The problem of oblique wave （internal wave） propagation over a small deformation in a channel flow consisting of two layers was considered. The upper fluid was assumed to be bounded above by a rigid lid, which is an...The problem of oblique wave （internal wave） propagation over a small deformation in a channel flow consisting of two layers was considered. The upper fluid was assumed to be bounded above by a rigid lid, which is an approximation for the free surface, and the lower one was bounded below by an impermeable bottom surface having a small deformation; the channel was unbounded in the horizontal directions. Assuming irrotational motion, the perturbation technique was employed to calculate the first-order corrections of the velocity potential in the two fluids by using Green＇s integral theorem suitably with the introduction of appropriate Green＇s functions. Those functions help in calculating the reflection and transmission coefficients in terms of integrals involving the shape ftmction c（x） representing the bottom deformation. Three-dimensional linear water wave theory was utilized for formulating the relevant boundary value problem. Two special examples of bottom deformation were considered to validate the results. Consideration of a patch of sinusoidal ripples （having the same wave number） shows that the reflection coefficient is an oscillatory function of the ratio of twice the x-component of the wave number to the ripple wave number. When this ratio approaches one, the theory predicts a resonant interaction between the bed and the interface, and the reflection coefficient becomes a multiple of the number of ripples. High reflection of incident wave energy occurs if this number is large. Similar results were observed for a patch of sinusoidal ripples having different wave numbers. It was also observed that for small angles of incidence, the reflected energy is greater compared to other angles of incidence up to π/ 4. These theoretical observations are supported by graphical results.展开更多
The scattering of SH wave by a cylindrical piezoelectric inclusion partially debonded from its surrounding piezoelectric material is investigated using the wave function expansion method and singular integral ...The scattering of SH wave by a cylindrical piezoelectric inclusion partially debonded from its surrounding piezoelectric material is investigated using the wave function expansion method and singular integral equation technique. The debonding regions are modeled as mul- tiple arc-shaped interface cracks with non-contacting faces. By expressing the scattered ?elds as wave function expansions with unknown coe?cients, the mixed boundary value problem is ?rstly reduced to a set of simultaneous dual series equations. Then dislocation density functions are introduced as unknowns to transform these dual series equations into Cauchy singular integral equations of the ?rst type, which can be numerically solved easily. The solution is valid for arbi- trary number and size of the debonds. Finally, numerical results of the dynamic stress intensity factors are presented for the cases of one debond and two debonds. The e?ects of incidence direc- tion, crack con?guration and various material parameters on the dynamic stress intensity factors are respectively discussed. The solution of this problem is expected to ?nd applications in the investigation of dynamic fracture properties of piezoelectric materials with cracks.展开更多
The adoption of slotted breakwaters can be an ideal option in the protection of very large near-shore floating struc-trees that may extend offshore to a considerable water depth. In this paper, we experimently investi...The adoption of slotted breakwaters can be an ideal option in the protection of very large near-shore floating struc-trees that may extend offshore to a considerable water depth. In this paper, we experimently investigated the behaviour of wave transmission and reflection coefficients of double slotted barriers in the presence of a steady opposing current. The experimental results show that opposing currents have only minor effects on wave reflection, but can significantly reduce the wave transmission through double slotted barriers. The experimental results suggest that coastal currents should be taken into consideration for an economical design of slotted breakwaters.展开更多
The problem of wave scattering by undulating bed topography in a two-layer ocean is investigated on the basis of linear theory. In a two-layer fluid with the upper layer having a free surface, there exist two modes of...The problem of wave scattering by undulating bed topography in a two-layer ocean is investigated on the basis of linear theory. In a two-layer fluid with the upper layer having a free surface, there exist two modes of waves propagating at both the free surface of the upper layer and the interface between the two layers. Due to a wave train of a particular mode incident on an obstacle which is bottom-standing on the lower layer, reflected and transmitted waves of both modes are created by the obstacle. For small undulations on the bottom of the lower layer, a perturbation method is employed to obtain first-order reflection and transmission coefficients of both modes for incident wave trains of again both modes in terms of integrals involving the bed-shape fimction. For sinusoidal undulations, numerical results are presented graphically to illustrate the energy transfer between the waves of different modes by the undulating bed.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 scattering of plane surface waves by bottom undulations in channel flow consisting of two layers is investigated by assuming that the bed of the channel is composed of porous material. The upper surface of the flu...The scattering of plane surface waves by bottom undulations in channel flow consisting of two layers is investigated by assuming that the bed of the channel is composed of porous material. The upper surface of the fluid is bounded by a rigid lid and the channel is unbounded in the horizontal directions. There exists only one wave mode corresponding to an internal wave. For small undulations, a simplified perturbation analysis is used to obtain first order reflection and transmission coefficients in terms of integrals involving the shape function describing the bottom. For sinusoidal bottom undulations and exponentially decaying bottom topography, the first order coefficients are computed. In the case of sinusoidal bottom the first order transmission coefficient is found to vanish identically. The numerical results are depicted graphically in a number of figures.展开更多
