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Showing papers in "Earthquake Engineering & Structural Dynamics in 1984"


Journal ArticleDOI
TL;DR: In this paper, the dynamic response of three-dimensional rigid surface foundations of arbitrary shape is numerically obtained by placing the foundations on a linear elastic, isotropic and homogeneous half-space representing the soil medium and are subjected to either external dynamic forces or seismic waves of various kinds and directions.
Abstract: The dynamic response of three-dimensional rigid surface foundations of arbitrary shape is numerically obtained. The foundations are placed on a linear elastic, isotropic and homogeneous half-space representing the soil medium and are subjected to either external dynamic forces or seismic waves of various kinds and directions, with a general transient time variation. The problem is formulated in the time domain by the boundary element method and the response is obtained by a time step-by-step integration. Two examples dealing with three-dimensional rectangular foundations are presented in detail, together with comparisons with other methods, in order to document the accuracy of the method. The main advantages of the proposed method are that, unlike frequency domain techniques, it provides directly the transient response and forms the basis for extension to the case of non-linear behaviour.

177 citations


Journal ArticleDOI
TL;DR: In this article, the Lanczos vectors are obtained by an inverse iteration procedure in which orthogonality is imposed between the vectors resulting from successive iteration cycles, which provides for a very efficient time-stepping solution.
Abstract: A procedure for deriving the Lanczos vectors is explained and their use in structural dynamics analysis as an alternative to modal co-ordinates is discussed. The vectors are obtained by an inverse iteration procedure in which orthogonality is imposed between the vectors resulting from successive iteration cycles. Using these Lanczos vectors the equations of motion are transformed to tridiagonal form, which provides for a very efficient time-stepping solution. The effectiveness of the method is demonstrated by a numerical example.

156 citations


Journal ArticleDOI
TL;DR: In this paper, the available substructure method for the earthquake analysis of concrete gravity dams, including the dynamic effects of impounded water and the flexible foundation rock, is extended to include the effects of alluvium and sediments invariably present at the bottom of actual reservoirs.
Abstract: The available substructure method for the earthquake analysis of concrete gravity dams, including the dynamic effects of the impounded water and the flexible foundation rock, is extended to include the effects of alluvium and sediments invariably present at the bottom of actual reservoirs. Modelled approximately by a reservoir bottom that partially absorbs incident hydrodynamic pressure waves, these effects are incorporated into the continuum solution for the hydrodynamic pressure. The dam-water-foundation rock system is idealized as a two-dimensional system and analysed under the assumption of linear behaviour. An example earthquake analysis is presented to demonstrate the results obtained from the analytical procedure. Computation times for several cases illustrate the efficiency of the analytical procedure. In particular, the additional computation time required to include reservoir bottom absorption is shown to be very small.

147 citations


Journal ArticleDOI
TL;DR: In this article, a modal decomposition procedure based on the complex eigenvectors and eigenvalues of the system is used to derive general expressions for the spectral moments of response.
Abstract: The stationary response of multi-degree-of-freedom non-classically damped linear systems subjected to stationary input excitation is studied. A modal decomposition procedure based on the complex eigenvectors and eigenvalues of the system is used to derive general expressions for the spectral moments of response. These expressions are in terms of cross-modal spectral moments and explicitly account for the correlation between modal responses; thus, they are applicable to structures characterized with significant non-classical damping as well as structures with closely spaced frequencies. Closed form solutions are presented for the important case of response to white-noise input. Various quantities of response of general engineering interest can be obtained in terms of these spectral moments. These include mean zero-crossing rate and mean, variance and distribution of peak response over a specified duration. Examples point out several instances where non-classical damping effects become significant and illustrate the marked improvement of the results of this study over conventional analysis based on classical damping approximations.

