In this paper, an analytic method is developed to address steady SH-wave scattering and perform dynamic analysisof multiple circular cavities in half space. The scattered wave function used for scattering of SH-waves ...In this paper, an analytic method is developed to address steady SH-wave scattering and perform dynamic analysisof multiple circular cavities in half space. The scattered wave function used for scattering of SH-waves by multiple circularcavities, which automatically satisfies the stress-free condition at the horizontal surface, is constructed by applying thesymmetry of the SH-wave scattering and the method of multi-polar coordinates system. Applying this scattered wave functionand method of moving coordinates, the original problem can be transformed to the problem of SH-wave scattering by multiplecircular cavities in the full space. Finally, the solution of the problem can be reduced to a series of algebraic equations andsolved numerically by truncating the infinite algebraic equations to the finite ones. Numerical examples are provided for casewith two cavities to show the effect of wave number, and the distances between the centers of the cavities and from the centersto the ground surface on the dynamic stress concentration around the cavity impacted by incident steady SH-wave.展开更多
By expressing the wave functions in the form of Fourier-Bessel series,the analytical solution for the two-dimension scattering problem of plane P waves by the cylindrical canyon topography that contains arbitrary numb...By expressing the wave functions in the form of Fourier-Bessel series,the analytical solution for the two-dimension scattering problem of plane P waves by the cylindrical canyon topography that contains arbitrary number of circular-arc-shaped layers is presented firstly.And then,the convergence of the proposed series solution with the truncation number of terms is discussed,which demonstrates that the analytical solution can converge even for very high frequencies of the incident P wave.Finally,using this solution,the influences that are imposed on the stationary ground motion by the number and the sequence of alluvial layers,as well as the stiffness of soft interlayer contained in the canyon,are studied.展开更多
In-situ measurement of internal solitary waves(ISWs)is complicated in the ocean due to their randomness.At present,the ISWs are mainly detected by the chain structure of conductivity-temperature-depth systems(CTDs)or ...In-situ measurement of internal solitary waves(ISWs)is complicated in the ocean due to their randomness.At present,the ISWs are mainly detected by the chain structure of conductivity-temperature-depth systems(CTDs)or temperature sensors.The high cost limits the spatial resolution,which ultimately affects the measuring accuracy of the ISW amplitude.In this paper,we developed an experimental measurement system for detecting ISWs based on the stimulated Raman scattering in distributed optical fibers.This system has the advantages of high precision,low cost,and easy operation.The experimental results show that the system is consistent with CTDs in the measurement of vertical ocean temperature variation.The spatial resolution of the system can reach 1.0 m and the measuring accuracy of temperature is 0.2℃.We successfully detected 3 ISWs by the system in the South China Sea and two optical remote sensing images collected on May 18,2021,the same day of two detected ISWs,verify the occurrence of the measured ISWs.We used the image pairs method to calculate the phase velocity of ISW and the result is 1.71 ms^(-1).By extracting the distances between wave packets,it can be found that the semi-diurnal tide generates the detected ISWs.The impact of the tidal current velocity on the ISW in amplitude is undeniable.Undoubtedly,the system has a great application prospect for detecting ISWs and other dynamic phenomena in the ocean.展开更多
Whistler mode waves are critical emissions in magnetized plasmas that usually influence the electron dynamics in a planetary magnetosphere.In this paper,we present a unique event in the Martian magnetosphere in which ...Whistler mode waves are critical emissions in magnetized plasmas that usually influence the electron dynamics in a planetary magnetosphere.In this paper,we present a unique event in the Martian magnetosphere in which enhanced whistler mode waves(~10^(−11) V^(2)/m^(2)/Hz)with frequency of 0.1 f_(ce)-0.5 f_(ce) occurred,based on MAVEN data,exactly corresponding to a significant decrease of suprathermal electron fluxes.The diffusion coefficients are calculated by using the observed electric field wave spectra.The pitch angle diffusion coefficient can approach 10^(−2) s^(−1),which is much larger,by~100 times,than the momentum diffusion coefficient,indicating that pitch angle scattering dominates the whistler-electron resonance process.The current results can successfully explain the dropout of the suprathermal electrons in this event.This study provides direct evidence for whistler-driven electron losses in the Martian magnetosphere.展开更多