In this paper, on the basis of Liu’s complex function and conformal mapping methods, supplemented by local coordinate system method, e-type piezoelectric material and elastic wave scattering and dynamic stress concen...In this paper, on the basis of Liu’s complex function and conformal mapping methods, supplemented by local coordinate system method, e-type piezoelectric material and elastic wave scattering and dynamic stress concentrations problems with double holes question are studied, and an analytical solution is given to the problems. On the basis of multiple scattering of elastic wave theory, put forward the study about microscopic dynamics model to dynamic stress in the structure of piezoelectric composites as well as dynamic playing field. As an example, the numerical results of the dynamic stress distribution around the hole in case double equal diameter holes are given in the paper, and the influence of incident wave number and hole-spacing parameters on the dynamic stress concentration factor is analyzed.展开更多
Assuming linear theory, the two-dimensional problem of water wave scattering by a horizontal nearly circular cylinder submerged in infinitely deep water with an ice cover modeled as a thin-elastic plate floating on wa...Assuming linear theory, the two-dimensional problem of water wave scattering by a horizontal nearly circular cylinder submerged in infinitely deep water with an ice cover modeled as a thin-elastic plate floating on water, is investigated here. The cross-section of the nearly circular cylinder is taken as r=a（1＋δC（θ））, where a is the radius of the corresponding circular cross-section of the cylinder, δ is a measure of small departure of the cross-section of the cylinder from its circularity and C（θ） is the shape function. Using a simplified perturbation technique the problem is reduced to two independent boundary value problems up to first order in δ. The first one corresponds to water wave scattering by a circular cylinder submerged in water with an ice-cover, while the second problem describes wave radiation by a submerged circular cylinder and involves first order correction to the reflection and transmission coefficients. The corrections are obtained in terms of integrals involving the shape function. Assuming a general Fourier expansion of the shape function, these corrections are evaluated approximately. It is well known that normally incident wave trains experience no reflection by a circular cylinder submerged in infinitely deep water with an ice cover. It is shown here that the reflection coefficient also vanishes up to first order for some particular choice of the shape function representing a nearly circular cylinder. For these cases, full transmission occurs, only change is in its phase which is depicted graphically against the wave number in a number of figures and appropriate conclusions are drawn.展开更多
Recent experimental results have shown that the presence of a steady current can significantly reduce the energy of transmitted waves. In this paper, a theory is developed to study the wave scattering by single or dou...Recent experimental results have shown that the presence of a steady current can significantly reduce the energy of transmitted waves. In this paper, a theory is developed to study the wave scattering by single or double vertical slotted barriers in the presence of a weak uniform current. The quasi-linear theory is based on an eigenfunction expansion method. Comparisons between theory and existing experimental results for both single slotted barrier and double slotted barriers show satisfactory agreements. In consideration of wave propagation in a weak current it is found that the friction factor used to characterize the head loss at the slotted barrier depends on both the geometry of the slotted barrier and the strength of the steady current.展开更多
Using linear water wave theory,three-dimensional problems concerning the interaction of waves with spherical structures in a fluid which contains a three-layer fluid consisting of a layer of finite depth bounded above...Using linear water wave theory,three-dimensional problems concerning the interaction of waves with spherical structures in a fluid which contains a three-layer fluid consisting of a layer of finite depth bounded above by freshwater of finite depth with free surface and below by an infinite layer of water of greater density are considered.In such a situation timeharmonic waves with a given frequency can propagate with three wavenumbers.The sphere is submerged in either of the three layers.Each problem is reduced to an infinite system of linear equations by employing the method of multipoles and the system of equations is solved numerically by standard technique.The hydrodynamic forces(vertical and horizontal forces)are obtained and depicted graphically against the wavenumber.When the density ratio of the upper and middle layer is made to approximately one,curves for vertical and horizontal forces almost coincide with the corresponding curves for the case of a two-layer fluid with a free surface.This means that in the limit,the density ratio of the upper and middle layer goes to approximately one,the solution agrees with the solution for the case of a two-layer fluid with a free surface.展开更多