145 citations


Journal ArticleDOI
TL;DR: In this article, two equivalent semi-discrete formulations are presented for the problem of the transient response of soil-structure interaction systems to seismic excitation, considering linear behaviour of the soil material and arbitrary non-linear structural properties.
Abstract: Two equivalent semi-discrete formulations are presented for the problem of the transient response of soil-structure interaction systems to seismic excitation, considering linear behaviour of the soil material and arbitrary non-linear structural properties. One formulation results in a direct method of analysis in which the motion in the structure and the entire soil medium, rendered finite by an artificial absorbing boundary, is determined simultaneously. The other represents a substructuring technique in which the structure and the soil are analysed separately. The forces induced in the discretized system by the incident seismic motion are obtained as part of the general formulation by using the free-field motion of the unaltered soil as the earthquake input. It is shown that these forces act within the soil region in the direct method, but only on the soil-structure interface in the substructure formulation. Both sets of forces, however, involve only the displacements and tractions acting on the fictitious surface in the unaltered (linear) soil which coincides with the soil-structure interface of the complete system. It is shown, further, that the free-field displacements alone define a minimal set of data for evaluating the seismic response of the structure, since the tractions and displacements on that surface are interrelated. In practice, the minimal set must be obtained by extrapolating the available information, as the free-field ground motion at a site is usually specified at a single reference point.

108 citations


Journal ArticleDOI
TL;DR: In this article, the authors present the main features of the computer program THGE for the construction of an accelerogram whose response spectrum matches a design spectrum, and discuss some related issues, such as response spectrum calculations, the statistical dependence between the three earthquake components, duration of the time history, variability of the secondary response to various samples, and the generation of an acceleration whose response spectra envelop a set of design spectra.
Abstract: Based on the main features of the computer program THGE, this paper reviews the techniques which are available for the construction of an accelerogram whose response spectrum matches a design spectrum. First, a sample accelerogram is generated as the product of the stationary random sequence by a deterministic shape function. It is assumed that the spectral properties of the stationary process have been determined in a previous step, in order to lead to the design spectrum as expected maximum responses of a set of single degree of freedom oscillators. The principal properties of the Fast Fourier Transform which is used for this first step are reviewed. The paper then describes th procedures which are available to improve agreement between the response spectrum and the target. It also discusses some related issues, such as response spectrum calculations, the statistical dependence between the three earthquake components, duration of the time history, variability of the secondary response to various samples, and the generation of an accelerogram whose response spectra envelop a set of design spectra. The point of view adopted is the one of the structural engineer.

94 citations


Journal ArticleDOI
TL;DR: In this article, the effects of transient foundation uplift on the earthquake response of flexible structures are investigated, based on the response spectra presented for several sets of system parameters, including earthquake intensity, structural slenderness ratio, ratio of foundation mass to structural mass, foundation flexibility and p-δ effects.
Abstract: The effects of transient foundation uplift on the earthquake response of flexible structures are investigated. The structural idealization chosen in this study is relatively simple but it incorporates the most important features of foundation uplift. In its fixed base condition the structure itself is idealized as a single-degree-of-freedom system attached to a rigid foundation mat which is flexibly supported. The flexibility and damping of the supporting soil are represented by a Winkler foundation with spring-damper elements distributed over the entire width of the foundation. Based on the response spectra presented for several sets of system parameters, the effects of foundation-mat uplift on the maximum response of structures are identified. The influence of earthquake intensity, structural slenderness ratio, ratio of foundation mass to structural mass, foundation flexibility and p-δ effects on the response of uplifting structures is also investigated.

93 citations


Journal ArticleDOI
TL;DR: In this paper, an analytical representation of the bilinear hysteretic characteristic is presented using this representation, and the response of a single-degree-of-freedom (SFO) bilinearly hystoretic system subjected to non-stationary random excitation is examined by equivalent linearization.
Abstract: An analytical representation of the bilinear hysteretic characteristic is presented Using this representation, the response of a single-degree-of-freedom bilinear hysteretic system subjected to non-stationary random excitation is examined by equivalent linearization An ordinary differential equation is derived for the covariance matrix of the response Numerical examples are presented and the accuracy of the approach is demonstrated Extension of the approach to a wider class of hysteretic systems is discussed

50 citations


Journal ArticleDOI
TL;DR: In this paper, the steady state solution for two parallel under ground tunnels of circular cross-section subjected to incident plane harmonic SH-waves is obtained in closed form, by using the method of wave function expansion.
Abstract: The steady-state solution for two parallel under ground tunnels of circular cross-section subjected to incident plane harmonic SH-waves is obtained in closed form, by using the method of wave function expansion. The image technique is employed to account for the reflection of waves at the ground surface. Numerical studies are carried out to determine the influence of spacing between the tunnels on the shear stresses in concrete and steel linings.