Target strength(TS)and circular synthetic aperture sonar(CSAS)images provide essential information for active acoustic detection and recognition of non-cooperative unmanned undersea vehicles(UUVs),which pose a signifi...Target strength(TS)and circular synthetic aperture sonar(CSAS)images provide essential information for active acoustic detection and recognition of non-cooperative unmanned undersea vehicles(UUVs),which pose a significant threat to underwater preset facilities.To access them,we propose an iterative physical acoustics(IPA)-based method to simulate the multiple acoustic scattered fields on rigid surfaces in high-frequency cases.It uses the Helmholtz integral equation with an appropriate Green's function in terms of the Neumann series,and then incorporates the ideas of triangulation and iteration into a numerical implementation.Then two approximate analytic formulae with precise physical meanings are derived to predict the TS and CSAS images of concave targets,respectively.There are no restrictions on the surface's curvature and the order of multiple scattering.The method is validated against the finite element method(FEM)for acoustic scattering from a sphere segment and against an experiment involving an X-rudder UUV's stern.On this basis,we simulate and analyze the TS and CSAS images of an X-rudder UUV.In addition,the influence of the angle of adjacent rudders on the multiple scattering characteristics is discussed.Results show that this method can potentially predict accurate UUV features,especially the multiple scattered features.展开更多
Based on the formulation of a multiple non-isotropic scattering process, a characteristic source time is introduced to define the initial impulse width of energy density at the source. An analytical expression of the ...Based on the formulation of a multiple non-isotropic scattering process, a characteristic source time is introduced to define the initial impulse width of energy density at the source. An analytical expression of the initial intensity spectral density of a seismic wave is incorporated into the integral equation of seismic wave energy density. And, a recursive formula of Green's function is derived to obtain the higher order Green's function, which is included to describe the stronger non-isotropic scattering process. Then, the effect of the scattering pattern on the energy density envelope is investigated by the modified scattering theory. Significant differences are found in the decay of the energy density envelopes with distances using different scattering patterns. The envelope synthesized by the forward dominated scattering pattern is larger than the results obtained by the isotropic and backward dominated scattering pattern. Different scattering patterns are also used to fit the observation data from the aftershocks of the 2008 Wenchuan earthquake. It is concluded that the envelopes synthesized by the forward scattering pattern can match the data better than the isotropic and backward dominated scattering cases, and a new interpretation of the coda wave is given. Finally, using the forward dominated scattering pattern, the envelope broadening of the observed data is reproduced.展开更多
Consider acoustic wave scattering by multiple obstacles with different sound properties on the boundary, which can be modeled by a mixed boundary value problem for the Helmholtz equation in frequency domain. Compared ...Consider acoustic wave scattering by multiple obstacles with different sound properties on the boundary, which can be modeled by a mixed boundary value problem for the Helmholtz equation in frequency domain. Compared with the standard scattering problem for one obstacle, the difficulty of such a new problem is the interaction of scattered wave by different obstacles. A decomposition method for solving this multiple scattering problem is developed. Using the boundary integral equation method, we decompose the total scattered field into a sum of contributions by separated obstacles. Each contribution corresponds to scattering problem of single obstacle. However, all the single scattering problems are coupled via the boundary conditions, representing the physical interaction of scattered wave by different obstacles. We prove the feasibility of such a decomposition. To compute these contributions efficiently, an iteration algorithm of Jacobi type is proposed, decoupling the interaction of scattered wave from the numerical points of view. Under the well-separation assumptions on multiple obstacles, we prove the convergence of iteration sequence generated by the Jacobi algorithm, and give the error estimate between exact scattered wave and the iteration solution in terms of the obstacle size and the minimal distance of multiple obstacles. Such a quantitative description reveals the essences of wave scattering by multiple obstacles. Numerical examples showing the accuracy and convergence of our method are presented.展开更多
An analytical solution for scattering of plane P waves by circular-arc layered alluvial valleys was derived by Fourier-Bessel series expansion technique, and the solution was utilized to analyze the effects of alluvia...An analytical solution for scattering of plane P waves by circular-arc layered alluvial valleys was derived by Fourier-Bessel series expansion technique, and the solution was utilized to analyze the effects of alluvial sequence and their relative stiffness on the scattering of incident waves.展开更多
Using the complex variable method and conformal mapping,scat-tering of flexural waves and dynamic stress concentrations in Mindlin’s thick plateswith a cutout have been studied.The general solution of the stress prob...Using the complex variable method and conformal mapping,scat-tering of flexural waves and dynamic stress concentrations in Mindlin’s thick plateswith a cutout have been studied.The general solution of the stress problem of thethick plate satisfying the boundary conditions on the contour of cutouts is obtained.Applying the orthogonal function expansion technique,the dynamic stress problemcan be reduced into the solution of a set of infinite algebraic equations.As examples,numerical results for the dynamic stress concentration factor in Mindlin’s plates witha circular,elliptic cutout are graphically presented in sequence.展开更多
