Thermoelastic response of a cylinder in the generalised dynamical theory of thermoelasticity

Summary Using the generalised dynamical theory of thermoelasticity, thermoelastic problem for an isotropic infinite circular cylinder has been solved by approximate techniques. A two dimensional harmonic problem for a cylinder has also been considered and small amplitude vibrations of the circular cylinder have been studied further.     

Dynamic response of a staggered wall-beam structure

A method for the dynamic analysis of staggered wall-beam frames is developed using consistent mass terms which are derived and given in simple terms. The method uses effective stiffnesses for wall-beam elements developed in an earlier paper. Experiments using a nine storey 1 : 15 scale perspex model are described. The first three natural frequencies of the model were obtained using two methods: sinusoidal external excitation of the structure with the base fixed and white noise excitation employing a single degree-of-freedom shake table, in the latter method with and without the addition of mass throughout the model. Agreement between analytical predictions of the first three natural frequencies and mode shapes and experimentally determined values is considered satisfactory, particularly for the first two modes. The lumped mass assumption gave reasonable results for these two cases, whereas the consistent mass theory gave reasonable results for the first three natural frequencies.     

Dynamic response of a multi-layered poroelastic medium

An exact stiffness matrix method is presented to evaluate the dynamic response of a multi-layered poroelastic medium due to time-harmonic loads and fluid sources applied in the interior of the layered medium. The system under consideration consists of N layers of different properties and thickness overlying a homogeneous half-plane or a rigid base. Fourier integral transform is used with respect to the x-co-ordinate and the formulation is presented in the frequency domain. Fourier transforms of average displacements of the solid matrix and pore pressure at layer interfaces are considered as the basic unknowns. Exact stiffness (impedance) matrices describing the relationship between generalized displacement and force vectors of a layer of finite thickness and a half-plane are derived explicitly in the Fourier-frequency space by using rigorous analytical solutions for Biot's elastodynamic theory for porous media. The global stiffness matrix and the force vector of a layered system is assembled by considering the continuity of tractions and fluid flow at layer interfaces. The numerical solution of the global equation system for discrete values of Fourier transform parameter together with the application of numerical quadrature to evaluate inverse Fourier transform integrals yield the solutions for poroelastic fields. Numerical results for displacements and stresses of a few layered systems and vertical impedance of a rigid strip bonded to layered poroelastic media are presented. The advantages of the present method when compared to existing approximate stiffness methods and other methods based on the determination of layer arbitrary coefficients are discussed.     

Quasi-static transient response of a covered permeable inhomogeneous cylinder to a line current source

Summary Transient electromagnetic response of a cylindrical conductor covered by (a) an insulated and (b) a galvanically connected coaxial shell has been obtained. The exciting pulse is produced by switching off a long alternating current source. The study incorporates the influence of magnetic permeability contrast of the cylinder with the surrounding medium and also that of the inhomogeneity in the conductivity. The generalised initial value problem is significant in the study of certain geomagnetic anomalies. The results will also aid to the interpretation of induction prospecting data for elongated porphyry conducting mineral deposits.N.G.R.I. Contribution No. 71-280.     

Dynamic response of a pair of walls retaining a viscoelastic solid

Making use of a previously reported, simple, approximate method of analysis, a critical evaluation is made of the dynamic pressures and forces induced by horizontal ground shaking on a pair of infinitely long, parallel walls retaining a uniform viscoelastic solid. The walls are presumed to be rigid but elastically constrained against rotation at their base. The effects of both harmonic and earthquake-induced excitations are examined. The accuracy of the method is assessed by comparing its predictions for the special case of fixed-based walls with those obtained by an exact method, and comprehensive numerical data are presented which elucidate the underlying response mechanisms, and the effects and relative importance of the parameters involved. The parameters examined include the characteristics of the ground motion, the ratio of the distance between walls to the height of the contained material, and the flexibility of the rotational wall constraints. In addition to valuable insights into the responses of the systems investigated, the results presented provide a convenient framework for the analysis of more complex systems as well.     

Dynamic response of framed structures

A method for analysing plane frames subjected to dynamic forces or to ground motion is presented and illustrated by a numerical example. Numerical integration uses the approximation of constant acceleration in each time interval, as in Newmark's β-method with β = 1/4. In space, calculations are carried out storey by storey, as in Holzer's or Myklestad's methods in the case of harmonic vibrations.     

Dynamic response of pile groups embedded in a poroelastic medium

The dynamic response of pile groups embedded in a homogeneous poroelastic medium and subjected to vertical loading is considered. The piles are represented by compressible beam-column elements and the porous medium uses Biot's three-dimensional elastodynamic theory. The dynamic impedance of pile groups can be computed directly by using pile–soil–pile dynamic interaction factors. The axial forces and pore pressures along the length of pile groups are computed by superposition method, which greatly reduces the computational time for the direct analysis of pile groups. Parametric studies are conducted for various conditions of pile groups. The superposition method is proposed for the dynamic response analysis of pile groups that is computationally feasible for practical applications.     

