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1.
The present work gives solutions of integrals resulting from Lamb's problem solution by an accurate and efficient approximation procedure. The formulation of the solutions requires the study of Green's function of Lamb problem solution. Unfortunately, this problem is associated to great mathematical difficulties and needs the evaluation of some complex integrals. We handled these integrals by an appropriate strategy based on decoupling their effects mathematically and solved by using the least squares method. The present solutions can be applied to study the dynamical interaction between soil and structures, to be used to determine the transient wave fields caused by a seismic source, and also to assess numerical computations with a different numerical methods program. 相似文献
2.
High-speed train seismology has come into being recently. This new kind of seismology uses a high-speed train as a repeatable moving seismic source. Therefore, Green's function for a moving source is needed to make theoretical studies of the high-speed train seismology. Green's function for three-dimensional elastic wave equation with a moving point source on the free surface is derived. It involves a line integral of the Green's function for a fixed point source with different positions and corresponding time delays. We give a rigorous mathematical proof of this Green's function. According to the principle of linear superposition, we have also obtained the Green's function for a group of moving sources which can be regarded as a model of a traveling high-speed train. Based on a temporal convolution, an analytical formula for other moving sources is also given. In terms of a moving Gaussian source, we deal with the issue of numerical calculations of the analytical formula. Applications to modelling of a traveling high-speed train are presented. We have considered both the land case and the bridge case for a traveling high-speed train. The theoretical seismograms show different waveform features for these two cases. 相似文献
3.
The basic equation of motion to analyse the interaction of a non-linear structure and an irregular soil with the linear unbounded soil is formulated in the time domain. The contribution of the unbounded soil involves convolution integrals of the dynamic-stiffness coefficients in the time domain and the corresponding motions. Alternatively, a flexibility formulation for the contribution of the unbounded soil using the dynamic-flexibility coefficients in the time domain, together with the direct-stiffness method for the structure and the irregular soil can be applied. The dynamic-stiffness or flexibility coefficient in the time domain is calculated as the inverse Fourier transform of the corresponding value in the frequency domain. The dynamic-stiffness coefficient's asymptotic behaviour for high frequencies determines the singular part whose transformation exists only in the sense of a distribution. As the dynamic-flexibility coefficient converges to zero for the frequency approaching infinity, the corresponding coefficient in the time domain is simpler to calculate, as no singular part exists. The salient features of the dynamic-stiffness and flexibility coefficients in the time domain are illustrated using a semi-infinite rod with exponentially increasing area. The dynamic-flexibility coefficients in the time domain are calculated for a rigid circular disc resting on the surface of an elastic halfspace and of a layer built-in at its base. Material damping is also introduced using the three-parameter Kelvin and the Voigt models. 相似文献
4.
The various boundary-element methods, well established in the frequency domain, are developed in the time domain for a foundation embedded in a layered halfspace. They are the weighted-residual technique and the indirect boundary-element method, based on a weighted-residual equation, and the direct boundary-element method based on a reciprocity equation, both equations involving time and space. In the indirect approach, formulating the weighted-residual equation over the last time step only results in the truncated indirect boundary-element formulation which requires a reduced computational effort. In all cases, convolution integrals occur. The truncated indirect boundary-element method leads to a highly reliable algorithm, as is verified when a linear analysis in the time domain is compared to the corresponding one in the frequency domain. This boundary-element formulation, which is non-local in space and time, represents a rigorous generally applicable method taking into account a layered halfspace in a non-linear soil-structure interaction analysis. As an example, the non-linear soil-structure interaction analysis of a structure embedded in a halfspace with partial uplift of the basemat and separation of the side wall is investigated. 相似文献
5.
John P. Wolf 《地震工程与结构动力学》1986,14(4):655-673
A non-linear interaction analysis with a (generalized) non-linear structure and a linear unbounded soil is analysed in the time domain, based either on the sub-structure method, which involves global convolution integrals, or on the direct method with local boundary conditions. Alternatively, the hybrid frequency–time-domain method of analysis, which is an iterative scheme, could be used. Approximate local boundary conditions to model the wave propagation towards infinity on the artificial boundary used in the direct method of non-linear soil–structure-interaction analysis to be performed in the time domain are examined. A semi-infinite rod supported elastically, which exhibits the same properties as certain unbounded soils such as dispersion and a cut-off frequency, is used for the investigation. For a transient excitation, the superposition boundary with frequent averaging, the well-known viscous damper and the extrapolation algorithm lead to good accuracy. Moving the artificial boundary further away from the structure (or more precisely, increasing the ratio of the distance of the artificial boundary to the wave length) improves the accuracy. 相似文献
6.