The Green’s function is used to solve the scattering far field solution of SH-wave by a mov-able rigid cylindrical interface inclusion in a linear elastic body.First,a suitable Green’s function is devel-oped,which i...The Green’s function is used to solve the scattering far field solution of SH-wave by a mov-able rigid cylindrical interface inclusion in a linear elastic body.First,a suitable Green’s function is devel-oped,which is the fundamental displacement solution of an elastic half space with a movable rigid half-cylin-drical inclusion impacted by out-of-plane harmonic line source loaded at any point of its horizontal surface.By using the Green’s function,a series of Fredholm integral equations of the first kind which determine thescattering far field can be set up.Then the paper gives the expressions on the far field including the displace-ment mode of scattering wave and the solution of scattering cross-section.Finally,some examples and nu-merical results are discussed to analyze the influence of the combination of different media parameters on theanswer of far field.展开更多
An analytical solution for scattering of incident SH waves by a circular-arc hill with a concentric circular tunnel was derived by Fourier-Bessel series expansion and auxiliary functions technique. The solution is red...An analytical solution for scattering of incident SH waves by a circular-arc hill with a concentric circular tunnel was derived by Fourier-Bessel series expansion and auxiliary functions technique. The solution is reduced to solving a set of infinite linear algebraic equations finally. The accuracies of the numerical results are checked by the residual errors of boundary conditions with the truncation order increasing. The numerical results show that the existence and dimension of the tunnel have great effect on motion of the ground surface nearby and dynamic stress concentration of the tunnel.展开更多
The scattering and reflection of SH waves by a slope on an elastic wedged space is investigated. A series solution is obtained by using the wave function expansion method. The slope on a wedged space is divided into t...The scattering and reflection of SH waves by a slope on an elastic wedged space is investigated. A series solution is obtained by using the wave function expansion method. The slope on a wedged space is divided into two subregions by an artificial, auxiliary circular arc. The wave fields with unknown complex coefficients within each sub-region are derived. Applying Graf addition theorem, the scattered waves in the sub-regions are expressed in a global coordinate system. Fourier transform is adopted to derive a consistent form of standing waves in the inner region using the orthogonality of the cosine functions. The boundary-valued problem is solved by stress and displacement continuity along the artificial, auxiliary arc to obtain the unknown complex coefficients. Parametric studies are next performed to investigate how the topography from the slope on the wedged space will affect the scattering and diffraction, and hence the amplification and de-amplification of the SH waves. Numerical results show that the surface motions on the slope of the wedged space is influenced greatly by the topography. Amplification of the surface motions near the slope vertex is significant. The corresponding phases along the wedged space surfaces are consistent with the direction that the SH waves are propagating.展开更多
A method and procedure is presented to reconstruct three-dimensional(3D) positions of scattering centers from multiple synthetic aperture radar(SAR) images. Firstly, two-dimensional(2D) attribute scattering centers of...A method and procedure is presented to reconstruct three-dimensional(3D) positions of scattering centers from multiple synthetic aperture radar(SAR) images. Firstly, two-dimensional(2D) attribute scattering centers of targets are extracted from 2D SAR images. Secondly, similarity measure is developed based on 2D attributed scatter centers' location, type, and radargrammetry principle between multiple SAR images. By this similarity, we can associate 2D scatter centers and then obtain candidate 3D scattering centers. Thirdly, these candidate scattering centers are clustered in 3D space to reconstruct final 3D positions. Compared with presented methods, the proposed method has a capability of describing distributed scattering center, reduces false and missing 3D scattering centers, and has fewer restrictionson modeling data. Finally, results of experiments have demonstrated the effectiveness of the proposed method.展开更多
Forward-/backward-facing steps in boundary-layer flows are often seen in engineering applications, and they have potential impacts on laminar-turbulent transition through scattering of the oncoming instability modes(e...Forward-/backward-facing steps in boundary-layer flows are often seen in engineering applications, and they have potential impacts on laminar-turbulent transition through scattering of the oncoming instability modes(e.g., Tollmien-Schlichting(T-S) waves). This issue is studied in the present paper by applying a local scattering framework, which is a rather generic mathematical framework on describing the mode scattering process. In this framework, a high-Reynolds-number triple-deck formalism is employed, and a transmission coefficient, defined as the ratio of the asymptotic amplitude of the instability mode downstream of the step to that upstream, is introduced. Through the systematical study, it has been found that both the forward-and backward-facing steps have a destabilizing effect on the oncoming T-S waves in subsonic boundary layers, this effect increases with the height of the step and/or the frequency of the T-S wave, and a backward-facing step(BFS) always has a greater impact than a forward-facing step(FFS). These facts agree with most of the previous investigations.However, one numerical study(WORNER, A., RIST, U., and WAGNER, S. Humps/steps influence on stability characteristics of two-dimensional laminar boundary layer. AIAA Journal, 41, 192–197(2003)), which was based on an ad-hoc configuration, showed an opposite impact of an FFS. Through the investigation on the specific configuration, it is revealed that the wrong conclusion was drawn by misinterpreting the numerical results.展开更多