Dynamic response of a submerged hemispherical shell to earthquake motions

The dynamic response to ground motion of hemispherical shells in a fluid, medium is studied numerically. In the analysis, linear thin shell theory is used and the fluid is assumed to be compressible and inviscid. The effect of the duration of the ground motion on the dynamic response is studied using two forcing functions, one with a very short duration and the other in the form of a Heaviside function. As special cases, dynamic responses of the shell in vacuo and of a rigid hemisphere in the fluid medium are investigated. The results are valid also for a ring-stiffened complete spherical shell accelerating in an acoustic medium.     

Dynamic response of a flexible plate on saturated soil layer

An analytical approach is developed to study the dynamic response of a flexible plate on single-layered saturated soil. The analysis is based on Biot's two-phased theory of poroelasticity and also on the classical thin-plate theory. First, the governing differential equations for saturated soil are solved by the use of Hankel transform. The general solutions of the skeleton displacements, stresses, and pore pressures, derived in the transformed domain, are subsequently incorporated into the imposed boundary conditions, which leads to a set of dual integral equations describing the corresponding mixed boundary value problem. These governing integral equations are finally reduced to the Fredholm integral equations of the second kind and solved by standard numerical procedures. The accuracy of the present solution is validated via comparisons with existing solutions for an ideal elastic half-space. Furthermore, some numerical results are presented to show the influences of the layer depth, the plate flexibility, and the soil porosity on the dynamic compliances.     

Dynamic response of a near-shore pile to lateral impact load

This paper presents the results of lateral impact load field tests conducted on a near-shore steel pipe pile vibro-driven into soft marine clay. Two series of tests are carried out, the first 1 week and the second 10 weeks after the vibro-driving. The pile is instrumented with an unconventional technique for field tests in marine environment which includes an accelerometer at the pile head, strain gauges and pore pressure transducers along the pile. Instruments are properly protected from marine environment and pile driving installation method. Tests are aimed at investigating the dynamic soil-water-pile interaction and determining the dynamic characteristics of the whole system at very small strain. The obtained results show the complex dynamic behaviour of the vibrating soil-water-pile system in terms of natural frequencies, damping and mode shapes. The variation in the dynamic behaviour in time, due to reconsolidation of soil subsequent to vibro-driving is also discussed. Furthermore, the horizontal dynamic impedance function of the whole system is derived from the experimental data over a wide frequency range and compared with that obtained from a numerical soil–pile interaction model.     

Dynamic response of a flexible pavement submitted by impulsive loading

The present paper introduces results from measurements on site using a falling weight deflectometer (FWD). This apparatus is used for non-destructive testing of damaged pavement in order to estimate the elastic modulus of each layer. The basin of deflection induced by a controlled load can be determined with precision and can reflect the behavior of the pavement structure. The interpretation of data generated by FWD leans on inverse analysis processes. Data from FWD combined with the thickness of layers inform on the evolution of the Young's modulus of each layer of the structure along the studied road profile. This information can be also used to estimate its lifespan and possible repairs to be carried out.     

Dynamic response of a piecewise circular tunnel embedded in a poroelastic medium

Recently, considerable efforts have been devoted to evaluation of seismic dynamic response of a circular tunnel. Conventional approaches have considered integral liners embedded in an elastic medium. In this study, we re-examine the problem with piecewise liners embedded in a porous medium. Surrounding saturated porous medium of tunnels is described by Biot's poroelastic theory, while the liner pieces and the connecting joints are treated as curved beams and characterized by curved beam theories. The scattered wave field in the porous medium is obtained by the wave function expansion method. The differential equations governing the vibration of a curved beam is discretized by the General Differential Quadrature (GDQ) method. The domain decomposition method is used to establish the global discrete dynamic equations for the piecewise tunnel. The surrounding soil and the tunnel are coupled together via the stress and the displacement continuation conditions which are implemented by the boundary collocation method. Numerical results demonstrate that the stiffness difference between the liner piece and the connecting joints has a considerable influence on the internal forces of the liner piece.     

Dynamic response analysis of a multiple-beam structure subjected to a moving load

In this study, the dynamic response of an elastically connected multi-beam structure subjected to a moving load with elastic boundary conditions is investigated. The boundary conditions and properties of each beam vary, and the difficulty of solving the motion equation is reduced by using a Fourier series plus three special transformations. By examining a high-speed railway (HSR) with mixed boundary conditions, the rationality for the newly proposed method is verified, the difference in simulated multiple-beam models with different beam numbers is explored, and the influence of material parameters and load speed on the dynamic response of multiple-beam structures is examined. Results suggest that the number of beams in the model should be as close to the actual beam number as possible. Models with an appropriate beam number can be used to describe in detail the dynamic response of the structure. Neglecting the track-structure can overestimate the resonant speed of a high-speed railway, simply-supported beam bridge. The effective interval of foundation stiffness (EIFS) can provide a reference for future engineering designs.