43 citations


Journal ArticleDOI
TL;DR: The first known solution of the title problem is presented in this article, where algebraic polynomials are used to form the set of trial functions, and the condition that all three components of displacement be zero at the four corners is straightforwardly enforced.
Abstract: The first known solution of the title problem is presented. The Ritz method is used, with algebraic polynomials forming the set of trial functions. The condition that all three components of displacement be zero at the four corners is straightforwardly enforced. Numerical studies show that the convergence is relatively slow, requiring more terms than for shells which are completely free. The class of problems studied includes independent, constant curvature in each of the directions parallel to the edges, yielding vibration modes which fall into one of four symmetry classes, with symmetry or antisymmetry of the displacements existing with respect to each of the two symmetry axes of the problem. Detailed results are given for the frequencies and mode shapes of the first two modes of each symmetry class for shells having square planform and circular cylindrical, spherical and hyperbolic paraboloidal curvatures. Accuracy of the results is partially established by comparison with other previously published, accurate results for the corner supported flat square plate.

41 citations


Journal ArticleDOI
TL;DR: In this article, the authors extended the use of Ritz vectors to the solution of wave propagation and foundation response problems and applied them to one-, two-and three-dimensional problems.
Abstract: The accuracy of a numerical method is demonstrated for the dynamic analysis of large complex finite element systems in which the spatial distribution of the loading is constant. The method is based on the use of a special class of Ritz vectors which were previously proposed and can be generated with minimum numerical effort. The purpose of this paper is to extend the use of these vectors to the solution of wave propagation and foundation response problems. The method is applied to one-, twoand three-dimensional problems in order to illustrate the efficiency and accuracy of the technique. Unless it is necessary to evaluate the very high-frequency behaviour of a structural system, it is shown that a small number of Ritz vectors will produce excellent results. Therefore, they can be very effective in the solution of three-dimensional soil-structure systems subjected to earthquake loading.

Journal ArticleDOI
TL;DR: In this paper, a modified procedure for evaluating the dynamic transient response of a classically damped linear system from its corresponding steady-state response is presented, which also appears to be highly efficient for non-classical damped systems of the type encountered in studies of soil-structure interaction.
Abstract: After reviewing briefly a recently proposed procedure for evaluating the dynamic transient response of a classically damped linear system from its corresponding steady-state response, a modified procedure is presented which also appears to be highly efficient for non-classically damped systems of the type encountered in studies of soil-structure interaction. The concepts involved are developed by reference to viscously damped single-degree-of-freedom systems, and numerical solutions are included to illustrate the accuracy and efficiency of the proposed procedure and its superiority over the classical Discrete Fourier Transform approach.

Journal ArticleDOI
TL;DR: In this paper, a simple and efficient finite rotor element based on a Galerkin formulation is proposed to model the rotor and the effects of disks and flywheels mounted on the rotor are also included in the analysis.
Abstract: The seismic analysis of a rotor-bearing system is presented in the time domain. The governing equations of motion for the rotor are derived including the effects of rotatory inertia, shear deformation, gyroscopic effects, axial force, axial torque, stiffness and damping provided by the lubricants in the bearings, base translation and base rotation. A simple and efficient finite rotor element based on a Galerkin formulation is proposed to model the rotor. The effects of disks and flywheels mounted on the rotor are also included in the analysis. An example problem for a rotor-bearing system is solved using El Centro earthquake data. Four cases are investigated that will permit one to study the influence of spin, base rotation, comparison between rigid body model and beam model and the influence of axial force and axial torque. The results of the above study show that the gyroscopic effects amplify the response of the rotor-bearing system. The base rotations of the rotor-bearing system under seismic excitation contribute significantly to the response.

Journal ArticleDOI
TL;DR: In this paper, a non-linear elasticity model was used to predict near-field ground motions in alluvial deposits, using local soil properties and a reasonable hypothesis for motion at the base of the superficial layers in question that included large values of acceleratio for highfrequency shear waves.
Abstract: Recordings of recent strong earthquakes obtained on alluvial sites show that the maximum horizonta accelerations tend towards a limit of about 0-45 to 0-50g, associated with large displacements. By contrast, vertical accelerations do not appear to be subject to such a limit (1.7g for the 1979 Imperial Valley earthquake). Theoretical linear elasticity models, when applied to superficial layers of low strength, seem to be inadequate for the prediction of near-field ground motions in alluvial deposits. A good approximation for the horizontal component of certain Imperial Valley records was, however, obtained through a non-linear approach, using local soil properties together with a reasonable hypothesis for motion at the base of the superficial layers in question that included large values of acceleratio for high-frequency shear waves.

