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1.
This paper presents analytical solutions for computing the 3D displacements in a flat solid elastic stratum bounded by a rigid base, when it is subjected to spatially sinusoidal harmonic line loads. These functions are also used as Greens functions in a boundary element method code that simulates the seismic wave propagation in a confined or semi-confined 2D valley, avoiding the discretization of the free and rigid horizontal boundaries.The models developed are then used to simulate wave propagation within a rigid stratum and valleys with different dimensions and geometries, when struck by a spatially sinusoidal harmonic vertical line load. Simulations are performed in the frequency domain, for varying spatial wave numbers in the axial direction of the valley. Time results are obtained by means of inverse Fourier transforms, to help understand how the geometry of the valley may affect the variation of the displacement field. 相似文献
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采用波函数展开法给出了板的横截面处孔洞在平面P波入射下动应力集中问题的解。本文使用大圆弧假定法来满足板中的自由表面的边界条件。数值结果表明,上表面和孔洞间的距离与下表面和孔洞间的距离都对结果有影响。如果孔洞半径相对板的厚度很小,解近似等于孔洞全空间解。所给出的解是半解析解。因此能被用来验证诸如BEM,FEM,FDM等数值法。 相似文献
4.
Summary Unsteady boundary layer flows generated in an incompressible, homogeneous, nonrotating viscous fluid bounded by a rigid wavy plate are studied theoretically. The Laplace transform method is employed to obtain exact solutions of the unsteady boundary layer equations in a wavy plate configuration. The structures of the unsteady velocity distribution and the associated boundary layers are determined explicitly and several particular solutions are recovered as special cases of this analysis. The physical interpretation of the mathematical results are examined. 相似文献
5.
Gin-Show Liou 《地震工程与结构动力学》1989,18(5):667-686
The total system studied in this paper is a layered soil stratum with a rigid bedrock and a cylindrical cavity on the surface. Analytic solutions for the layered medium with prescribed harmonic displacement time history on the surface of the cylindrical cavity are presented. The whole soil domain is divided into interior and exterior domains. The interior domain is the projection of the cylindrical cavity down to the rigid bedrock, whereas the exterior domain is then the soil medium complement to the interior domain. The displacement and stress fields in both domains are expanded as an infinite series of Fourier components with respect to the azimuth. For each Fourier component in the infinite series, the solutions for both domains are found independently by solving the general differential equations of wave propagation satisfying the boundary conditions of the top surface and the lower rigid boundary. Displacement and stress continuity conditions are then imposed on the vertical interface between the two domains using the formulation of a weighted residual. For the soil-structure interaction problem, the impedance matrix at the interface between the structure and the soil medium can be easily generated using the analytic solutions, which can then be combined with the finite element model of the structure. A simple example is presented to demonstrate the effectiveness of the procedure presented. 相似文献
6.
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. 相似文献
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The radial pattern of syenite and syenodiorite dikes of the Spanish Peaks region is analysed using theories of elasticity and dike emplacement. The three basic components of Odé's model for the dike pattern (a pressurized, circular hole; a rigid, planar boundary; and uniform regional stresses) are adopted, but modified to free the regional stresses from the constraint of being orthogonal to the rigid boundary. Dike areal density, the White Peaks intrusion, the strike of the upturned Mesozoic strata, and the contact between these strata and the intensely folded and faulted Paleozoic rocks are used to brient the rigid boundary along a north-south line. The line of dike terminations locates the rigid boundary about 8 km west of West Peak. The location of a circular plug, Goemmer Butte, is chosen as a point of isotropic stress. A map correlating the location of isotropic stress points with regional stress parameters is derived from the theory and used to determine a regional stress orientation (N82E) and a normalized stress magnitude. The stress trajectory map constructed using these parameters mimics the dike pattern exceptionally well. The model indicates that the regional principal stress difference was less than 0.05 times the driving pressure in the West Peak intrusion. The regional stress difference probably did not exced 5 MN/m2. 相似文献
8.