     

The response of a horizontal conducting cylinder embedded in a uniform earth for uniform and line current sources

The response of a horizontal conducting cylinder embedded in a uniform conducting earth is studied using mathematical models of uniform and line current source excitation for the period range 10 to 10⁴ s. The line current source is located at heights ranging from 100–750 km above the surface of the earth. From the calculated results, it is shown that for periods greater than 10³ s the ratioE _x /H _y at the surface of the earth for localized fields, such as the auroral and equatorial electrojet normally situated at heights of about 100 km, is considerably different from that for a uniform source. The results presented also show that the magneto-telluric method of geophysical prospecting for ore bodies in regions of the electrojet may not be very practicable for periods exceeding 10³ s.     

Dynamic response of a geotechnical rigid model container with absorbing boundaries

One of the major challenges encountered in earthquake geotechnical physical modelling is to determine the effects induced by the artificial boundaries of the soil container on the dynamic response of the soil deposit. Over the past years, the use of absorbing material for minimising boundaries effects has become an increasing alternative solution, yet little systematic research has been carried out to quantify the dynamic performance of the absorbing material and the amount of energy dissipated by it. This paper aims to examine the effects induced by the absorbing material on the dynamic response of the soil, and estimate the amount of energy reduced by the absorbing boundaries. The absorbent material consisted of panels made of commercially available foams, which were placed on both inner sides of end-walls of the soil container. These walls are perpendicular to the shaking direction. Three types of foam with different mechanical properties were used in this study. The results were obtained from tests carried out using a shaking table and Redhill 110 sand for the soil deposit. It was found that a considerably amount of energy was dissipated, in particular within the frequency range close to the resonance of the soil deposit. This feature suggests that the presence of foams provides a significant influence to the dynamic response of the soil. The energy absorbed by the boundaries was also quantified from integrals of the Power Spectral Density of the accelerations. It was found that the absorbed energy ranged between a minimum of 41% to a maximum of 92% of the input levels, depending mainly on the foam used in the test. The effects provided by the acceleration levels and depth at which the energy was evaluated were practically negligible. Finally, practical guidelines for the selection of the absorbing material are provided.     

双层岛式地铁车站结构地震反应分析

以深圳某双层两跨岛式地铁车站为工程背景,考虑水平地震和水平、竖向地震耦合2种工况,采用ANSYS分析软件,研究SSI(土与结构相互作用)效应下结构的水平位移特征和内力响应规律.结果表明:与水平地震工况相比,耦合地震作用下结构最大内力增幅较大,由于竖向惯性荷载作用,产生最大内力位置不同;周围土体介质的变形与结构在震动中的变形关系密切;沿车站侧墙高度的相对水平位移在2种地震工况作用下的变化不容忽视,不可忽略竖向地震的影响,耦合地震作用下的相对水平位移可用线性曲线拟合.研究成果可为地铁车站的抗震设计提供参考.     

Dynamic response of skew bridge decks

In this paper the dynamic response of a skew bridge deck has been investigated, treating it as an orthotropic plate and using the finite strip method. Employing the normal mode method, the response of the deck due to a moving force has been calculated. Williams' method has been used to accelerate the convergence of the solution. Numerical work has been done for different skew angles and speed ranges. In this study, the history curves and the maximum amplification spectra for deflection and bending moment are presented.     

Dynamic response of circular bridge decks

A method has been developed for the study of the dynamic response of curved bridge decks on the basis of plate equations in polar co-ordinates. A general solution for the forced motion of annular sector plates has been obtained by the method of spectral representation. The specific problem of a moving force on the bridge deck is discussed in detail. A method for obtaining the static response from dynamic analysis is suggested. Numerical results are presented to illustrate the influence of the speed of travel of the force and of the physical parameters of the bridge decks on the deformation. A detailed discussion on the numerical results is also included.     

Dynamic response of axisymmetric embedded foundations

The boundary element method is used to obtain dynamic stiffness functions of rigid cylindrical foundations embedded in a uniform or layered viscoelastic half-space. Dynamic stiffness functions of hemispherical foundations embedded in a uniform half-space are also computed. The direct integral equation formulation is used in combination with the complete space point load fundamental solution that is integrated numerically along the azimuthal coordinate. The approach is easy to implement because of the simplicity of the fundamental solution. The numerical results obtained by this method for cylindrical and hemispherical foundations are very close to corresponding published results obtained by different procedures. A parametric study shows the important effects of the Poisson's ratio on the dynamic stiffness functions of cylindrical foundations embedded in a uniform viscoelastic half-space. The effect of the bedrock compliance on the stiffness functions is also shown in the case of cylindrical foundations embedded in a soil layer that rests on a bedrock.