The solution of water wave scattering problem involving small deformation on a porous bed in a channel, where the upper surface is bounded above by an infinitely extent rigid horizontal surface, is studied here within...The solution of water wave scattering problem involving small deformation on a porous bed in a channel, where the upper surface is bounded above by an infinitely extent rigid horizontal surface, is studied here within the framework of linearized water wave theory. In such a situation, there exists only one mode of waves propagating on the porous surface. A simplified perturbation analysis, involving a small parameter ε （≤1） , which measures the smallness of the deformation, is employed to reduce the governing Boundary Value Problem （BVP） to a simpler BVP for the first-order correction of the potential function. The first-order potential function and, hence, the first-order reflection and transmission coefficients are obtained by the method based on Fourier transform technique as well as Green＇s integral theorem with the introduction of appropriate Green＇s function. Two special examples of bottom deformation： the exponentially damped deformation and the sinusoidal ripple bed, are considered to validate the results. For the particular example of a patch of sinusoidal ripples, the resonant interaction between the bed and the upper surface of the fluid is attained in the neighborhood of a singularity, when the ripples wavenumbers of the bottom deformation become approximately twice the components of the incident field wavenumber along the positive x -direction. Also, the main advantage of the present study is that the results for the values of reflection and transmission coefficients are found to satisfy the energy-balance relation almost accurately.展开更多
In this paper, based on complex variables and conformal mapping methods, using the refined dynamic equation of plates, elastic wave scattering and dynamic stress concentrations in plates with two cutouts were studied....In this paper, based on complex variables and conformal mapping methods, using the refined dynamic equation of plates, elastic wave scattering and dynamic stress concentrations in plates with two cutouts were studied. Applying the orthogonal function expansion method, the problem to be solved can be reduced into the solution of a set of infinite algebraic equations. According to free boundary conditions, numerical results of dynamic moment concentration factors in thick plates with two circular cutouts analyze that: there will be more complex interaction changes between two-cutout situation than single cutout situation. In the case of low frequency or high frequency and thin plate, the hole-spacing in the absence of coupling interactions was larger or smaller. The numerical results and method can be used to analyze the dynamics and strength of plate-like structures.展开更多
We present a theoretical investigation of the scattering of high frequency S0 Lamb mode from a circular blind hole defect in a plate based on the 3D theory. The SO wave is incident at the frequency above the A1 mode c...We present a theoretical investigation of the scattering of high frequency S0 Lamb mode from a circular blind hole defect in a plate based on the 3D theory. The SO wave is incident at the frequency above the A1 mode cut-off frequency, in which the popular approximate plate theories are inapplicable. Due to the non-symmetric blind hole defect, the scattered fields will contain higher order converted modes in addition to the fundamental SO and AO modes. The far-field scattering amplitudes of various propagating Lamb modes for different hole sizes are inspected. The results are compared with those of lower frequencies and some different phenomena are found. Two-dimensional Fourier transform （2DFT） results of transient scattered Lamb and SH wave signals agree well with the analytical dispersion curves, which check the validity of the solutions from another point of view.展开更多
A new method to solve the boundary value problem arising in the study of scattering of two-dimensional surface water waves by a discontinuity in the surface boundary conditions is presented in this paper. The disconti...A new method to solve the boundary value problem arising in the study of scattering of two-dimensional surface water waves by a discontinuity in the surface boundary conditions is presented in this paper. The discontinuity arises due to the floating of two semi-infinite inertial surfaces of different surface densities. Applying Green＇s second identity to the potential functions and appropriate Green＇s functions, this problem is reduced to solving two coupled Fredholm integral equations with regular kernels. The solutions to these integral equations are used to determine the reflection and the transmission coefficients. The results for the reflection coefficient are presented graphically and are compared to those obtained earlier using other research methods. It is observed from the graphs that the results computed from the present analysis match exactly with the previous results.展开更多