We extend the multiple-scattering theory (MST) for elastic wave scattering and propagating in two-dimensional composite. The formalism for the band structure calculation is presented by taking into account the full ve...We extend the multiple-scattering theory (MST) for elastic wave scattering and propagating in two-dimensional composite. The formalism for the band structure calculation is presented by taking into account the full vector character of the elastic wave. As a demonstration of application of the formalism, we calculate the band structure of elastic wave propagating in a two-dimensional periodic arrangement of cylinders. The results manifest that the MST shows great promise in complementing the plane-wave (PW) approach for the study of elastic wave.展开更多
The theory of elastic wave scattering is a fundamental concept in the study of elastic dynamics and wave motion,and the wave function expansion technique has been widely used in many subjects.To supply the essential t...The theory of elastic wave scattering is a fundamental concept in the study of elastic dynamics and wave motion,and the wave function expansion technique has been widely used in many subjects.To supply the essential tools for solving wave scattering problems induced by an eccentric source or multi-sources as well as multi-scatters,a whole-space transform formula of cylindrical wave functions is presented and its applicability to some simple cases is demonstrated in this study.The transforms of wave functions in cylindrical coordinates can be classifi ed into two basic types: interior transform and exterior transform,and the existing Graf's addition theorem is only suitable for the former.By performing a new replacement between the two coordinates,the exterior transform formula is fi rst deduced.It is then combined with Graf's addition theorem to establish a whole-space transform formula.By using the whole-space transform formula,the scattering solutions by the sources outside and inside a cylindrical cavity are constructed as examples of its application.The effectiveness and advantages of the whole-space transform formula is illustrated by comparison with the approximate model based on a large cycle method.The whole-space transform formula presented herein can be used to perform the transform between two different cylindrical coordinates in the whole space.In addition,its concept and principle are universal and can be further extended to establish the coordinate transform formula of wave functions in other coordinate systems.展开更多
Based on the theory of elastic dynamics,the scattering of elastic waves and dynamic stressconcentration in fiber-reinforced composite with interfaces are studied.Analytical expressions of elastic wavesin different med...Based on the theory of elastic dynamics,the scattering of elastic waves and dynamic stressconcentration in fiber-reinforced composite with interfaces are studied.Analytical expressions of elastic wavesin different medium areas are presented and an analytic method of solving this problem is established.Themode coefficients are determined by means of the continuous conditions of displacement and stress on theboundary of the interfaces.The influence of material properties and structural size on the dynamic stress con-centration factors near the interfaces is analyzed.It indicates that they have a great influence on the dynamicproperties of fiber-reinforced composite.As examples,numerical results of dynamic stress concentration fac-tors near the interfaces are presented and discussed.This paper provides reliable theoretical evidence for thestudy of dynamic properties in fiber-reinforced composite.展开更多
Shear wave velocity has numerous applications in geomechanical, petrophysical and geophysical studies of hydrocarbon reserves. However, data related to shear wave velocity isn’t available for all wells, especially ol...Shear wave velocity has numerous applications in geomechanical, petrophysical and geophysical studies of hydrocarbon reserves. However, data related to shear wave velocity isn’t available for all wells, especially old wells and it is very important to estimate this parameter using other well logging. Hence, lots of methods have been developed to estimate these data using other available information of reservoir. In this study, after processing and removing inappropriate petrophysical data, we estimated petrophysical properties affecting shear wave velocity of the reservoir and statistical methods were used to establish relationship between effective petrophysical properties and shear wave velocity. To predict (VS), first we used empirical relationships and then multivariate regression methods and neural networks were used. Multiple regression method is a powerful method that uses correlation between available information and desired parameter. Using this method, we can identify parameters affecting