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Elastic Waves (elastic + wave)
Selected AbstractsElastic waves at a corrugated interface between two dissimilar fibre-reinforced elastic half-spacesINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 9 2007Sanasam Sarat Singh Abstract The reflection and transmission phenomena of elastic waves incident at a corrugated interface between two dissimilar fibre-reinforced elastic half-spaces have been analysed. Using Rayleigh method of approximation, the expressions of the reflection and transmission coefficients are obtained in closed form for the plane interface as well as for the first order approximation of the periodic interface , = d cos px. All these reflection and transmission coefficients of regular and irregular waves are found to be the functions of angle of incidence and elastic parameters of the media. Moreover, the coefficients of irregularly reflected and transmitted waves are found to be proportional to the amplitude of the corrugated interface and are functions of the frequency of the incident wave. Numerical computations have been performed for a specific model to compute these coefficients and results obtained are shown graphically. The results of Singh and Singh (Sadhana 2004; 29:249,257) and Ben-Menahem and Singh (Seismic Waves and Sources. Springer: New York) have been derived from our analysis as particular cases. Copyright © 2006 John Wiley & Sons, Ltd. [source] Traveltime approximation for a reflected wave in a homogeneous anisotropic elastic layerGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2002M. Zillmer Summary An approximation to the traveltime field is calculated for an elastic wave that propagates in a homogeneous anisotropic layer and is reflected at a plane boundary. The traveltime is approximated by a Taylor series expansion with the third derivative of the traveltime being taken into account. The coefficients of the series refer to the seismic ray, which is locally the fastest ray. Simple formulae are obtained for orthorhombic media in the crystal coordinate system, which relate the traveltimes of the reflected waves to the elastic constants of the medium. A numerical example is presented for wave propagation in orthorhombic olivine, which is a constituent of the Earth's mantle. A second example is given by an isotropic host rock with a set of parallel cracks, which is an important model for wave propagation in the Earth's crust. The elastic parameters can be determined by measuring the reflection times as a function of source,receiver offset. The approximate traveltime,distance curves are compared with traveltimes obtained from seismic ray tracing. [source] BEM-analysis of interaction of elastic waves with unilateral interface crackINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 3 2001Gai Bing-Zheng Abstract In this paper, to solve the problems of the interaction between the unilateral interface cracks and elastic wave, a new numerical method based on boundary element method (BEM) has been proposed. In this method, an iterating,correcting process of the solution in frequency domain and the correction in time domain has been designed to eliminate the mutual interference between the time and frequency domain. As an illustration to the algorithm, an interface crack between two half-planes under the attack of harmonic plane elastic wave has been analysed in detail. The contact configurations and stress field at the crack surface, and dynamic stress intensity factor (DSIF) at the crack tip have been given. Copyright © 2001 John Wiley & Sons, Ltd. [source] Numerical modelling of elastic wave scattering in frequency domain by the partition of unity finite element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2009A. El Kacimi Abstract In this paper, we investigate a numerical approach based on the partition of unity finite element method, for the time-harmonic elastic wave equations. The aim of the proposed work is to accurately model two-dimensional elastic wave problems with fewer elements, capable of containing many wavelengths per nodal spacing, and without refining the mesh at each frequency. The approximation of the displacement field is performed via the standard finite element shape functions, enriched by superimposing pressure and shear plane wave basis, which incorporate knowledge of the wave propagation. A variational framework able to handle mixed boundary conditions is described. Numerical examples dealing with the radiation and the scattering of elastic waves by a circular body are presented. The results show the performance of the proposed method in both accuracy and efficiency. Copyright © 2008 John Wiley & Sons, Ltd. [source] Existence of solution in elastic wave scattering by unbounded rough surfacesMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 6 2002T. Arens We consider the two-dimensional problem of the scattering of a time-harmonic wave, propagating in an homogeneous, isotropic elastic medium, by a rough surface on which the displacement is assumed to vanish. This surface is assumed to be given as the graph of a function ,,C1,1(,). Following up on earlier work establishing uniqueness of solution to this problem, existence of solution is studied via the boundary integral equation method. This requires a novel approach to the study of solvability of integral equations on the real line. The paper establishes the existence of a unique solution to the boundary integral equation formulation in the space of bounded and continuous functions as well as in all Lp spaces, p,[1, ,] and hence existence of solution to the elastic wave scattering problem. Copyright © 2002 John Wiley & Sons, Ltd. [source] Scattering of elastic waves in media with a random distribution of fluid-filled cavities: theory and numerical modellingGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2004Tae-Kyung