Based on the theory of elastic dynamics, multiple scattering of elastic waves and dynamic stress concentrations in fiber_reinforced composite were studied. The analytical expressions of elastic waves in different regi...Based on the theory of elastic dynamics, multiple scattering of elastic waves and dynamic stress concentrations in fiber_reinforced composite were studied. The analytical expressions of elastic waves in different region were presented and an analytic method to solve this problem was established. The mode coefficients of elastic waves were determined in accordance with the continuous conditions of displacement and stress on the boundary of the multi_interfaces. By making use of the addition theorem of Hankel functions, the formulations of scattered wave fields in different local coordinates were transformed into those in one local coordinate to determine the unknown coefficients and dynamic stress concentration factors. The influence of distance between two inclusions, material properties and structural size on the dynamic stress concentration factors near the interfaces was analyzed. It indicates in the analysis that distance between two inclusions, material properties and structural size has great influence on the dynamic properties of fiber_reinforced composite near the interfaces. As examples, the numerical results of dynamic stress concentration factors near the interfaces in a fiber_reinforced composite are presented and discussed.展开更多
We consider a numerical algorithm for the two-dimensional time-harmonic elastic wave scattering by unbounded rough surfaces with Dirichlet boundary condition.A Nystr¨om method is proposed for the scattering probl...We consider a numerical algorithm for the two-dimensional time-harmonic elastic wave scattering by unbounded rough surfaces with Dirichlet boundary condition.A Nystr¨om method is proposed for the scattering problem based on the integral equation method.Convergence of the Nystr¨om method is established with convergence rate depending on the smoothness of the rough surfaces.In doing so,a crucial role is played by analyzing the singularities of the kernels of the relevant boundary integral operators.Numerical experiments are presented to demonstrate the effectiveness of the method.Mathematics subject classification:35P25,45P05.展开更多
Elastic wave inverse scattering theory plays an important role in parameters estimation of heterogeneous media.Combining inverse scattering theory,perturbation theory and stationary phase approximation,we derive the P...Elastic wave inverse scattering theory plays an important role in parameters estimation of heterogeneous media.Combining inverse scattering theory,perturbation theory and stationary phase approximation,we derive the P-wave seismic scattering coefficient equation in terms of fluid factor,shear modulus and density of background homogeneous media and perturbation media.With this equation as forward solver,a pre-stack seismic Bayesian inversion method is proposed to estimate the fluid factor of heterogeneous media.In this method,Cauchy distribution is utilized to the ratios of fluid factors,shear moduli and densities of perturbation media and background homogeneous media,respectively.Gaussian distribution is utilized to the likelihood function.The introduction of constraints from initial smooth models enhances the stability of the estimation of model parameters.Model test and real data example demonstrate that the proposed method is able to estimate the fluid factor of heterogeneous media from pre-stack seismic data directly and reasonably.展开更多
Based on Biot’s theory and considering the properties of a cavity,the boundary integral equations for the numerical simulation of wave scattering around a cavity with a circular cross-section embedded in saturated so...Based on Biot’s theory and considering the properties of a cavity,the boundary integral equations for the numerical simulation of wave scattering around a cavity with a circular cross-section embedded in saturated soil are obtained using integral transform methods.The Cauchy type singularity of the boundary integral equation is discussed.The effectiveness of the properties of soil mass and incident field on the dynamic stress concentration and pore pressure concentration around a cavity is analyzed.Our results are in good agreement with the existing solution.The numerical results of this work show that the dynamic stress concentration and pore pressure concentration are influenced by the degree of fluid–solid coupling as well as the pore compressibility and water permeability of saturated soil.With increased degree of fluid–solid coupling,the dynamic stress concentration improves from 1.87 to 3.42 and the scattering becomes more significant.With decreased index of soil mass compressibility,the dynamic stress concentration increases and its maximum reaches 3.67.The dynamic stress concentration increases from 1.64 to 3.49 and pore pressure concentration improves from 0.18 to 0.46 with decreased water permeability of saturated soil.展开更多
Slotted breakwaters have been used to provide economical protection from waves in harbors where surface waves and currents may co-exist. In this paper, the effects of currents on the wave scattering by slotted breakwa...Slotted breakwaters have been used to provide economical protection from waves in harbors where surface waves and currents may co-exist. In this paper, the effects of currents on the wave scattering by slotted breakwaters are investigated by using a simple model. The model is based on a long wave approximation. The effects of wave height, barrier geometry and current strength on the reflection and transmission coefficients are examined by the model. The model results are compared with recent experimental data. It is found that both the wave-following and wave-opposing currents can increase the reflection coefficient and reduce the transmission coefficient. The model can be used to study the interaction between long waves and slotted breakwaters in coastal waters.展开更多