Journal ArticleDOI
TL;DR: In this article, the same type of boundary matrices which have a clear physical interpretation are identified in the three boundary-element methods, each of which is illustrated with a simple static example.
Abstract: Starting from a weighted-residual formulation, the various boundary-element methods, i.e. the weighted-residual technique, the indirect boundary-element method and the direct boundary-element method, are systematically developed for the calculation of the dynamic-stiffness matrix of an embedded foundation. In all three methods, loads whose analytical response in the unbounded domain can be determined are introduced acting on the continuous soil towards the region to be excavated. In the weighted-residual technique and in the indirect boundary-element method, a weighting function is used; in the latter case, it is selected as the Green's function for the surface traction. In the direct boundary-element method, the surface traction along the structure-soil interface is interpolated. The same type of boundary matrices which have a clear physical interpretation are identified in the three formulations, each of which is illustrated with a simple static example. The indirect boundary-element method leads to the most accurate results. The guaranteed symmetry and the fact that the displacement arising from the applied loads can easily be calculated and compared to the prescribed displacement makes the indirect boundary-element method especially attractive for calculating the dynamic-stiffness matrix of the soil. Instead of calculating the dynamic-stiffness matrix of the embedded foundation with the boundary-element method, it can be determined as the difference of those of the regular free field and of the excavated part. The calculation of the former does not require the Green's function for the surface traction. The dynamic stiffness of the excavated part can be calculated by the finite-element method.

Journal ArticleDOI
TL;DR: In this paper, a linear multistorey structure with a seismic base isolation system consisting of rubber bearings and frictional elements is considered, and the non-linear equations of motion are derived for the first mode vibration and the stochastic response to a white noise ground acceleration is determined.
Abstract: A linear multistorey structure with a seismic base isolation system consisting of rubber bearings and frictional elements is considered. The non-linear equations of motion are derived for the first mode vibration and the stochastic response to a white noise ground acceleration is determined. Based on this response, suitable objective functions are defined and the optimum design of the isolation system is performed. It is shown that a small amount offriction increases the effectiveness of the system compared with the same system but without frictional elements.

Journal ArticleDOI
TL;DR: In this article, a thin shell model has been used for the pipeline, which is assumed to be lying in an infinite isotropic homogeneous elastic medium, in order to allow for the possible motion of the pipe out of phase with the surrounding ground.
Abstract: Vibration of buried pipelines induced by moving axial and radial loads has been studied in this paper. A thin shell model has been used for the pipeline, which is assumed to be lying in an infinite isotropic homogeneous elastic medium. In order to allow for the possible motion of the pipe out of phase with the surrounding ground a very thin layer of viscoelastic material is assumed to separate the pipe from the ground. Calculations indicate the presence of the interfacial viscoelastic layer does not influence the pipe response in a significant manner. So all the numerical results presented here are for the case when the pipe is assumed to be perfectly bonded. These show that the maximum pipewall displacements and stresses occur in a soft soil at long wavelengths.

Journal ArticleDOI
TL;DR: In this article, the authors derived the Green's influence functions for a linearly distributed load acting on part of a layered elastic halfplane on a line which is inclined to the horizontal.
Abstract: Green's influence functions are derived for a linearly distributed load acting on part of a layered elastic halfplane on a line which is inclined to the horizontal. Using these Green's functions as fundamental solutions in the boundary-element method, the dynamic-stiffness matrices of the unbounded soil with excavation, of the excavated part and of the free field are calculated. The indirect boundary-element method using distributed loads and no offset leads to more accurate results than the weighted-residual technique and the direct boundary-element method. At the natural frequencies of the undamped excavated part built-in along the structure-soil interface, the spring coefficients associated with the dynamic-stiffness matrices of the excavated part and of the free field will become infinite. If the dynamic-stiffness matrix of the soil with excavation is calculated as the difference of that of the free field and that of the excavated part, the difference of two large numbers will arise in the vicinity of these frequencies. A consistent discretization must then be used. In particular, the dynamic-stiffness matrix of the embedded part cannot be determined by the finite-element method in this case. A parametric study is performed for the dynamic-stiffness matrix of the free field for a rectangular foundation embedded in a halfplane and in a layer built-in at its base; the aspect ratio and the damping of the soil are varied.

