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1.
H. Wada 《地震工程与结构动力学》1984,12(2):169-179
Transient flexural vibrations of an elastic column supported by an elastic half-space are investigated analytically under the condition that an arbitrarily shaped free-field lateral acceleration is given as an input. Applying the Timoshenko theory to the column and making use of Laplace transformations with respect to time and numerical inverse Laplace transformations, the time histories of the column free end acceleration are presented. Numerical results obtained from the Timoshenko theory are compared with those of a previous paper1 (applying the Bernoulli-Euler theory to the column), and the effects of column slenderness and foundation stiffness on the transient flexural vibrations of the column are clarified. 相似文献
2.
This paper examines the axisymmetric torsional vibrations of an elastic pile and a hemispherical foundation embedded in a homogeneous elastic half-space. The embedded foundation–half-space system is decomposed into an extended half-space and a fictitious foundation. The deformations of the fictitious system are specified by an admissible function containing a set of generalized coordinates. The Lagrangian equations of motion are used to determine these coordinates associated with the assumed displacement function. Numerical results are presented for torsional impedance of an elastic pile and a hemisphere to illustrate the effects of relative flexibility and geometry. By employing certain simplifications on the pile–half-space system an approximate closed form solution is presented for the torsional impedance of an elastic pile. 相似文献
3.
The response of a rigid rectangular foundation block resting on an elastic half-space has been determined by considering first the displacement functions for any position on the surface of an unloaded half-space due to a harmonic point force. The influence of the foundation has been taken into account by assuming a relaxed condition at the interface, i.e. a uniform displacement under the foundation and that the sum of the point forces must equal the total applied force. The three motions of vertical, horizontal and rocking have been considered and numerical values for the in-phase and the quadrature components of the displacement functions are presented for a Poisson's ratio of 0.25. The effect of the mass and inertia of the foundation can be allowed for by an impedance matching technique. Response curves and non-dimensional resonant frequency curves are given for a square and a rectangular foundation for different mass and inertia ratios and for several values of Poisson's ratio. These curves are for design purposes and are an addition to similar published curves for circular and infinitely long rectangular foundations. Some of the calculated results have been verified by a laboratory experiment. 相似文献
4.
An alternative technique to obtain the dynamic response of a massless rigid circular foundation resting on a uniform elastic half-space when subjected to harmonic plane waves is presented. The technique relies on the use of an integral representation involving the free-field ground motion and the contact tractions obtained in the course of calculating the dynamic force–displacement relationship of the foundation for external forces. Tables listing the translational and rotational components of the response of the foundation for non-vertically incident SH, P, SV and Rayleigh waves are presented. 相似文献
5.
The fundamental solution for a periodic point force in the interior of a three-dimensional, homogeneous, isotropic, elastic half-space is derived. The method of synthesis and superposition is employed to obtain the solution in the Laplace transform as well as the frequency domain. These correspond to the dynamic equivalent of Mindlin's static half-space point force solutions. It is reduced, for certain limiting conditions, to the dynamic equivalent of Boussinesq's and Cerruti's problems of a normal and tangential periodic point force respectively, on the boundary of a half-space. Also, static solutions of Mindlin, Boussinesq and Cerruti are recovered for small frequency parameters. Finally, results are presented and compared with other available solutions. 相似文献
6.
Sakti Kanta Chakrabarty 《Pure and Applied Geophysics》1973,102(1):73-77
Summary The response of an elastic half-space with a non-homogeneous surface layer due to aSH-source operating in the non-homogeneous layer of an elastic half-space have been studied. The elastic and physical constants vary exponentially in the surface layer. The surface displacement consists of several integrals. On approximate evaluation of these integrals, they are identified as direct or reflected pulses. 相似文献
7.
Marijan Dravinski 《地震工程与结构动力学》1983,11(3):313-335
Scattering of plane harmonic SH, P, SV and Rayleigh waves by several inclusions of arbitrary shape, completely embedded into an elastic half-space, is considered. Perfect bonding between the half-space and the inclusions is assumed. The problem is investigated for linear, isotropic and homogeneous elastic materials. The displacement field is evaluated throughout the elastic medium so that the continuity conditions between the half-space and the inclusions are satisfied in mean-square sense. Numerical results of the surface displacement field are evaluated for single and two elliptic inclusions. The results show the following: (a) presence of a subsurface inhomogeneity may lead to large amplifications of the surface ground motion; (2) different surface displacement patterns emerge for different incident waves; (3) the presence of an additional inclusion may change significantly the surface displacement response of a single inclusion; (4) the surface motion extremes strongly depend upon (i) angle of incidence; (ii) frequency of incident field; (iii) embedment depth of the inclusions; (iv) separation distance between the inclusions; (v) material properties of the half-space and the inclusions; and (vi) location of observation point on the surface of the half-space. 相似文献
8.