A vibration analysis for viscoplastic, shear deformable composite beams is presented, where non-linear strains consistently are treated as an additional loading of the linear elastic structure due to fictitious sources of eigenstresses. Therefore, linear solution methods such as mode superposition and Green's functions become applicable, and a fast, computer-oriented solution strategy is developed. The non-linear structural response is found as the sum of the corresponding linear elastic response and the solution due to the additional loading by the inelastic strains, where the sources of eigenstresses are calculated from the material's law in a time-stepping procedure. The method is demonstrated using a composite sandwich beam with thin surface layers on multiple supports, which are excited independently. Elastoplastic material behaviour of endochronic type as well as a viscoplastic material's law are considered simultaneously. 相似文献
7.
The interaction forces representing the contribution of the linear unbounded soil to the equations of motion of a nonlinear soil-structure-interaction analysis are specified in the form of convolution integrals. They can be evaluated recursively in the time domain. In this procedure, the forces at a specific time are computed from the displacements at the same time and from the most recent forces and most recent past displacements. It is, in principle, only approximate. When the dynamic-stiffness coefficients can be expressed as the ratios of two polynomials in frequency, the appropriately chosen recursive equations are exact. Two possibilities of choosing a recursive equation are discussed.
- (i) The impulse-invariant method, where the unknown recursive coefficients are calculated by solving a system of equations which are established by equating the rigorous and recursive formulations for a discretized unit impulse displacement.
- (ii) In the segment approach, the dynamic-stiffness coefficients in the time domain are interpolated piecewise. Applying the z-transformation analytically then results in an explicit recursive equation without solving a system of equations.
8.
建筑物的抗震设防需要尽可能地掌握未来大地震强震动记录信息,但大地震强震动记录的匮乏阻碍了抗震设防实践的发展。经验格林函数方法作为模拟地震动的主要方法,可以提供可靠的大地震强震动记录,但也存在着许多问题,如缺乏对大地震断层滑动分布不均匀的描述、用经验确定小震数目、模拟方法受到大小地震相似条件的限制等。文中对上述经验格林函数方法存在的问题进行了研究,改进的经验格林函数方法,有效地解决了上述问题。并用其对唐山大地震进行了模拟,并把模拟的地震动时程和反应谱与实际记录相比较,发现用改进方法模拟的地震动加速度反应谱比用未改进方法模拟结果更接近实际的地震动记录加速度反应谱。由此说明改进的经验格林函数可更准确的模拟地震动。 相似文献
9.
Least-squares reverse time migration is often formulated as an iterative updating process, where estimating the gradient of the misfit function is necessary. Traditional time domain shot-profile least-squares reverse time migration is computationally expensive because computing the gradient involves solving the two-way wave equation several times in every iteration. To reduce the computational cost of least-squares reverse time migration, we propose a double-plane-wave least-squares reverse time migration method based on a misfit function for frequency-domain double-plane-wave data. In double-plane-wave least-squares reverse time migration, the gradient is computed by multiplying frequency-domain plane-wave Green's functions with the corresponding double-plane-wave data residual. Because the number of plane-wave Green's functions used for migration is relatively small, they can be pre-computed and stored in a computer's discs or memory. We can use the pre-computed plane-wave Green's functions to obtain the gradient without solving the two-way wave equation in each iteration. Therefore, the migration efficiency is significantly improved. In addition, we study the effects of using sparse frequency sampling and sparse plane-wave sampling on the proposed method. We can achieve images with correct reflector amplitudes and reasonable resolution using relatively sparse frequency sampling and plane-wave sampling, which are larger than that determined by the Nyquist theorem. The well-known wrap-around artefacts and linear artefacts generated due to under-sampling frequency and plane wave can be suppressed during iterations in cases where the sampling rates are not excessively large. Moreover, implementing the proposed method with sparse frequency sampling and sparse plane-wave sampling further improves the computational efficiency. We test the proposed double-plane-wave least-squares reverse time migration on synthetic models to show the practicality of the method. 相似文献
10.
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
11.
The spectrum of a magnetic or a gravity anomaly due to a body of a given shape with either homogeneous magnetization or uniform density distribution can be expressed as a product of the Fourier transforms of the source geometry and the Green's function. The transform of the source geometry for any irregularly-shaped body can be accurately determined by representing the body as closely as possible by a number of prismatic bodies. The Green's function is not dependent upon the source geometry. So the analytical expression for its transform remains the same for all causative bodies. It is, therefore, not difficult to obtain the spectrum of an anomaly by multiplying the transform of the source geometry by that of the Green's function. Then the inverse of this spectrum, which yields the anomaly in the space domain, is calculated by using the Fast Fourier Transform algorithm. Many examples show the reliability and accuracy of the method for calculating potential field anomalies. 相似文献
12.