Journal ArticleDOI
TL;DR: In this paper, a non-linear finite element model for plain masonry structures under lateral static loads and seismic base inputs is presented, where three superimposed elasto-plastic shear elements are used in order to approximate the typical force-displacement curve for masonry.
Abstract: A non-linear finite element model for plain masonry structures under lateral static loads and seismic base inputs is presented. Three super-imposed elasto-plastic shear elements are used in order to approximate the typical force-displacement curve for masonry. Material properties are identified with respect to results of shear tests on single piers. Modelling of entire structures is then performed and the numerical results are satisfactorily checked against the experimental outputs of static and shaking table tests of simple 1 and 2 storey buildings. The out of plane behaviour of walls is accounted for by means of a simplified method.

Journal ArticleDOI
TL;DR: In this article, an analytical method based on matrix perturbation theory is developed whereby a simple estimate can be obtained of the maximum dynamic response of lightly damped, light equipment (modelled as a n(2)-degree-of-freedom system) attached to a structure subjected to ground motion or impact.
Abstract: An analytical method, based on matrix perturbation theory, is developed whereby a simple estimate can be obtained of the maximum dynamic response of lightly damped, light equipment (modelled as a n(2)-degree-of-freedom system) attached to a structure (modelled as a n(1)-degree-of-freedom system) subjected to ground motion or impact. A natural frequency of the equipment is considered close or equal to a natural frequency of the structure. It is assumed that the information available to the designer is a time history of the ground motion or impact, or an associated design spectrum; the fixed base modal properties of the structure; and the fixed base modal properties of the equipment. The method employed avoids the direct conventional analysis of a n(2) + n(1)-degree-of-freedom system either by modal or by matrix time-marching methods; as well as errors in estimates of peak response due to the possible unreliability of numerical schemes because of the lightness of the equipment, or due to uncertainty as to the appropriate procedure for summing the contributions of the two closely spaced modes which occur in the system. The proposed procedure is demonstrated for an example equipment-structure system. Computed results based on the method are in close agreement with results obtained through a Newmark time-integration scheme.

Journal ArticleDOI
TL;DR: In this paper, the sliding behavior of a rigid mass supported on a randomly vibrating foundation through a non-symmetric Coulomb-friction contact is studied both analytically and by numerical simulation.
Abstract: The sliding behaviour of a rigid mass supported on a randomly vibrating foundation through a non-symmetric Coulomb-friction contact is studied both analytically and by numerical simulation. The analysis is based on a stationary solution of the associated Fokker-Planck equation, and makes use of equivalent linearization and of a suitable decomposition of the non-zero mean non-stationary sliding process. It is shown that the analytical results yield several exact asymptotic expansions for both small and large values of time. An extensive Monte Carlo type numerical simulation study produces non-stationary response statistics which are in very good accord with the analytical results. Furthermore, it is found that Gumbel's Extreme Value Distribution reproduces with remarkable accuracy the observed cumulative frequency of maximum slip displacement. The results of this paper may find application in seismic design of embankment dams, earth retaining walls and base ‘isolation’ systems.

Journal ArticleDOI
TL;DR: In this paper, the Galerkin method of weighted residuals is used to determine the frequencies and associated mode shapes of asymmetric shear wall-frame structures, and the governing equations are formulated using the continuum approach by idealizing the structure as a shear-flexure beam.
Abstract: The Galerkin method of weighted residuals is used to determine the frequencies and associated mode shapes of asymmetric shear wall-frame structures. The governing equations are formulated using the continuum approach by idealizing the structure as a shear-flexure beam. Varying properties along the height of the building are considered. The effect of translational, rocking and torsional flexibilities of the foundation on the natural frequencies is also investigated. The method presented herein utilizes polynomial and transcendental displacement functions, and is found to be simple, versatile and efficient.