estimation of shear wave velocity. Neural networks can also be trained quickly and present a stable model for predicting shear wave velocity. For this reason, this method is known as “dynamic regression” compared with multiple regression. Neural network used in this study is not like a black box because we have used the results of multiple regression that can easily modify prediction of shear wave velocity through appropriate combination of data. The same information that was intended for multiple regression was used as input in neural networks, and shear wave velocity was obtained using compressional wave velocity and well logging data (neutron, density, gamma and deep resistivity) in carbonate rocks. The results show that methods applied in this carbonate reservoir was successful, so that shear wave velocity was predicted with about 92 and 95 percents of correlation coefficient in multiple regression and neural network method, respectively. Therefore, we propose using these methods to estimate shear wave velocity in wells without this parameter.展开更多
文摘In this paper, an analytic method is developed to address steady SH-wave scattering and perform dynamic analysisof multiple circular cavities in half space. The scattered wave function used for scattering of SH-waves by multiple circularcavities, which automatically satisfies the stress-free condition at the horizontal surface, is constructed by applying thesymmetry of the SH-wave scattering and the method of multi-polar coordinates system. Applying this scattered wave functionand method of moving coordinates, the original problem can be transformed to the problem of SH-wave scattering by multiplecircular cavities in the full space. Finally, the solution of the problem can be reduced to a series of algebraic equations andsolved numerically by truncating the infinite algebraic equations to the finite ones. Numerical examples are provided for casewith two cavities to show the effect of wave number, and the distances between the centers of the cavities and from the centersto the ground surface on the dynamic stress concentration around the cavity impacted by incident steady SH-wave.
基金supported by the National Natural Science Foundation of China under grant No.50608066Chinese Earthquake Science Foundation under grant No.A07045
文摘By expressing the wave functions in the form of Fourier-Bessel series,the analytical solution for the two-dimension scattering problem of plane P waves by the cylindrical canyon topography that contains arbitrary number of circular-arc-shaped layers is presented firstly.And then,the convergence of the proposed series solution with the truncation number of terms is discussed,which demonstrates that the analytical solution can converge even for very high frequencies of the incident P wave.Finally,using this solution,the influences that are imposed on the stationary ground motion by the number and the sequence of alluvial layers,as well as the stiffness of soft interlayer contained in the canyon,are studied.
基金National Natural Science Foundation of China(Nos.61871353,62031005)。
文摘In-situ measurement of internal solitary waves(ISWs)is complicated in the ocean due to their randomness.At present,the ISWs are mainly detected by the chain structure of conductivity-temperature-depth systems(CTDs)or temperature sensors.The high cost limits the spatial resolution,which ultimately affects the measuring accuracy of the ISW amplitude.In this paper,we developed an experimental measurement system for detecting ISWs based on the stimulated Raman scattering in distributed optical fibers.This system has the advantages of high precision,low cost,and easy operation.The experimental results show that the system is consistent with CTDs in the measurement of vertical ocean temperature variation.The spatial resolution of the system can reach 1.0 m and the measuring accuracy of temperature is 0.2℃.We successfully detected 3 ISWs by the system in the South China Sea and two optical remote sensing images collected on May 18,2021,the same day of two detected ISWs,verify the occurrence of the measured ISWs.We used the image pairs method to calculate the phase velocity of ISW and the result is 1.71 ms^(-1).By extracting the distances between wave packets,it can be found that the semi-diurnal tide generates the detected ISWs.The impact of the tidal current velocity on the ISW in amplitude is undeniable.Undoubtedly,the system has a great application prospect for detecting ISWs and other dynamic phenomena in the ocean.
基金the National Natural Science Foundation of China grants 42230209, 42241136, 42374199, 42204171, 42274212the Natural Science Foundation of Hunan province Grant 2021JJ20010, 2023JJ20038
文摘Whistler mode waves are critical emissions in magnetized plasmas that usually influence the electron dynamics in a planetary magnetosphere.In this paper,we present a unique event in the Martian magnetosphere in which enhanced whistler mode waves(~10^(−11) V^(2)/m^(2)/Hz)with frequency of 0.1 f_(ce)-0.5 f_(ce) occurred,based on MAVEN data,exactly corresponding to a significant decrease of suprathermal electron fluxes.The diffusion coefficients are calculated by using the observed electric field wave spectra.The pitch angle diffusion coefficient can approach 10^(−2) s^(−1),which is much larger,by~100 times,than the momentum diffusion coefficient,indicating that pitch angle scattering dominates the whistler-electron resonance process.The current results can successfully explain the dropout of the suprathermal electrons in this event.This study provides direct evidence for whistler-driven electron losses in the Martian magnetosphere.