Using linear water-wave theory,wave scattering by a horizontal circular cylinder submerged in a three-layer ocean consisting of a layer of finite depth bounded above by finite depth water with free surface and below b...Using linear water-wave theory,wave scattering by a horizontal circular cylinder submerged in a three-layer ocean consisting of a layer of finite depth bounded above by finite depth water with free surface and below by an infinite layer of fluid of greater density is considered.The cylinder is submerged in either of the three layers.In such a situation time-harmonic waves with given frequency can propagate with three different wave numbers.Employing the method of multipoles the problem is reduced to an infinite system of linear equations which are solved numerically by standard technique after truncation.The transmission and reflection coefficients are obtained and depicted graphically against the wave number for all cases.In a two-layer fluid there are energy identities that exist connecting the transmission and reflection coefficients that arise.These energy identities are systematically extended to the three-fluid cases which are obtained.展开更多
文摘The problem of oblique wave （internal wave） propagation over a small deformation in a channel flow consisting of two layers was considered. The upper fluid was assumed to be bounded above by a rigid lid, which is an approximation for the free surface, and the lower one was bounded below by an impermeable bottom surface having a small deformation; the channel was unbounded in the horizontal directions. Assuming irrotational motion, the perturbation technique was employed to calculate the first-order corrections of the velocity potential in the two fluids by using Green＇s integral theorem suitably with the introduction of appropriate Green＇s functions. Those functions help in calculating the reflection and transmission coefficients in terms of integrals involving the shape ftmction c（x） representing the bottom deformation. Three-dimensional linear water wave theory was utilized for formulating the relevant boundary value problem. Two special examples of bottom deformation were considered to validate the results. Consideration of a patch of sinusoidal ripples （having the same wave number） shows that the reflection coefficient is an oscillatory function of the ratio of twice the x-component of the wave number to the ripple wave number. When this ratio approaches one, the theory predicts a resonant interaction between the bed and the interface, and the reflection coefficient becomes a multiple of the number of ripples. High reflection of incident wave energy occurs if this number is large. Similar results were observed for a patch of sinusoidal ripples having different wave numbers. It was also observed that for small angles of incidence, the reflected energy is greater compared to other angles of incidence up to π/ 4. These theoretical observations are supported by graphical results.
基金Project supported by the Research Fund for Doctors of Hebei Province China (No. B2001213).
文摘The scattering of SH wave by a cylindrical piezoelectric inclusion partially debonded from its surrounding piezoelectric material is investigated using the wave function expansion method and singular integral equation technique. The debonding regions are modeled as mul- tiple arc-shaped interface cracks with non-contacting faces. By expressing the scattered ?elds as wave function expansions with unknown coe?cients, the mixed boundary value problem is ?rstly reduced to a set of simultaneous dual series equations. Then dislocation density functions are introduced as unknowns to transform these dual series equations into Cauchy singular integral equations of the ?rst type, which can be numerically solved easily. The solution is valid for arbi- trary number and size of the debonds. Finally, numerical results of the dynamic stress intensity factors are presented for the cases of one debond and two debonds. The e?ects of incidence direc- tion, crack con?guration and various material parameters on the dynamic stress intensity factors are respectively discussed. The solution of this problem is expected to ?nd applications in the investigation of dynamic fracture properties of piezoelectric materials with cracks.
基金The work was partially supported bythe Nanyang Technological University,Singapore(Grant No.SUG03/07)partially supported by RGC,Hong Kong,China(Grant No.DAG03/04.EG39)
文摘The adoption of slotted breakwaters can be an ideal option in the protection of very large near-shore floating struc-trees that may extend offshore to a considerable water depth. In this paper, we experimently investigated the behaviour of wave transmission and reflection coefficients of double slotted barriers in the presence of a steady opposing current. The experimental results show that opposing currents have only minor effects on wave reflection, but can significantly reduce the wave transmission through double slotted barriers. The experimental results suggest that coastal currents should be taken into consideration for an economical design of slotted breakwaters.
文摘The problem of wave scattering by undulating bed topography in a two-layer ocean is investigated on the basis of linear theory. In a two-layer fluid with the upper layer having a free surface, there exist two modes of waves propagating at both the free surface of the upper layer and the interface between the two layers. Due to a wave train of a particular mode incident on an obstacle which is bottom-standing on the lower layer, reflected and transmitted waves of both modes are created by the obstacle. For small undulations on the bottom of the lower layer, a perturbation method is employed to obtain first-order reflection and transmission coefficients of both modes for incident wave trains of again both modes in terms of integrals involving the bed-shape fimction. For sinusoidal undulations, numerical results are presented graphically to illustrate the energy transfer between the waves of different modes by the undulating bed.