This paper presents an indirect boundary integration equation method for diffraction of plane SV waves by a 2-D cavity in a poroelastic half-space.The Green’s functions of compressive and shear wave sources are derived based on Biot’s theory. The scattered waves are constructed using fi ctitious wave sources close to the boundary of the cavity, and their magnitudes are determined by the boundary conditions. Verifi cation of the accuracy is performed by: (1) checking the satisfaction extent of the boundary c... 相似文献
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Summary An investigation is carried out on the unsteady boundary layer induced in an incompressible, homogeneous, viscous fluid bounded by (i) an infinite horizontal porous plate aty=0, or (ii) two parallel horizontal rigid porous plates aty=0 andy=d. The unsteady motion is generated in the above fluid configurations by moving the plate(s) impulsively in its (their) own plane with a prescribed time-dependent velocity. Solutions for the unsteady velocity field are exactly solved by the Laplace transform treatment combined with the theory of residues. The structures of the associated boundary layers are determined. The effects of suction on the solutions and the boundary layers are investigated in detail, the limiting behaviour of the unsteady solution as timet is examined and Physical interpretations of the mathematical results are given. Finally, the frictional stresses on the plates are stated without detailed calculation. 相似文献
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The result of a theoretical study on the rocking response of rigid blocks subjected to sinusoidal base motion is presented. The study indicates that, for a given excitation amplitude and frequency, a rigid block can respond in several different ways. Based on analysis, the regions of different classes of steady state symmetric response solutions are mapped on the excitation amplitude-frequency parameter space. The steady state response solutions (both harmonic and subharmonic) are classified into two classes, out-of-phase and in-phase with respect to the excitation. Only out-of-phase solutions are found to be stable. A parametric study shows that steady rocking response amplitude is highly sensitive to the size of the block and the excitation frequency in the low frequency range. It is relatively insensitive to the excitation amplitude and the system's coefficient of restitution of impact. For two blocks of the same aspect ratio and coefficient of restitution subjected to the same excitation, the larger block always responds in smaller amplitude than the smaller block. Computer simulation is carried out to study the stability of the symmetric steady state response solutions obtained from analysis. It is found that as the excitation frequency is decreased beyond the boundary of stable symmetric response, the response becomes unsymmetric where the mean amplitude of oscillation is non-zero. Further decrease in excitation frequency beyond the stable unsymmetric response boundary causes instability in the form of overturning. 相似文献
11.
S. Ghoshal 《Pure and Applied Geophysics》1972,99(1):201-208
Summary A unified analysis has been made to obtain all possible similarity solutions of the steady and unsteady, forced flow, inside a boundary layer along a flat plate. Though previously, attempts were made to obtain similarity solutions of a steady boundary layer flow neglecting viscous dissipation term in the energy conservation equation but the treatments were not complete. Here we have taken account of the viscous dissipation term. In the steady case it has been shown that for a similarity solution of both velocity and temperature, there should be a relation between the undisturbed flow outside the boundary layer and the temperature of the plate. It has been shown that the similarity solution exists in the unsteady case if we neglet the viscous dissipation term in the energy equation. 相似文献
12.