基金supported by the National Youth Science Foundation of China(Grant No.52001211).
文摘Target strength(TS)and circular synthetic aperture sonar(CSAS)images provide essential information for active acoustic detection and recognition of non-cooperative unmanned undersea vehicles(UUVs),which pose a significant threat to underwater preset facilities.To access them,we propose an iterative physical acoustics(IPA)-based method to simulate the multiple acoustic scattered fields on rigid surfaces in high-frequency cases.It uses the Helmholtz integral equation with an appropriate Green's function in terms of the Neumann series,and then incorporates the ideas of triangulation and iteration into a numerical implementation.Then two approximate analytic formulae with precise physical meanings are derived to predict the TS and CSAS images of concave targets,respectively.There are no restrictions on the surface's curvature and the order of multiple scattering.The method is validated against the finite element method(FEM)for acoustic scattering from a sphere segment and against an experiment involving an X-rudder UUV's stern.On this basis,we simulate and analyze the TS and CSAS images of an X-rudder UUV.In addition,the influence of the angle of adjacent rudders on the multiple scattering characteristics is discussed.Results show that this method can potentially predict accurate UUV features,especially the multiple scattered features.
基金the State Key Program of National Natural Science of China under Grant No. 51138001Science Fund for Creative Research Groups of the National Natural Science Foundation of China under Grant No. 51121005Open Research Fund Program of State key Laboratory of Hydro science and Engineering under Grant No. shlhse-2010-C-03
文摘Based on the formulation of a multiple non-isotropic scattering process, a characteristic source time is introduced to define the initial impulse width of energy density at the source. An analytical expression of the initial intensity spectral density of a seismic wave is incorporated into the integral equation of seismic wave energy density. And, a recursive formula of Green's function is derived to obtain the higher order Green's function, which is included to describe the stronger non-isotropic scattering process. Then, the effect of the scattering pattern on the energy density envelope is investigated by the modified scattering theory. Significant differences are found in the decay of the energy density envelopes with distances using different scattering patterns. The envelope synthesized by the forward dominated scattering pattern is larger than the results obtained by the isotropic and backward dominated scattering pattern. Different scattering patterns are also used to fit the observation data from the aftershocks of the 2008 Wenchuan earthquake. It is concluded that the envelopes synthesized by the forward scattering pattern can match the data better than the isotropic and backward dominated scattering cases, and a new interpretation of the coda wave is given. Finally, using the forward dominated scattering pattern, the envelope broadening of the observed data is reproduced.
基金supported by NSFC (11071039,11161130002)Natural Science Foundation of Jiangsu Province (BK2011584)
文摘Consider acoustic wave scattering by multiple obstacles with different sound properties on the boundary, which can be modeled by a mixed boundary value problem for the Helmholtz equation in frequency domain. Compared with the standard scattering problem for one obstacle, the difficulty of such a new problem is the interaction of scattered wave by different obstacles. A decomposition method for solving this multiple scattering problem is developed. Using the boundary integral equation method, we decompose the total scattered field into a sum of contributions by separated obstacles. Each contribution corresponds to scattering problem of single obstacle. However, all the single scattering problems are coupled via the boundary conditions, representing the physical interaction of scattered wave by different obstacles. We prove the feasibility of such a decomposition. To compute these contributions efficiently, an iteration algorithm of Jacobi type is proposed, decoupling the interaction of scattered wave from the numerical points of view. Under the well-separation assumptions on multiple obstacles, we prove the convergence of iteration sequence generated by the Jacobi algorithm, and give the error estimate between exact scattered wave and the iteration solution in terms of the obstacle size and the minimal distance of multiple obstacles. Such a quantitative description reveals the essences of wave scattering by multiple obstacles. Numerical examples showing the accuracy and convergence of our method are presented.
基金State Natural Science Foundation of China (No.59878032).
文摘An analytical solution for scattering of plane P waves by circular-arc layered alluvial valleys was derived by Fourier-Bessel series expansion technique, and the solution was utilized to analyze the effects of alluvial sequence and their relative stiffness on the scattering of incident waves.