Based on the analytical layer-element method, an analytical solution is proposed to determine the dynamic interaction between the elastic circular plate and transversely isotropic multilayered half-space. The dynamic response of the elastic circular plate is governed by the classical thin-plate theory with the assumption that the contact surface between the plate and soil is frictionless. The total stiffness matrix of the transversely isotropic multilayered half-space is acquired by assembling the analytical layer-element of each soil layer with the aid of the continuity conditions between adjacent layers. According to the displacement condition of coordination between the plate and soil, the dynamic interaction problem is reduced to that of multilayered transversely isotropic half-space subjected to axisymmetric harmonic vertical loading. Some numerical examples are given to study the vertical vibration of the plate, and the results indicate that the dynamic response of elastic circular plate depends strongly on the material properties of the soils, the rigidity of the plate, the frequency of excitation and the external load form. 相似文献
9.
G. B. Warburton 《地震工程与结构动力学》1978,6(6):535-556
The soil-structure system is modelled as a uniform vertical beam, which terminates in a base or foundation mass; this mass is attached to the surface of an elastic half-space. Using known force-displacement relations for the coupled vibrations of a rigid disc on an elastic half-space, the natural frequencies and response to a transverse harmonic force, applied at the tip of the beam, are determined through a continuum approach. Effectively the problem reduces to a beam with frequency-dependent boundary conditions. A parametric study shows that changes in the three ratios, Young's modulus for the beam to that for the half-space, the radius of the base mass to the length of the beam, L, and the second moment of area of the beam cross-section/L4, cause large variations in the maximum response, which due to interaction can be considerably smaller or larger than that for a comparable fixed-base cantilever beam. This dynamic behaviour can be explained by considering the variation of natural frequencies, mode shapes and modal damping factors with these ratios. A brief study of the response of the structure to a free-field harmonic acceleration, applied at the soil-structure interface, suggests that interaction depends upon material and geometric properties of the system, rather than on the nature of the excitation. 相似文献
10.
A three-layer elastic-gravitational fault displacement model using dislocation theory has been developed and used to examine the effect of layering of earth elastic moduli on surface and subsurface displacement fields for a vertical strike-slip fault. The model has been used to examine the effect of depth variation of elastic properties at coseismic and postseismic time scales. For pure strike-slip motion the effect of gravity on coseismic and postseismic horizontal deformation is negligible. For coseismic deformation the model predicts that (for constant Poisson's ratio) an increase in elastic moduli with depth attenuates the displacements within the upper layers with respect to displacement distribution for a uniform half-space, while an inclusion of a soft layer between the top layer and lower half-space amplifies upper layer displacements. The effect of variation in Poisson's ratio on surface and subsurface displacements has also been examined.The effect of postseismic stress relaxation on surface and subsurface displacements for a three-layer model has been calculated and compared with that of a uniformly relaxed half-space model. Layer 1 is assumed to correspond to the upper crust, layer 2 the lower crust and layer 3 the upper mantle. The effect of postseismic stress relaxation within a uniform half-space and within just the lower crust and upper mantle has been examined. Stress relaxation within the whole half-space decreases the amplitude and shortens the wavelength of displacements, while stress relaxation within the lower two layers increases the amplitude and broadens the wavelength of displacements. The difference between uniform and layered postseismic relaxation is particularly pronounced at the base of the crust.Coseismic and postseismic normal and volumetric strains for a vertical strike-slip fault have also been examined. For a uniformly relaxed half-space model, an increase in normal strains is shown with respect to the coseismic elastic solution, whereas the postseismic volumetric strain is effectively zero. For a three-layer model with stress relaxation in the lower layers only, the normal and volumetric strains within the top elastic layer resemble coseismic strains, while in the lower layers which suffer a rigidity decrease, the postseismic volumetric strain is effectively zero. 相似文献
11.
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. 相似文献
12.
Analytical results are presented for the dynamic interaction of an elastic flexural plate and an elastic half-space subjected to harmonic seismic waves. Displacements and contact stresses are presented for square, massless plates having a practical range of flexural stiffness and subjected to incident waves oriented parallel to either an edge or a diagonal of the plate. The behaviour of massive plates is also briefly discussed; such plates exhibit additional resonances higher than those normally associated with the motion of a rigid mass. 相似文献
13.
The dynamics of an elastic column subjected to vertical as well as horizontal ground acceleration during an earthquake strong motion is considered. The Liapunov method of stability analysis is employed and several bounds on the maximum lateral displacement and bending stress are obtained and discussed. 相似文献
14.