Abstract Chandrasekhar (1961) has summarized the stability results of Bénard convection in a rotating fluid for the cases where the boundary surfaces are both rigid and free, and for both exchange of stabilities and overstability. His analysis provides very accurate results for a limited range of Taylor number J. Bisshopp and Niiler (1965) presented an asymptotic analysis of the rigid boundary problem for exchange of stabilities which is valid for very large Taylor number. The present paper makes use of modern rotating fluid theory to develop an approximate scheme for evaluating the Rayleigh number and other parameters and variables. Known asymptotic results for the free boundary problem at large J are used and an expansion in powers of E1/6 (the Ekman number, E = 2J ?½) yields a sequence of equations and appropriate boundary conditions for the rigid boundary problem. After the algorithm for the calculation is developed, results are given for the problem to second order in the expansion parameter for the case of exchange of stabilities and to first order in the expansion parameters for the overstable case. Ekman boundary layers are important in the development as one might expect. However, an additional, diffusive boundary layer of thickness E? is necessary to provide the details of the temperature field. This boundary layer is the thermal response in the vertical direction to the horizontal spacing of the cells which is also order E?. The horizontal spacing of the cells is essentially a series of contiguous, Stewartson (1957) layers of thickness E?. 相似文献
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Edward H. Stehmeyer III Dimitris C. Rizos 《Soil Dynamics and Earthquake Engineering》2006,26(5):421-434
This work presents a simplified, yet accurate model of rigid foundation-soil systems for the dynamic analysis of structures including SSI effects. The simplified model is based on closed form solutions that reproduce the characteristic B-spline impulse response functions (BIRF) of 3D continuous soil-foundation systems, as obtained from rigorous boundary element method (BEM) analysis. The proposed simplified model is used within the framework of B-spline impulse response techniques and can be coupled directly to other solution techniques, such as the finite element method (FEM). Validation and application studies demonstrate the accuracy and versatility of the simplified model for the direct time domain solution of dynamic SSI problems involving rigid square surface foundations of any size. The proposed model, although simplified, demonstrates similar high accuracy to that of more rigorous solutions based on domain discretizations. 相似文献
14.
Time harmonic point load and dynamic contact problem of contacting fluid and poroelastic half-spaces
The dynamic response of contacting fluid and fluid-saturated poroelastic half- spaces to a time-harmonic vertical point force or a point pore pressure is investigated. The solutions are formulated using the boundary conditions at the fluid-porous medium interface. The point load solutions are then used to solve the dynamic problem of the vertical vibration of a rigid disc (both permeable and impermeable discs are included) on the surface of the poroelastic half-space. The contact problems are solved by integrating the point force and point pore pressure solutions over the contact area with unknown discontinuous force and pore pressure distributions, which are determined from the boundary conditions. The solutions are expressed in terms of dual integral equations, which are converted to Fredholm integral equations of the second kind and solved numerically. Selected numerical results for the vertical dynamic compliance coefficient for the cases with or without fluid overlying the poroelastic half-space are presented to show the effects of the fluid. The influence of the permeability condition of the disc on the compliance of the poroelastic half-space is investigated. The displacement, vertical stress, pore pressure in the poroelastic half-space and water pressure in the fluid half-space are also examined for different poroelastic materials and frequencies of excitation. The present results are helpful in the study of the dynamic response of foundations on the seabed under seawater. 相似文献
15.
This study is concerned with the dynamic response of an arbitrary shaped rigid strip foundation embedded in an orthotropic elastic soil. The foundation is subjected to time-harmonic vertical, horizontal and moment loadings. The boundary-value problem related to an embedded foundation is analysed by using the indirect boundary integral equation method. The kernel functions of the integral equations are displacement and traction Green's functions of an anisotropic elastic half plane. Exact analytical solutions are used for the Green's functions. The boundary integral equation is solved by using numerical techniques. Selected numerical results are presented for the impedances of rectangular and semi-circular rigid strip foundations embedded in four types of anisotropic soils. A discussion on the influence of soil anisotropy and frequency of excitation on the impedances is presented. The versatility of the analysis is demonstrated by considering the through soil interaction between two semi-circular strip foundations. 相似文献
16.
The dynamic behaviour of a system of three-dimensional, massless, rigid, surface foundations of arbitrary shape perfectly bonded to the elastic half-space is numerically studied with the frequency domain boundary element method. This method employs the dynamic Green's function for the surface of the half-space and this results in a discretization of only the soil-foundation interfaces. In addition, use of isoparametric quadratic quadrilateral boundary elements increases the accuracy of the method, which is confirmed by comparison with other known numerical solutions. Externally applied loads, harmonically varying with time, are considered. The through the soil coupling effect between the foundations as a function of distance and frequency is assessed through extensive parametric studies involving two and four rigid foundations being isolated or interconnected. It is found that the assertion of ATC-3 regulations that omission of coupling effects leads to conservative results is not always correct for all frequencies. 相似文献
17.