Werner Rüucker 《地震工程与结构动力学》1982,10(5):675-690
An approximate method for computation of the compliance functions of rigid plates resting on an elastic or visco-elastic halfspace excited by forces and moments in all degrees of freedon is presented. The method is based on a Green's function approach. These functions are given for all degrees of freedom in form of well-behaved integrals. The numerical procedure is described and is used to evaluate the vertical, horizontal, rocking and torsion compliance functions of rectangular plates with side ratios 1 ≤ b/a ≤ 10 and non-dimensional frequency 0≤a0≤10. It is shown how this method can be extended to problems concerning a linear visco-elastic halfspace and a halfspace with variable stiffness. 相似文献
13.
MONIKA BREITZKE 《Geophysical Prospecting》1992,40(1):31-70
In spite of a geometrical rotation into radial and transverse parts, two- or three-component in-seam seismic data used for underground fault detection often suffer from the problem of overmoding ‘noise’. Special recompression filters are required to remove this multimode dispersion so that conventional reflection seismic data processing methods, e.g. CMP stacking techniques, can be applied afterwards. A normal-mode superposition approach is used to design such multimode recompression filters. Based on the determination of the Green's function in the far-field, the normal-mode superposition approach is usually used for the computation of synthetic single- and multi-mode (transmission) seismograms for vertically layered media. From the filter theory's point of view these Green's functions can be considered as dispersion filters which are convolved with a source wavelet to produce the synthetic seismograms. Thus, the design of multimode recompression filters can be reduced to a determination of the inverse of the Green's function. Two methods are introduced to derive these inverse filters. The first operates in the frequency domain and is based on the amplitude and phase spectrum of the Green's function. The second starts with the Green's function in the time domain and calculates two-sided recursive filters. To test the performance of the normal-mode superposition approach for in-seam seismic problems, it is first compared and applied to synthetic finite-difference seismograms of the Love-type which include a complete solution of the wave equation. It becomes obvious that in the case of one and two superposing normal modes, the synthetic Love seam-wave seismograms based on the normal-mode superposition approach agree exactly with the finite-difference data if the travel distance exceeds two dominant wavelengths. Similarly, the application of the one- and two-mode recompression filters to the finite-difference data results in an almost perfect reconstruction of the source wavelet already two dominant wavelengths away from the source. Subsequently, based on the dispersion analysis of an in-seam seismic transmission survey, the normal-mode superposition approach is used both to compute one- and multi-mode synthetic seismograms and to apply one- and multimode recompression filters to the field data. The comparison of the one- and two-mode synthetic seismograms with the in-seam seismic transmission data reveals that arrival times, duration and shape of the wavegroups and their relative excitation strengths could well be modelled by the normal-mode superposition approach. The one-mode recompressions of the transmission seismograms result in non-dispersive wavelets whose temporal resolution and signal-to-noise ratio could clearly be improved. The simultaneous two-mode recompressions of the underground transmission data show that, probably due to band-limitation, the dispersion characteristics of the single modes could not be evaluated sufficiently accurately from the field data in the high-frequency range. Additional techniques which overcome the problem of band-limitation by modelling all of the enclosed single-mode dispersion characteristics up to the Nyquist frequency will be mandatory for future multimode applications. 相似文献
14.
Scattering of elastic waves by a three‐dimensional transversely isotropic basin of arbitrary shape embedded in a half‐space is considered using an indirect boundary integral equation approach. The unknown scattered waves are expressed in terms of point sources distributed on the so‐called auxiliary surfaces. The sources are expressed in terms of the full‐space Green's functions with their intensities determined from the requirement that the boundary and the continuity conditions are to be satisfied in the least‐squares sense. Steady‐state results were obtained for incident plane pseudo‐P‐, SH‐, SV‐, and Rayleigh waves. Using the Radon transform the Green's functions are obtained in the form of finite integrals over a unit sphere or a unit circle which can be numerically evaluated very efficiently. Detailed analysis of the method includes the discussion on the shape of the auxiliary surfaces and the distribution of the collocation points and sources. The convergence criteria is defined in terms of transparency tests, isotropic limit test, and minimization of a certain norm. The isotropic limit tests show excellent agreement with the isotropic results available in literature. For anisotropic materials the numerical results are given for a semispherical basin. The results show that presence of an anisotropic basin may result in significant amplification of surface motion atop the basin. While the amplitude of peak surface motion may be similar to the corresponding isotropic results, the difference in the displacement patterns may be quite different between the two. Therefore, this study clearly demonstrates that material anisotropy may be very important for accurate assessment of surface ground motion amplification atop basins. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
15.
