plan systems: Effects of system parameters and yielding
Authors: Goel Rakesh K. , Chopra Anil K.
Published: April 2007

The inelastic response of one‐storey, asymmetric‐plan systems to two excitations is presented and analysed with the objective of identifying the influence of system parameters: uncoupled lateral vibration period, uncoupled torsional‐to‐lateral frequency ratio, stiffness eccentricity, relative values of the strength and stiffness eccentricities, and yield factor. Furthermore, the influence of yielding on the response of asymmetric‐plan systems is examined. In particular, we determine whether the well known relationship between the response of yielding and elastic single‐degree‐of‐freedom (SDF) systems is also applicable to asymmetric‐plan systems.
Dynamic response of buildings due to trains in underground tunnels
Authors: Balendra T. , Koh C. G. , Ho Y. C.
Published: April 2007

The interaction of a tunnel‐soil‐building system due to trains is investigated by a substructure technnique. The soil medium is assumed to be a viscoelastic halfspace. The method of wave function expansion is used to construct the displacement fields in terms of potentials. The total soil‐structure interaction problem is decomposed into a foundation radiation problem and a tunnel radiation problem. The impedance matrices for the corresponding substructure problems are obtained using a collocation technique. The steady state response of buildings for a given tunnel‐foundation geometry is determined using the impedance matrix. Hence, the response of the building to train loading at different speeds is evaluated and compared with allowable vibration limits.
Earthquake induced hydrodynamic pressure on axisymmetric offshore structures
Authors: Sun Keming , Nogami Toyoaki
Published: April 2007

The horizontal earthquake induced hydrodynamic pressure acting on the surface of axisymmetric offshore and coastal structures is explored. A semi‐analytical and semi‐numerical approach based on the use of a complete and non‐singular set of Trefftz functions is developed. Using this method, one can model accurately the compressibility of the sea water and gravity waves on the water surface. The proposed method shows a relatively simple and efficient approach. This is because the number of degrees of freedom in the matrix equation depends only on the number of selected Trefftz functions and because the discretization of the fluid domain into boundary elements is restricted to the structural surface only. This method is also easy to apply in engineering analysis of hydrodynamic pressure induced by an actual earthquake acceleration. Numerical examples are presented to illustrate the results obtained from this method. Several special interesting topics, such as the effects of the water compressibility, the gravity waves on the water surface and the geometrical shape of the structural surface, are also discussed.
Dynamic interaction between flexible strip foundations
Authors: Wang Y. , Rajapakse R. K. N. D. , Shah A. H.
Published: April 2007

This paper is concerned with the dynamic response of a system of flexible strip foundations resting in smooth contact with a homogeneous isotropic viscoelastic half space. An arbitrary number of foundations with different flexibilities and geometries subjected to time‐harmonic distributed loadings are considered in the formulation. The response of each strip foundation is governed by the classical plate theory and its transverse deflection is represented by an admissible function containing a set of generalized co‐ordinates. A coupled variational‐Green's function scheme is employed to establish the equations of motion of the strip foundation system. The numerical stability and convergence of the solution scheme are established. The influence of the foundation flexibility, distance between adjacent foundations and frequency of motion on the response of the foundation system is investigated in the numerical study.
An assessment of seaonc draft code for resilient sliding isolators
Authors: Mostaghel N. , Mortazavi A. R.
Published: April 2007

The displacement responses of rigid structures supported on resilient sliding isolation systems with various frictions to six different ground motions normalized to ground velocity levels from 1 to 25 in per sec are evaluated. Through the application of an equivalent damping procedure, the minimum required displacement capacities as dictated by the SEAONC draft code are also estimated. It is concluded that, even though the code displacement requirement is on the conservative side, the displacement capacity requirement is not excessive.
Dynamic behaviour of R/C highway bridges under the combined effect of vertical and horizontal earthquake motions
Authors: Saadeghvariri M. Ala , Foutch D. A.
Published: April 2007

Measurements of ground motions during past earthquakes indicate that the vertical acceleration can reach values comparable to horizontal accelerations or may even exceed these accelerations. Furthermore, measurements of structural response show the possibility of significant amplification in the response of bridges in the vertical direction that can be attributed to the vertical component of ground motion. In this study, the relative importance of the vertical component of ground motion on the inelastic response of R/C highway bridges is investigated. Particular emphasis is placed on modelling of the deck and piers to account for complex loading histories under combined vertical and horizontal earthquake motions. Analyses of actual bridges indicate that, in general, the vertical motion will increase the level of response and the amount of damage sustained by a highway bridge. Vertical motion generates fluctuating axial forces in the columns, which cause unstability of the hysteresis loops and increase the ductility demand. Furthermore, vertical motion can generate forces of high magnitude in the abutments and foundations that are not accounted for by the current seismic design guidelines. Thus, it is important to consider this component of the ground motion in the design of highway bridges, especially for those located in regions near seismic faults.
Periodic response of a rigid block resting on a footing subjected to harmonic excitation
Authors: Matsui Kunihito , Iura Masashi , Sasaki Toshimi , Kosaka Iku
Published: April 2007