Journal ArticleDOI
TL;DR: In this paper, the influence of precast concrete panels on lateral and torsional stiffness of a 25-storey building was investigated, and a modified cladding panel connection was developed based on previously reported studies for panelized construction.
Abstract: Precast concrete panels form attractive facades for steel frame buildings and are generally regarded as non-structural by structural engineers. However, panels have been found to add lateral stiffness until their capacity or that of their connections is exceeded. Consequently, the computed dynamic response based on a model of the structural framing alone may be quite different from that experienced by the actual structure. As a case study, the influence of precast concrete panels on lateral and torsional stiffness of a 25-storey building was investigated. The effect of cladding on dynamic properties and linear seismic response was explored by varying panel stiffness. Cladding stiffness was added to the bare frame model until analytical frequency values matched vibration test results. Then, using the cladding stiffness values obtained, an accidental eccentricity between centres of mass and rigidity at each floor level was imposed and linear seismic response computed. Torsional response effects were increased substantially. Finally, a modified cladding panel connection was developed based on previously-reported studies for panelized construction. The influence of the proposed connection on overall structural response was determined for different ground motion inputs.

Journal ArticleDOI
TL;DR: In this paper, the effect of topography and subsurface inhomogeneity on surface motion is investigated in the case of Rayleigh waves, and a new hybrid method combining a particle model with a finite element method is proposed.
Abstract: The effect of topography and subsurface inhomogeneity on surface motion is investigated in the case of Rayleigh waves. In the previous paper, the same effect was investigated in the case of SV waves. Several types of topography, such as cliffs both with and without a soft layer at the foot of the slope, are considered. Computations are made using a new hybrid method combining a particle model with a finite element method. In cases of harmonic Rayleigh waves, surface motions with amplitudes as large as 1.5 to 5 times the horizontal surface displacement of the incident Rayleigh waves are produced near the slope and the sloping interface. When a Rayleigh wave propagating through a hard single-layered ground encounters a sloping interface where hard ground and soft ground make contact with each other, Rayleigh waves having two different, phase velocities are produced and they correspond to the fundamental mode, and the first mode determined by Haskell's method. In addition, the transient response when Rayleigh waves propagate through the cliff is also simulated. Assuming the vertical component of the Tokachi-oki Earthquake (1968) measured on the surface to be a Rayleigh wave, the incident Rayleigh wave can be obtained by a Fourier synthesis of eigenfunctions of Rayleigh waves.

Journal ArticleDOI
TL;DR: In this article, the effect of the foundation flexibility on the coupled lateral-torsional response of single-storey buildings excited by translational ground motion is investigated, and it is concluded that for a particular range of values of these parameters (representing most cases of actual buildings) their effect on the coupling of lateral and torsion response is not qualitatively affected by increases in the flexibility of the base medium.
Abstract: The work presented in this paper investigates the effect of the foundation flexibility on the coupled lateral-torsional response of single-storey buildings excited by translational ground motion. The eccentricity between the centre of mass and the centre of resistance is considered to be the only cause of coupling of the lateral and torsional response of the building. The study is confined to the steady-state response of rigidly supported and flexibly supported torsionally coupled buildings subjected to harmonic free-field ground displacement perpendicular to the direction of the eccentricity. In the case of the flexibly supported building the foundation medium is assumed to be an elastic homogeneous isotropic half-space. The effect of the controlling parameters on lateral-torsional coupling is investigated. It is concluded that for a particular range of values of these parameters (representing most cases of actual buildings) their effect on the coupling of lateral and torsional response is not qualitatively affected by increases in the flexibility of the foundation medium.

Journal ArticleDOI
TL;DR: In this article, a comparison of results between a detailed finite element analysis and several simplified models for hand calculation of buried tunnels is carried out, where the free field motions and the interaction motions are superimposed.
Abstract: Seismic analysis of buried tunnels is considered herein. A comparison of results is carried out between a detailed finite element analysis and several simplified models for hand calculation. The finite element analysis is conducted by superimposing the free field motions and the interaction motions. The latter are calculated in a plane strain geometry taking into account the influence of adjacent structures with an approximation for 3-D effects and for soil non-linearities. Simplified models give, in general, conservative results, although better approximations are obtained by modelling the tunnel bends, where stress concentration occurs.