Hong SUMMARY The propagation of elastic waves is modelled in media with a random distribution of fluid-filled circular cavities, which display high physical impedance in contrast to background media. Theoretical attenuation expressions for media with circular cavities, which may be filled with any material (e.g. vacuum, fluid, elastic materials), are formulated using an ensemble treatment for first-order transmitted waves. Numerical estimates of scattering attenuation rates agree with the theoretical results well. The scattering attenuations (Q,1) are proportional to the scale of cavities and the number density (,, number of cavities per area in a medium). The decrease of primary energy with the size of cavities does not result in the increase of coda energy owing to the increase of both purely backscattered waves from cavities and the trapped waves inside cavities. Scattering properties (e.g. scattering attenuation, coda energy, phase fluctuation of primary waves) in media with randomly distributed cavities are very different from those in stochastic random media. It appears that heterogeneities with high impedance in the earth may not be well represented with stochastic random heterogeneities. [source] The effect of inertial coupling on seismic reflection amplitudesGEOPHYSICAL PROSPECTING, Issue 5 2008Ashish Arora ABSTRACT A problem of reflection and transmission of elastic waves at a plane interface between a uniform elastic solid half-space and a porous elastic half-space containing two immiscible fluids is investigated. The theory developed by Lo, Sposito and Majer for porous media containing two immiscible fluids is employed to find out the reflection and transmission coefficients. The incident wave is assumed to propagate through the uniform elastic half-space and two cases are considered. In the first case, a beam of plane longitudinal wave is assumed to be incident and in the second case, a beam of transverse wave is assumed to be incident at the interface. By taking granite as impervious elastic medium and columbia fine sandy loam containing air-water mixture as porous medium, reflection and transmission coefficients are obtained. By neglecting the inertial coupling coefficients, these coefficients are reduced to those obtained by Tomar and Arora using the theory of Tuncay and Corapcioglu. It is found that the inertial coupling parameters significantly affect the phase speeds and the amplitude ratios of the transmitted waves. [source] Effective elastic properties of randomly fractured soils: 3D numerical experimentsGEOPHYSICAL PROSPECTING, Issue 3 2004Erik H. Saenger ABSTRACT This paper is concerned with numerical tests of several rock physical relationships. The focus is on effective velocities and scattering attenuation in 3D fractured media. We apply the so-called rotated staggered finite-difference grid (RSG) technique for numerical experiments. Using this modified grid, it is possible to simulate the propagation of elastic waves in a 3D medium containing cracks, pores or free surfaces without applying explicit boundary conditions and without averaging the elastic moduli. We simulate the propagation of plane waves through a set of randomly cracked 3D media. In these numerical experiments we vary the number and the distribution of cracks. The synthetic results are compared with several (most popular) theories predicting the effective elastic properties of fractured materials. We find that, for randomly distributed and randomly orientated non-intersecting thin penny-shaped dry cracks, the numerical simulations of P- and S-wave velocities are in good agreement with the predictions of the self-consistent approximation. We observe similar results for fluid-filled cracks. The standard Gassmann equation cannot be applied to our 3D fractured media, although we have very low porosity in our models. This is explained by the absence of a connected porosity. There is only a slight difference in effective velocities between the cases of intersecting and non-intersecting cracks. This can be clearly demonstrated up to a crack density that is close to the connectivity percolation threshold. For crack densities beyond this threshold, we observe that the differential effective-medium (DEM) theory gives the best fit with numerical results for intersecting cracks. Additionally, it is shown that the scattering attenuation coefficient (of the mean field) predicted by the classical Hudson approach is in excellent agreement with our numerical results. [source] Source signature and elastic waves in a half-space under a sustainable line-concentrated impulsive normal forceINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 4 2002Moche Ziv Abstract First, the response of an ideal elastic half-space to a line-concentrated impulsive normal load applied to its surface is obtained by a computational method based on the theory of characteristics in conjunction with kinematical relations derived across surfaces of strong discontinuities. Then, the geometry is determined of the obtained waves and the source signature,the latter is the imprint of the spatiotemporal configuration of the excitation source in the resultant response. Behind the dilatational precursor wave, there exists a pencil of three plane waves extending from the vertex at the impingement point of the precursor wave on the stress-free surface of the half-space to three points located on the other two boundaries of the solution domain. These four wave-arresting points (end points) of the three plane waves constitute the source signature. One wave is an inhibitor front in the behaviour of the normal stress components and the particle velocity, while in the behaviour of the shear stress component, it is a surface-axis wave. The second is a surface wave in the behaviour of the horizontal components of the dependent variables, while the