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.
文摘The scattering of plane surface waves by bottom undulations in channel flow consisting of two layers is investigated by assuming that the bed of the channel is composed of porous material. The upper surface of the fluid is bounded by a rigid lid and the channel is unbounded in the horizontal directions. There exists only one wave mode corresponding to an internal wave. For small undulations, a simplified perturbation analysis is used to obtain first order reflection and transmission coefficients in terms of integrals involving the shape function describing the bottom. For sinusoidal bottom undulations and exponentially decaying bottom topography, the first order coefficients are computed. In the case of sinusoidal bottom the first order transmission coefficient is found to vanish identically. The numerical results are depicted graphically in a number of figures.
文摘In this paper, on the basis of Liu’s complex function and conformal mapping methods, supplemented by local coordinate system method, e-type piezoelectric material and elastic wave scattering and dynamic stress concentrations problems with double holes question are studied, and an analytical solution is given to the problems. On the basis of multiple scattering of elastic wave theory, put forward the study about microscopic dynamics model to dynamic stress in the structure of piezoelectric composites as well as dynamic playing field. As an example, the numerical results of the dynamic stress distribution around the hole in case double equal diameter holes are given in the paper, and the influence of incident wave number and hole-spacing parameters on the dynamic stress concentration factor is analyzed.
基金the financial support from CTS Visitors Program, Indian Institute of Technology, Kharagpur during the tenure of which the revision of the paper has been made
文摘Assuming linear theory, the two-dimensional problem of water wave scattering by a horizontal nearly circular cylinder submerged in infinitely deep water with an ice cover modeled as a thin-elastic plate floating on water, is investigated here. The cross-section of the nearly circular cylinder is taken as r=a（1＋δC（θ））, where a is the radius of the corresponding circular cross-section of the cylinder, δ is a measure of small departure of the cross-section of the cylinder from its circularity and C（θ） is the shape function. Using a simplified perturbation technique the problem is reduced to two independent boundary value problems up to first order in δ. The first one corresponds to water wave scattering by a circular cylinder submerged in water with an ice-cover, while the second problem describes wave radiation by a submerged circular cylinder and involves first order correction to the reflection and transmission coefficients. The corrections are obtained in terms of integrals involving the shape function. Assuming a general Fourier expansion of the shape function, these corrections are evaluated approximately. It is well known that normally incident wave trains experience no reflection by a circular cylinder submerged in infinitely deep water with an ice cover. It is shown here that the reflection coefficient also vanishes up to first order for some particular choice of the shape function representing a nearly circular cylinder. For these cases, full transmission occurs, only change is in its phase which is depicted graphically against the wave number in a number of figures and appropriate conclusions are drawn.
基金This work was financially supported bythe Nanyang Technological University,Singapore(Grant No.SUG03/07)
文摘Recent experimental results have shown that the presence of a steady current can significantly reduce the energy of transmitted waves. In this paper, a theory is developed to study the wave scattering by single or double vertical slotted barriers in the presence of a weak uniform current. The quasi-linear theory is based on an eigenfunction expansion method. Comparisons between theory and existing experimental results for both single slotted barrier and double slotted barriers show satisfactory agreements. In consideration of wave propagation in a weak current it is found that the friction factor used to characterize the head loss at the slotted barrier depends on both the geometry of the slotted barrier and the strength of the steady current.
文摘Using linear water wave theory,three-dimensional problems concerning the interaction of waves with spherical structures in a fluid which contains a three-layer fluid consisting of a layer of finite depth bounded above by freshwater of finite depth with free surface and below by an infinite layer of water of greater density are considered.In such a situation timeharmonic waves with a given frequency can propagate with three wavenumbers.The sphere is submerged in either of the three layers.Each problem is reduced to an infinite system of linear equations by employing the method of multipoles and the system of equations is solved numerically by standard technique.The hydrodynamic forces(vertical and horizontal forces)are obtained and depicted graphically against the wavenumber.When the density ratio of the upper and middle layer is made to approximately one,curves for vertical and horizontal forces almost coincide with the corresponding curves for the case of a two-layer fluid with a free surface.This means that in the limit,the density ratio of the upper and middle layer goes to approximately one,the solution agrees with the solution for the case of a two-layer fluid with a free surface.