Journal ArticleDOI
TL;DR: In this paper, the Rayleigh-Ritz method with B-spline functions was used for vibration analysis of continuous skew plates with intermediate supports. But the results were compared with existing results based on other numerical methods and were in good agreement.
Abstract: This note presents vibration analysis of continuous skew plates with intermediate supports by the Rayleigh-Ritz method with B-spline functions. The accuracy of the present method is shown in a few typical cases. The results are compared with existing results based on other numerical methods and found to be in good agreement. Natural frequencies of continuous skew plates with several elastic point supports are also analysed for different skew angles and for different stiffnesses of point supports.

Journal ArticleDOI
TL;DR: In this article, the response of the ground is simulated using a hybrid method which combines a particle model and finite element method (FEM), which is in good agreement with observed ones.
Abstract: Observation has been conducted on soft surface ground with a sloping basement to clarify the effects of lateral inhomogeneity on ground motions and strains induced by seismic waves and to examine the frequency characteristics of the ground surface motions. The scattered Rayleigh wave from the vicinity of the sloping basement has been detected on seismograms and is observed to have a large influence on the ground motions and strains. In this paper the response of the ground is simulated using a hybrid method which combines a particle model and finite element method (FEM). The computed seismograms are in good agreement with observed ones. It is found from the calculations that large ground strains are produced by the scattered Rayleigh waves as well as by the incident shear waves in the surface ground overlying the sloping basement. In addition, the effects of lateral inhomogeneity on an embedded pipeline are examined. The present results are considered to be significant from the viewpoint of earthquake engineering.

Journal ArticleDOI
TL;DR: In this paper, a base-isolated building is modeled as a rigid block with tributary masses supported on massless elastomeric rubber bearings placed at a constant elevation below the center of mass.
Abstract: A base-isolated building is liable to have a small horizontal eccentricity between the centre of mass of the superstructure and the centre of rigidity of the supporting bearings. In seismic analysis, the structure is modelled as a rigid block with tributary masses supported on massless elastomeric rubber bearings placed at a constant elevation below the centre of mass. This simplified system has three degrees of freedom: two translations and one rotation in the vertical plane. The investigation of the dynamic behaviour of a base-isolated building is carried out for both the detuned and the perfectly tuned cases. In the detuned case, the natural frequencies of the system are assumed to be well separated. In the perfectly tuned case, the uncoupled rocking frequency is assumed to be identical to the vertical translational frequency, which may result from an unusual mass distribution and/or an extreme aspect ratio of the superstructure. Perturbation methods are implemented in finding the dynamic characteristics for both cases. However, the dynamic response of the perfectly tuned case is the major concern in this investigation. The Green's functions for the displacement response of the three-degree-of-freedom system are derived for both the undamped and damped conditions. The response spectrum modal superposition method is used in estimating the maximum acceleration response. A simple method, accounting for the effect of closely spaced modes, is proposed for combining modal maxima and results in an approximate solution corresponding to a single-degree-of-freedom system. This approximate solution may be used for the preliminary design of a base-isolated structure. Numerical results for a base-isolated building subjected to the vertical component of the El Centro earthquake of 1940 were carried out for comparison with these analytical results. The proposed modal combination method showed superiority over the conventional Square Root of the Sum of the Squares method in estimating maximum responses. The results also indicated that the approximate single-degree-of-freedom system yields accurate estimations. It is shown that the effect of rocking coupling on the vertical response of base-isolated structures subjected to transient loadings, such as earthquake motions, can generally be neglected as a result of the combined effects of the time lag between the maximum translational and rotational responses and the influence of damping in the isolation system, which for elastomeric bearings can be as high as 8 to 10 per cent of critical.

Journal ArticleDOI
TL;DR: In this paper, the authors evaluate les performances of modeles mathematiques valables de propagation of l'onde sismique en prenant les donnees des dommages actuels de le tunnel ferroviaire.
Abstract: Lors de ce seisme le tunnel ferroviaire a une seule voie de Inatori au Japon a ete serieusement endommage. Ces deteriorations etaient principalement causees par la faille principale et une faille subsidiaire qui a traverse le tunnel. On evalue les performances de modeles mathematiques valables de propagation de l'onde sismique en prenant les donnees des dommages actuels de ce tunnel. L'etude a aussi pour but de contribuer a un procede de calcul parasismique de tunnel dans la region de la source en estimant de ses deformations utilisant le modele mecanique de la faille