The wave-induced velocity and pressure fields beneath a large amplitude internal solitary wave of depression propagating over
a smooth, flat, horizontal, and rigid boundary in a shallow two-layer fluid are computed numerically. A numerical ocean model
is utilised, the set-up of which is designed and tuned to replicate the previously published experimental results of Carr
and Davies (Phys Fluids 18(1):016,601–1–016,601–10, 2006). Excellent agreement is found between the two data sets and, in particular, the numerical simulation replicates the finding
of a reverse flow along the bed aft of the wave. The numerically computed velocity and pressure gradients confirm that the
occurrence of the reverse flow is a consequence of boundary layer separation in the adverse pressure gradient region. In addition,
vortices associated with the reverse flow are seen to form near the bed. 相似文献
18.
On the disturbance produced in a semi-infinite poroelastic medium by a surface load 总被引：13，自引：0，他引：13
S. Paul 《Pure and Applied Geophysics》1976,114(4):615-627
Summary Biot's theory of dynamical poroelasticity is used to solve the axisymmetric problem of deformation of a semi-infinite proelastic medium which is subjected to a uniform load within a circular area of its boundary. The solutions valid for large time have been derived. In some limiting cases, the solutions are shown to reduce to those of classical elasticity. The solutions for the point load case have also been deduced. Lastly, the variations with time of the solid displacements, the normal stress and the fluid pressure for the point load case after the arrival of the shear wave are exhibited graphically and the results for the classical case are included for the sake of comparison. 相似文献
19.
In wetlands wind-induced turbulence significantly affects the bottom boundary, and the interaction between turbulence and plant canopies is therefore particularly important. The aim of this study is to advance understanding of the impact of this interaction in submerged aquatic vegetation (SAV)1 on vertical mixing in a fluid dominated by turbulence. Wind-generated turbulence was simulated in the laboratory using an oscillating grid. We quantify the vertical distribution of turbulent kinetic energy (TKE)2 above and within different types of vegetation, measured by an acoustic Doppler velocimeter. Experimental conditions are analysed in two canopy models (rigid and semi-rigid) with seven solid plant fractions (SPFs)3, three stem diameters (d)4 and three oscillation grid frequencies (f)5 and four natural SAVs (Cladium mariscus, Potamogeton nodosus, Myriophyllum verticillatum and Ruppia maritima). 相似文献
20.
Stephen R. Tait Gerhard Wrner Paul Van Den Bogaard Hans-Ulrich Schmincke 《Journal of Volcanology and Geothermal Research》1989,37(1)
The physical mechanism by which chemical zonation develops in magma chambers has been controversial partly because unambiguous geological constraints have been lacking. The 11,000 years B.P. eruption of Laacher See Volcano produced a zoned tephra deposit and also ejected crystal-rich nodules which provide a snapshot of the materials crystallising at the magma chamber margins. New data on petrography and chemical compositions of nodules, their cumulate minerals and interstitial glasses are used to deduce the chemical evolution of the phonolite melt due to fractional crystallisation of the mineral assemblages. These data, together with those on the vertical zonation of the melt in the bulk of the chamber, are shown to be consistent with a model of stratification of the chamber by convective fractionation, in which a thin boundary layer of residual melt from fractional crystallisation ascends at the chamber side and accumulates at the roof. Crystallisation could have provided buoyancy to drive convection by enriching incompatible volatile components (mainly water) in the residual melt. Available fluid dynamic studies of single- and double-diffusive boundary layers are used to assess convection in the Laacher See chamber. The boundary layer is likely to have been: (1) laminar, which implies that the density gradient in the chamber steepened upwards; (2) in the counterflow regime, in which compositional and thermal layers flow in opposite directions; and (3) thin ( 10 cm), estimated from theory for a flat wall, suggesting that wall morphology could be important in determining boundary layer characteristics. Estimates of mass transfer rates due to this mechanism suggest that the chamber could have become stratified in a time of the order of 103 years. 相似文献