基金Partially supported by a research grant from Department of Science and Technology(DST),India(No.SB/FTP/MS-003/2013)
文摘The solution of water wave scattering problem involving small deformation on a porous bed in a channel, where the upper surface is bounded above by an infinitely extent rigid horizontal surface, is studied here within the framework of linearized water wave theory. In such a situation, there exists only one mode of waves propagating on the porous surface. A simplified perturbation analysis, involving a small parameter ε （≤1） , which measures the smallness of the deformation, is employed to reduce the governing Boundary Value Problem （BVP） to a simpler BVP for the first-order correction of the potential function. The first-order potential function and, hence, the first-order reflection and transmission coefficients are obtained by the method based on Fourier transform technique as well as Green＇s integral theorem with the introduction of appropriate Green＇s function. Two special examples of bottom deformation： the exponentially damped deformation and the sinusoidal ripple bed, are considered to validate the results. For the particular example of a patch of sinusoidal ripples, the resonant interaction between the bed and the upper surface of the fluid is attained in the neighborhood of a singularity, when the ripples wavenumbers of the bottom deformation become approximately twice the components of the incident field wavenumber along the positive x -direction. Also, the main advantage of the present study is that the results for the values of reflection and transmission coefficients are found to satisfy the energy-balance relation almost accurately.
文摘In this paper, based on complex variables and conformal mapping methods, using the refined dynamic equation of plates, elastic wave scattering and dynamic stress concentrations in plates with two cutouts were studied. Applying the orthogonal function expansion method, the problem to be solved can be reduced into the solution of a set of infinite algebraic equations. According to free boundary conditions, numerical results of dynamic moment concentration factors in thick plates with two circular cutouts analyze that: there will be more complex interaction changes between two-cutout situation than single cutout situation. In the case of low frequency or high frequency and thin plate, the hole-spacing in the absence of coupling interactions was larger or smaller. The numerical results and method can be used to analyze the dynamics and strength of plate-like structures.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11474195,11274226 and 61171145
文摘We present a theoretical investigation of the scattering of high frequency S0 Lamb mode from a circular blind hole defect in a plate based on the 3D theory. The SO wave is incident at the frequency above the A1 mode cut-off frequency, in which the popular approximate plate theories are inapplicable. Due to the non-symmetric blind hole defect, the scattered fields will contain higher order converted modes in addition to the fundamental SO and AO modes. The far-field scattering amplitudes of various propagating Lamb modes for different hole sizes are inspected. The results are compared with those of lower frequencies and some different phenomena are found. Two-dimensional Fourier transform （2DFT） results of transient scattered Lamb and SH wave signals agree well with the analytical dispersion curves, which check the validity of the solutions from another point of view.
基金Partially Supported by a DST Research Project to RG(No.SR/FTP/MS-020/2010)
文摘A new method to solve the boundary value problem arising in the study of scattering of two-dimensional surface water waves by a discontinuity in the surface boundary conditions is presented in this paper. The discontinuity arises due to the floating of two semi-infinite inertial surfaces of different surface densities. Applying Green＇s second identity to the potential functions and appropriate Green＇s functions, this problem is reduced to solving two coupled Fredholm integral equations with regular kernels. The solutions to these integral equations are used to determine the reflection and the transmission coefficients. The results for the reflection coefficient are presented graphically and are compared to those obtained earlier using other research methods. It is observed from the graphs that the results computed from the present analysis match exactly with the previous results.
文摘Based on the theory of elastic dynamics, multiple scattering of elastic waves and dynamic stress concentrations in fiber_reinforced composite were studied. The analytical expressions of elastic waves in different region were presented and an analytic method to solve this problem was established. The mode coefficients of elastic waves were determined in accordance with the continuous conditions of displacement and stress on the boundary of the multi_interfaces. By making use of the addition theorem of Hankel functions, the formulations of scattered wave fields in different local coordinates were transformed into those in one local coordinate to determine the unknown coefficients and dynamic stress concentration factors. The influence of distance between two inclusions, material properties and structural size on the dynamic stress concentration factors near the interfaces was analyzed. It indicates in the analysis that distance between two inclusions, material properties and structural size has great influence on the dynamic properties of fiber_reinforced composite near the interfaces. As examples, the numerical results of dynamic stress concentration factors near the interfaces in a fiber_reinforced composite are presented and discussed.