基金The project supported by the National Natural Science Foundation of China
文摘Using the complex variable method and conformal mapping,scat-tering of flexural waves and dynamic stress concentrations in Mindlin’s thick plateswith a cutout have been studied.The general solution of the stress problem of thethick plate satisfying the boundary conditions on the contour of cutouts is obtained.Applying the orthogonal function expansion technique,the dynamic stress problemcan be reduced into the solution of a set of infinite algebraic equations.As examples,numerical results for the dynamic stress concentration factor in Mindlin’s plates witha circular,elliptic cutout are graphically presented in sequence.
文摘The Green’s function is used to solve the scattering far field solution of SH-wave by a mov-able rigid cylindrical interface inclusion in a linear elastic body.First,a suitable Green’s function is devel-oped,which is the fundamental displacement solution of an elastic half space with a movable rigid half-cylin-drical inclusion impacted by out-of-plane harmonic line source loaded at any point of its horizontal surface.By using the Green’s function,a series of Fredholm integral equations of the first kind which determine thescattering far field can be set up.Then the paper gives the expressions on the far field including the displace-ment mode of scattering wave and the solution of scattering cross-section.Finally,some examples and nu-merical results are discussed to analyze the influence of the combination of different media parameters on theanswer of far field.
基金National Natural Science Foundation of China (50378063), Excellent Young Teachers Program of MOE and SRF for ROCS, MOE.
文摘An analytical solution for scattering of incident SH waves by a circular-arc hill with a concentric circular tunnel was derived by Fourier-Bessel series expansion and auxiliary functions technique. The solution is reduced to solving a set of infinite linear algebraic equations finally. The accuracies of the numerical results are checked by the residual errors of boundary conditions with the truncation order increasing. The numerical results show that the existence and dimension of the tunnel have great effect on motion of the ground surface nearby and dynamic stress concentration of the tunnel.
文摘The scattering and reflection of SH waves by a slope on an elastic wedged space is investigated. A series solution is obtained by using the wave function expansion method. The slope on a wedged space is divided into two subregions by an artificial, auxiliary circular arc. The wave fields with unknown complex coefficients within each sub-region are derived. Applying Graf addition theorem, the scattered waves in the sub-regions are expressed in a global coordinate system. Fourier transform is adopted to derive a consistent form of standing waves in the inner region using the orthogonality of the cosine functions. The boundary-valued problem is solved by stress and displacement continuity along the artificial, auxiliary arc to obtain the unknown complex coefficients. Parametric studies are next performed to investigate how the topography from the slope on the wedged space will affect the scattering and diffraction, and hence the amplification and de-amplification of the SH waves. Numerical results show that the surface motions on the slope of the wedged space is influenced greatly by the topography. Amplification of the surface motions near the slope vertex is significant. The corresponding phases along the wedged space surfaces are consistent with the direction that the SH waves are propagating.
文摘A method and procedure is presented to reconstruct three-dimensional(3D) positions of scattering centers from multiple synthetic aperture radar(SAR) images. Firstly, two-dimensional(2D) attribute scattering centers of targets are extracted from 2D SAR images. Secondly, similarity measure is developed based on 2D attributed scatter centers' location, type, and radargrammetry principle between multiple SAR images. By this similarity, we can associate 2D scatter centers and then obtain candidate 3D scattering centers. Thirdly, these candidate scattering centers are clustered in 3D space to reconstruct final 3D positions. Compared with presented methods, the proposed method has a capability of describing distributed scattering center, reduces false and missing 3D scattering centers, and has fewer restrictionson modeling data. Finally, results of experiments have demonstrated the effectiveness of the proposed method.
基金supported by the National Natural Science Foundation of China(Nos.11472189 and11772224)
文摘Forward-/backward-facing steps in boundary-layer flows are often seen in engineering applications, and they have potential impacts on laminar-turbulent transition through scattering of the oncoming instability modes(e.g., Tollmien-Schlichting(T-S) waves). This issue is studied in the present paper by applying a local scattering framework, which is a rather generic mathematical framework on describing the mode scattering process. In this framework, a high-Reynolds-number triple-deck formalism is employed, and a transmission coefficient, defined as the ratio of the asymptotic amplitude of the instability mode downstream of the step to that upstream, is introduced. Through the systematical study, it has been found that both the forward-and backward-facing steps have a destabilizing effect on the oncoming T-S waves in subsonic boundary layers, this effect increases with the height of the step and/or the frequency of the T-S wave, and a backward-facing step(BFS) always has a greater impact than a forward-facing step(FFS). These facts agree with most of the previous investigations.However, one numerical study(WORNER, A., RIST, U., and WAGNER, S. Humps/steps influence on stability characteristics of two-dimensional laminar boundary layer. AIAA Journal, 41, 192–197(2003)), which was based on an ad-hoc configuration, showed an opposite impact of an FFS. Through the investigation on the specific configuration, it is revealed that the wrong conclusion was drawn by misinterpreting the numerical results.