A five-parameter discrete model that approximates the dynamic force4isplacement relationship for rigid foundations undergoing vertical vibrations on a uniform elastic half-space is presented. The model involves a combination of two springs, two viscous dampers and a mass. Values of the parameters for circular, square and rectangular foundations placed on the surface or embedded in an elastic half-space are listed. The parameters are obtained by minimizing the discrepancy between the force4isplacement relation for the model and that obtained by solution of the mixed boundary-value problem of the rigid foundation on an elastic half-space. The definition of an appropriate input motion to represent wave excitation is also discussed. The input motion to the discrete model differs from the input motion that should be used in a continuum model. 相似文献
15.
Scattering of elastic waves by dipping layers of arbitrary shape embedded within an elastic half-space is investigated for a plane strain model by using a boundary method. Unknown scattered waves are expressed in the frequency domain in terms of wave functions which satisfy the equations of motion and appropriate radiation conditions at infinity. The steady state displacement field is evaluated throughout the elastic medium for different incident waves so that the continuity conditions along the interfaces between the layers and the traction-free conditions along the surface of the half-space are satisfied in the least-squares sense. Transient response is constructed from the steady state one through the Fourier synthesis. The results presented show that scattering of waves by dipping layers may cause locally very large amplification of surface ground motion. This amplification depends upon the type and frequency of the incident wave, impedance contrast between the layers, component of displacement which is being observed, location of the observation station and the geometry of the subsurface irregularity. These results are in agreement with recent experimental observations. 相似文献
16.
Scattering of elastic waves by an orthotropic sedimentary basin is investigated for antiplane strain model using an indirect boundary integral equation approach. Both steady state and transient response were obtained for semicircular and semielliptical basins with different material properties. The results indicate that the basin geometry and the impedance contrast between the half-space and the basin have similar effects on the surface ground motion amplification as for the isotropic case. However, the material anisotropy may change significantly the fundamental resonant frequencies of the basin, resulting in different surface displacement amplification patterns. In addition, it was observed that the arrival time of the main disturbance on the surface strongly depends on material anisotropy for different angles of incidence. The results demonstrate that material anisotropy may be very important in explaining surface ground motion amplification for sedimentary basins. © 1998 John Wiley & Sons, Ltd. 相似文献
17.
On the displacements produced in a porous elastic half-space by an impulsive line load. (Non-dissipative case) 总被引：8，自引：0，他引：8
S. Paul 《Pure and Applied Geophysics》1976,114(4):605-614
Summary On the basis of Biot's dynamical theory of poroelasticity the disturbance produced by an impulsive line load in a porous elastic half-space is studied. Using the Laplace-Fourier transform we have solved for the displacement potentials in terms of which the displacements and stresses in the transformed space are expressible. The expressions for the solid displacements in the interior as well as on the surface of the half-space are obtained by Cagniard's technique. The displacements are expressed in terms of six algebraic terms — three of which are identified as the disturbance due to specific wave fronts and the others represent the head wave contributions. When specialized our results agree with those for the common elastic half-space. 相似文献
18.
A seismic free field input formulation of the coupling procedure of the finite element (FE) and the scaled boundary finite-element
(SBFE) is proposed to perform the unbounded soil-structure interaction analysis in time domain. Based on the substructure
technique, seismic excitation of the soil-structure system is represented by the free-field motion of an elastic half-space.
To reduce the computational effort, the acceleration unit-impulse response function of the unbounded soil is decomposed into
two functions; linear and residual. The latter converges to zero and can be truncated as required. With the prescribed tolerance
parameter, the balance between accuracy and efficiency of the procedure can be controlled. The validity of the model is verified
by the scattering analysis of a hemi-spherical canyon subjected to plane harmonic P, SV and SH wave incidence. Numerical results
show that the new procedure is very efficient for seismic problems within a normal range of frequency. The coupling procedure
presented herein can be applied to linear and nonlinear earthquake response analysis of practical structures which are built
on unbounded soil.
Supproted by: the National Key Basic Research and Development Program under Grant No. 2002CB412709 相似文献
19.
Lateral spreads are complex dynamic phenomena that are challenging to represent numerically. In this paper numerical models are developed and calibrated using the displacement, acceleration, and pore water pressure time histories recorded in a free-field lateral spreading centrifuge test. The calibrated numerical model then is used to predict another free-field lateral spreading centrifuge test using the same soil profile but different input acceleration time history. The computed response shows good agreement with the centrifuge test measurements. This paper demonstrates that even in a large strain problem, such as lateral spreading, small strain damping plays an important role in numerical simulation results; it also shows the need to have pressure dependent dilation parameters in the employed soil constitutive model implemented in order to simultaneously reproduce measurements of pore water pressure, acceleration and lateral displacement. 相似文献