This study presents the dynamic behaviour of a rigid block which rests on a footing supported by a spring and a dashpot on a rigid base. The response of the rigid body is examined carefully when the base is excited by a harmonic force. It is found that a periodic motion appears in three different modes: stick‐stick, stick‐slip and slip‐slip. The conditions that initiate the stick‐stick and slip‐slip modes are derived in explicit forms and the maximum sliding displacement is also obtained analytically. Useful dimensionless parameters are proposed for the presentation of the dynamic behaviour. The accuracy of results is confirmed by the response history computed by the Nigam‐Jennings method.
Ambient vibration measurements on a cable‐stayed bridge
Authors: Wilson John C. , Liu Tao
Published: April 2007

An extensive programme of full‐scale ambient vibration tests has been conducted to measure the dynamic response of a 542 m (centre span of 274 m) cable‐stayed bridge—the Quincy Bayview Bridge in Illinois. A microcomputer‐based system was used to collect and analyse the ambient vibration data. A total of 25 modal frequencies and associated mode shapes were identified for the deck structure within the frequency range of 0–2 Hz. Also, estimations were made for damping ratios. The experimental data clearly indicated the occurrence of many closely spaced modal frequencies and spatially complicated mode shapes. Most tower modes were found to be associated with the deck modes, implying a considerable interaction between the deck and tower structure. No detectable levels of motion were evident at the foundation support of the pier. The results of the ambient vibration survey were compared to modal frequencies and mode shapes computed using a three‐dimensional finite element model of the bridge. For most modes, the analytic and experimental modal frequencies and mode shapes compare quite well, especially for the vertical modes. Based on the findings of this study, a linear elastic finite element model appears to be capable of capturing much of the complex dynamic behaviour of the bridge with very good accuracy, when compared to the low‐level dynamic responses induced by ambient wind and traffic excitations.
Control of seismic response of turbomachin foundations
Authors: Pantelides C. P.
Published: April 2007

The safety of structures built in seismic regions can be improved by energy absorbing devices. Passive isolation systems such as base isolators are suitable for low‐rise structures, but they provide only a partial solution to the problem. Three active control techniques for reducing the dynamic response of machine supporting foundations using various control strategies are presented. The active tendon, active mass damper and active base control systems are studied for active control of machine foundations in seismic regions. Numerical simulations show that active control can reduce the dynamic response of turbomachine foundations under seismic loads. This reduction in dynamic response can limit damage to power plants during earthquakes and restore their operation in a short time.
Scattering of obliquely incident seismic waves by a cylindrical valley in a layered half‐space
Authors: Liu S. W. , Datta S. K. , Bouden M. , Shah A. H.
Published: April 2007

Three‐dimensional scattering of seismic waves by a cylindrical alluvial valley embedded in a layered half‐space is investigated by using the combination of the boundary integral representation and the finite element method. The surface displacements due to incident plane harmonic body waves (P, SV and SH) propagating at an arbitrary angle to the axis of the cylindrical valley are evaluated numerically for two semi‐elliptical alluvial valleys. The presence of the layer is found to have a strong effect on the amplification of the surface displacements in some cases. The three‐dimensional motion seems to be quite critical and may cause large amplification. The surface ground motion becomes significant when compared with corresponding free‐field motion as the wavelengths become comparable to the characteristic length of the valley. The maximum amplification always occurs atop the valley. Numerical results show that the amplitude and the amplification pattern of the surface displacement strongly depend upon the frequency, the angle and the type of the incident waves.
A simple error estimator and adaptive time stepping procedure for dynamic analysis
Authors: Zienkiewicz O. C. , Xie Y. M.
Published: April 2007

A simple local error estimator is presented for time integration schemes in dynamic analysis. This error estimator involves only a small computational cost. The time step size is adaptively adjusted so that the local error at each time step is within a prescribed accuracy. It is found that the estimator performs well under various circumstances and provides an economical adaptive process. Attempts to estimate the global time integration error are also reported.
Three‐dimensional analysis of spatially varying ground motions around a uniform canyon in a homogeneous half‐space
Authors: Zhang Liping , Chopra Anil K.
Published: April 2007

Department of Civil Engineering, University of California, Berkeley, CA 94720, U.S.A.

A direct boundary element method to determine the three‐dimensional seismic response of an infinitely‐long canyon of arbitrary but uniform cross‐section cut in a homogeneous viscoelastic half‐space is presented. The seismic excitation is represented by P, SV, SH or Rayleigh waves at arbitrary angles with respect to the axis of the canyon. The accuracy of the procedure and implementing computer program is demonstrated by comparison with previous solutions for the limiting case of two‐dimensional response, recently obtained three‐dimensional response results for infinitely‐long canyons, and three‐dimensional boundary method solutions presented in this paper for finite canyons.