基金supported by the National Key R&D Program of China(Grant 2018YFA0702502)the Beijing Natural Science Foundation(Grant Z210001)+2 种基金the NNSF of China(Grants 12171057,12271515,12201023)the Youth Innovation Promotion Association CAS,by the Education Department of Hunan Province(Grant 21B0299)the Fundamental Research Funds for the Central Universities(Grant YWF-23-Q-1026,YWF-22-T-204)。
文摘We consider a numerical algorithm for the two-dimensional time-harmonic elastic wave scattering by unbounded rough surfaces with Dirichlet boundary condition.A Nystr¨om method is proposed for the scattering problem based on the integral equation method.Convergence of the Nystr¨om method is established with convergence rate depending on the smoothness of the rough surfaces.In doing so,a crucial role is played by analyzing the singularities of the kernels of the relevant boundary integral operators.Numerical experiments are presented to demonstrate the effectiveness of the method.Mathematics subject classification:35P25,45P05.
基金supported by the National Basic Research Program of China(Grant No.2013CB228604)the National Grand Project for Science and Technology(Grant Nos.2011ZX05030-004-002,2011ZX05019-003&2011ZX05006-002)
文摘Elastic wave inverse scattering theory plays an important role in parameters estimation of heterogeneous media.Combining inverse scattering theory,perturbation theory and stationary phase approximation,we derive the P-wave seismic scattering coefficient equation in terms of fluid factor,shear modulus and density of background homogeneous media and perturbation media.With this equation as forward solver,a pre-stack seismic Bayesian inversion method is proposed to estimate the fluid factor of heterogeneous media.In this method,Cauchy distribution is utilized to the ratios of fluid factors,shear moduli and densities of perturbation media and background homogeneous media,respectively.Gaussian distribution is utilized to the likelihood function.The introduction of constraints from initial smooth models enhances the stability of the estimation of model parameters.Model test and real data example demonstrate that the proposed method is able to estimate the fluid factor of heterogeneous media from pre-stack seismic data directly and reasonably.
基金Projects(50969007,51269021) supported by the National Natural Science Foundation of ChinaProjects(20114BAB206012,20133ACB20006) supported by the Natural Science Foundation of Jiangxi Province of China
文摘Based on Biot’s theory and considering the properties of a cavity,the boundary integral equations for the numerical simulation of wave scattering around a cavity with a circular cross-section embedded in saturated soil are obtained using integral transform methods.The Cauchy type singularity of the boundary integral equation is discussed.The effectiveness of the properties of soil mass and incident field on the dynamic stress concentration and pore pressure concentration around a cavity is analyzed.Our results are in good agreement with the existing solution.The numerical results of this work show that the dynamic stress concentration and pore pressure concentration are influenced by the degree of fluid–solid coupling as well as the pore compressibility and water permeability of saturated soil.With increased degree of fluid–solid coupling,the dynamic stress concentration improves from 1.87 to 3.42 and the scattering becomes more significant.With decreased index of soil mass compressibility,the dynamic stress concentration increases and its maximum reaches 3.67.The dynamic stress concentration increases from 1.64 to 3.49 and pore pressure concentration improves from 0.18 to 0.46 with decreased water permeability of saturated soil.
基金The project partially supported by the Hong Kong Research Grant Council under Grant NoHKUST-DAG03/04.EG39 and HKUST6227/04E.
文摘Slotted breakwaters have been used to provide economical protection from waves in harbors where surface waves and currents may co-exist. In this paper, the effects of currents on the wave scattering by slotted breakwaters are investigated by using a simple model. The model is based on a long wave approximation. The effects of wave height, barrier geometry and current strength on the reflection and transmission coefficients are examined by the model. The model results are compared with recent experimental data. It is found that both the wave-following and wave-opposing currents can increase the reflection coefficient and reduce the transmission coefficient. The model can be used to study the interaction between long waves and slotted breakwaters in coastal waters.
文摘Using linear water-wave theory,wave scattering by a horizontal circular cylinder submerged in a three-layer ocean consisting of a layer of finite depth bounded above by finite depth water with free surface and below by an infinite layer of fluid of greater density is considered.The cylinder is submerged in either of the three layers.In such a situation time-harmonic waves with given frequency can propagate with three different wave numbers.Employing the method of multipoles the problem is reduced to an infinite system of linear equations which are solved numerically by standard technique after truncation.The transmission and reflection coefficients are obtained and depicted graphically against the wave number for all cases.In a two-layer fluid there are energy identities that exist connecting the transmission and reflection coefficients that arise.These energy identities are systematically extended to the three-fluid cases which are obtained.