We present the theory and numerical results for interferometrically interpolating 2D and 3D marine surface seismic profiles data. For the interpolation of seismic data we use the combination of a recorded Green's function and a model‐based Green's function for a water‐layer model. Synthetic (2D and 3D) and field (2D) results show that the seismic data with sparse receiver intervals can be accurately interpolated to smaller intervals using multiples in the data. An up‐ and downgoing separation of both recorded and model‐based Green's functions can help in minimizing artefacts in a virtual shot gather. If the up‐ and downgoing separation is not possible, noticeable artefacts will be generated in the virtual shot gather. As a partial remedy we iteratively use a non‐stationary 1D multi‐channel matching filter with the interpolated data. Results suggest that a sparse marine seismic survey can yield more information about reflectors if traces are interpolated by interferometry. Comparing our results to those of f‐k interpolation shows that the synthetic example gives comparable results while the field example shows better interpolation quality for the interferometric method. 相似文献
16.
Numerical computations using the integral equation method are presented for resistivity and IP responses due to arbitrarily shaped 3-dimensional bodies in a layered earth. The unknown surface charge density distribution is expressed as the solution of Fredholm's integral equation of the second kind. Use of moment method (with pulse basis function and point-collocation) yields the matrix equations for the unknowns. The contributions to Green's function are solved (a) analytically for the primary and (b) by convolution for the secondary contributions resulting in a fast algorithm. The further step of computing potential, apparent resistivity, chargeability etc., for any electrode system, is straightforward. Our results show a good agreement with those from finite difference methods and physical tank experiments. The CPU time is only 138 s on a super-minicomputer for an apparent resistivity pseudo-section, even with 96 elementary cells as used for discretization. A large number of models for different geological situations were studied; some are presented here. 相似文献
17.
Khiem T. Tran Michael McVay Rodrigo Herrera Peter Lai 《Soil Dynamics and Earthquake Engineering》2011
A numerical technique is presented to estimate ultimate skin friction of a driven pile using instrumentation installed at the top and bottom of a pile. The scheme is based on an analytical solution of the 1D wave equation with static skin friction and damping along with a genetic algorithm for solution. Specifically, acceleration and strains measured at both the top and bottom of the pile are used to develop an observed Green's function, which is matched to an analytical Green's function, which is a function of secant stiffness and viscous damping. Requiring 1–3 s of analysis time per blow, the algorithm provides a real time assessment of average skin friction along the pile. The technique was applied to four driven piles having ultimate skin frictions varying from 700 to 2000 kN, with the predicted skin frictions generally consistent with measured static load test results. 相似文献
18.
One of the severe problems in the semi-empirical method for the prediction of strong ground motions is that there is no objective criterion for choosing empirical Green's functions. It is undesirable that synthesized strong ground motions are affected by the source process of an earthquake whose record is adopted as an empirical Green's function. Through the analysis of strong motion accelerograms of two aftershocks of the 1983 Japan Sea earthquakes, it is found that characteristics of the accelerograms are dependent on the moment rate function derived from teleseismic observations. A procedure is presented for removing the effect of the source process from observed strong motion accelerograms. The thus obtained empirical Green's function expresses approximately the impulse response of the medium between the earthquake source and the observation site. 相似文献
19.
Francisco Luzón Francisco J. Sánchez-Sesma J. Alfonso Pérez-Ruiz Leonardo Ramírez-Guzmán Andrés Pech 《Soil Dynamics and Earthquake Engineering》2009
The propagation of seismic P and SV waves within inhomogeneous alluvial valleys has been investigated using the indirect boundary element method (IBEM). An improvement on the formulae published early, for the 2D Green's functions in an inhomogeneous medium is presented in this work. A modification has been done over these functions in view of its connection to the ray theory. An accuracy analysis validates these modified Green's functions computing the relative error in frequency domain for the SH case, and with a quantitative analysis obtaining envelope and phase misfits of the solution in time domain, for the P–SV case. 相似文献
20.
Formulation of a matrix‐valued force–displacement relationship which can take radiation damping into account is of major importance when modelling unbounded domains. This can be done by means of fundamental solutions in space and time in connection with convolution integrals or by means of a frequency dependent boundary element representation, but for discrete frequencies Ω only. In this paper a method for interpolating discrete values of dynamic stiffness matrices by a continuous matrix valued rational function is proposed. The coupling between interface degrees of freedom is fully preserved. Another crucial point in soil–structure interaction analysis is how to implement an approximation in the spectral domain into a time‐domain analysis. Well‐known approaches for the scalar case are based on the partial‐fraction expansion of a scalar rational function. Here, a more general procedure, applicable to MDOF‐systems, for the transformation of spectral rational approximations into the time‐domain is introduced. Evaluation of the partial‐fraction expansion is avoided by using the so‐called mixed variables. Thus, unknowns in the time‐domain are displacements as well as forces. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献