third is an inhibitor wave in the behaviour of the shear stress component. An inhibitor wave is so named, since beyond it, the material motion is dying or becomes uniform. A surface-axis wave is so named, since upon its arrival, like a surface wave, the dependent variable in question features an extreme value, but unlike a surface wave, it exists in the entire depth of the solution domain. It is evident from this work that Saint-Venant's principle for wave propagation problems cannot be formulated; therefore, the above results are a consequence of the particular model proposed here for the line-concentrated normal load. Copyright © 2002 John Wiley & Sons, Ltd. [source] P-wave and S-wave decomposition in boundary integral equation for plane elastodynamic problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2003Emmanuel Perrey-Debain Abstract The method of plane wave basis functions, a subset of the method of Partition of Unity, has previously been applied successfully to finite element and boundary element models for the Helmholtz equation. In this paper we describe the extension of the method to problems of scattering of elastic waves. This problem is more complicated for two reasons. First, the governing equation is now a vector equation and second multiple wave speeds are present, for any given frequency. The formulation has therefore a number of novel features. A full development of the necessary theory is given. Results are presented for some classical problems in the scattering of elastic waves. They demonstrate the same features as those previously obtained for the Helmholtz equation, namely that for a given level of error far fewer degrees of freedom are required in the system matrix. The use of the plane wave basis promises to yield a considerable increase in efficiency over conventional boundary element formulations in elastodynamics. Copyright © 2003 John Wiley & Sons, Ltd. [source] BEM-analysis of interaction of elastic waves with unilateral interface crackINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 3 2001Gai Bing-Zheng Abstract In this paper, to solve the problems of the interaction between the unilateral interface cracks and elastic wave, a new numerical method based on boundary element method (BEM) has been proposed. In this method, an iterating,correcting process of the solution in frequency domain and the correction in time domain has been designed to eliminate the mutual interference between the time and frequency domain. As an illustration to the algorithm, an interface crack between two half-planes under the attack of harmonic plane elastic wave has been analysed in detail. The contact configurations and stress field at the crack surface, and dynamic stress intensity factor (DSIF) at the crack tip have been given. Copyright © 2001 John Wiley & Sons, Ltd. [source] Numerical modelling of elastic wave scattering in frequency domain by the partition of unity finite element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2009A. El Kacimi Abstract In this paper, we investigate a numerical approach based on the partition of unity finite element method, for the time-harmonic elastic wave equations. The aim of the proposed work is to accurately model two-dimensional elastic wave problems with fewer elements, capable of containing many wavelengths per nodal spacing, and without refining the mesh at each frequency. The approximation of the displacement field is performed via the standard finite element shape functions, enriched by superimposing pressure and shear plane wave basis, which incorporate knowledge of the wave propagation. A variational framework able to handle mixed boundary conditions is described. Numerical examples dealing with the radiation and the scattering of elastic waves by a circular body are presented. The results show the performance of the proposed method in both accuracy and efficiency. Copyright © 2008 John Wiley & Sons, Ltd. [source] A continued-fraction-based high-order transmitting boundary for wave propagation in unbounded domains of arbitrary geometryINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2008Mohammad Hossein Bazyar Abstract A high-order local transmitting boundary is developed to model the propagation of elastic waves in unbounded domains. This transmitting boundary is applicable to scalar and vector waves, to unbounded domains of arbitrary geometry and to anisotropic materials. The formulation is based on a continued-fraction solution of the dynamic-stiffness matrix of an unbounded domain. The coefficient matrices of the continued fraction are determined recursively from the scaled boundary finite element equation in dynamic stiffness. The solution converges rapidly over the whole frequency range as the order of the continued fraction increases. Using the continued-fraction solution and introducing auxiliary variables, a high-order local transmitting boundary is formulated as an equation of motion with symmetric and frequency-independent coefficient matrices. It can be coupled seamlessly with finite elements. Standard procedures in structural dynamics are directly applicable for evaluating the response in the frequency and time domains. Analytical and numerical examples demonstrate the high rate of convergence and efficiency of this high-order local transmitting boundary. Copyright © 2007 John Wiley & Sons, Ltd. [source] The scattering theory of C. Wilcox in elasticityMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 12 2002Mongi Mabrouk Abstract We extend the abstract time-dependent scattering theory of C.H. Wilcox to the case of elastic waves. Most of the results are proved with the minimal assumption that the obstacle satisfies the energy local compactness condition (ELC). This holds especially for the existence and unitarity of the wave operators. Copyright © 2002 John Wiley & Sons, Ltd. [source] | |||||||||||||