文摘We extend the multiple-scattering theory (MST) for elastic wave scattering and propagating in two-dimensional composite. The formalism for the band structure calculation is presented by taking into account the full vector character of the elastic wave. As a demonstration of application of the formalism, we calculate the band structure of elastic wave propagating in a two-dimensional periodic arrangement of cylinders. The results manifest that the MST shows great promise in complementing the plane-wave (PW) approach for the study of elastic wave.
基金the National Natural Science Foundation of China under Grand No.549974011
文摘The theory of elastic wave scattering is a fundamental concept in the study of elastic dynamics and wave motion,and the wave function expansion technique has been widely used in many subjects.To supply the essential tools for solving wave scattering problems induced by an eccentric source or multi-sources as well as multi-scatters,a whole-space transform formula of cylindrical wave functions is presented and its applicability to some simple cases is demonstrated in this study.The transforms of wave functions in cylindrical coordinates can be classifi ed into two basic types: interior transform and exterior transform,and the existing Graf's addition theorem is only suitable for the former.By performing a new replacement between the two coordinates,the exterior transform formula is fi rst deduced.It is then combined with Graf's addition theorem to establish a whole-space transform formula.By using the whole-space transform formula,the scattering solutions by the sources outside and inside a cylindrical cavity are constructed as examples of its application.The effectiveness and advantages of the whole-space transform formula is illustrated by comparison with the approximate model based on a large cycle method.The whole-space transform formula presented herein can be used to perform the transform between two different cylindrical coordinates in the whole space.In addition,its concept and principle are universal and can be further extended to establish the coordinate transform formula of wave functions in other coordinate systems.
基金the National Natural Science Foundation of China(No.19972018)
文摘Based on the theory of elastic dynamics,the scattering of elastic waves and dynamic stressconcentration in fiber-reinforced composite with interfaces are studied.Analytical expressions of elastic wavesin different medium areas are presented and an analytic method of solving this problem is established.Themode coefficients are determined by means of the continuous conditions of displacement and stress on theboundary of the interfaces.The influence of material properties and structural size on the dynamic stress con-centration factors near the interfaces is analyzed.It indicates that they have a great influence on the dynamicproperties of fiber-reinforced composite.As examples,numerical results of dynamic stress concentration fac-tors near the interfaces are presented and discussed.This paper provides reliable theoretical evidence for thestudy of dynamic properties in fiber-reinforced composite.
文摘Shear wave velocity has numerous applications in geomechanical, petrophysical and geophysical studies of hydrocarbon reserves. However, data related to shear wave velocity isn’t available for all wells, especially old wells and it is very important to estimate this parameter using other well logging. Hence, lots of methods have been developed to estimate these data using other available information of reservoir. In this study, after processing and removing inappropriate petrophysical data, we estimated petrophysical properties affecting shear wave velocity of the reservoir and statistical methods were used to establish relationship between effective petrophysical properties and shear wave velocity. To predict (VS), first we used empirical relationships and then multivariate regression methods and neural networks were used. Multiple regression method is a powerful method that uses correlation between available information and desired parameter. Using this method, we can identify parameters affecting estimation of shear wave velocity. Neural networks can also be trained quickly and present a stable model for predicting shear wave velocity. For this reason, this method is known as “dynamic regression” compared with multiple regression. Neural network used in this study is not like a black box because we have used the results of multiple regression that can easily modify prediction of shear wave velocity through appropriate combination of data. The same information that was intended for multiple regression was used as input in neural networks, and shear wave velocity was obtained using compressional wave velocity and well logging data (neutron, density, gamma and deep resistivity) in carbonate rocks. The results show that methods applied in this carbonate reservoir was successful, so that shear wave velocity was predicted with about 92 and 95 percents of correlation coefficient in multiple regression and neural network method, respectively. Therefore, we propose using these methods to estimate shear wave velocity in wells without this parameter.
