We introduce the Thomsen anisotropic parameters into the approximate linear reflection coefficient equation for P-SV wave in weakly anisotropic HTI media. From this we get a new, more effective, and practical reflecti...We introduce the Thomsen anisotropic parameters into the approximate linear reflection coefficient equation for P-SV wave in weakly anisotropic HTI media. From this we get a new, more effective, and practical reflection coefficient equation. We performed forward modeling to AVO attributes, obtaining excellent results. The combined AVO attribute analysis of PP and PS reflection data can greatly reduce ambiguity, obtain better petrophysical parameters, and improve parameter accuracy.展开更多
The reflection coefficient and the total horizontal forces of regular waves acting on theperforated caisson are experimentally investigated. The empirical relationship between reflection coefficient and the ratio of t...The reflection coefficient and the total horizontal forces of regular waves acting on theperforated caisson are experimentally investigated. The empirical relationship between reflection coefficient and the ratio of the total horizontal forces acting on the perforated caisson to those on solid vertical walls with the relative chamber width, relative water depth and porosity of perforated wall, etc. are given. Moreover, the results of the ratio of the total horizontal forces are also compared with formulas given by Chinese Harbour Design Criteria and Takahashi, which may be useful for the practical engineering application.展开更多
Although the Zoeppritz equation is suitable for a single interface in a thick deposit, it has some limitations for composite reflection waves from both the floor and the roof of coal seams. Based on the ray model, the...Although the Zoeppritz equation is suitable for a single interface in a thick deposit, it has some limitations for composite reflection waves from both the floor and the roof of coal seams. Based on the ray model, the relationship of the overall reflection coefficient of composite reflection P waves, from coal seam versus incidence angle (AVO), is dis- cussed. The result shows that: 1) the overall reflection coefficient of composite reflection waves from coal seams is a negative value and is determined mainly by the lithology of roof and floor, which is different from the reflection coeffi- cient of a single interface; 2) if the incidence angle ranges from 0° to 6°, the reflection coefficient of composite waves of a coal seam does not change with the incidence angle and 3) if the incidence angle ranges from 6–60° , the reflection coefficient increases monotonically.展开更多
The hollow-pipe perforated breakwater is of low reflection. In this paper the functions of reflection coefficients of both regular and random waves are theoretically derived, based on the concept of linear superimposi...The hollow-pipe perforated breakwater is of low reflection. In this paper the functions of reflection coefficients of both regular and random waves are theoretically derived, based on the concept of linear superimposition of reflected and incident waves and with the total flow rate continuity of integral form instead of the non-continuity of the boundary condition, and based on the concept of linear wave spectrum theory. Comparisons between theoretical results presented here and measurements of model tests show reasonable agreement.展开更多
In this paper, the modified Bayesian method for the analysis of directional wave spectra and reflection coefficients is verified by numerical and physical simulation of waves. The results show that the method can basi...In this paper, the modified Bayesian method for the analysis of directional wave spectra and reflection coefficients is verified by numerical and physical simulation of waves. The results show that the method can basically separate the incident and reflected directional spectra. In addition, the effect of the type of wave gage arrays, the number of measured wave properties, and the distance between the wave gage array and the reflection line on the resolution of the method are investigated. Some suggestions are proposed for practical application.展开更多
The wave reflection coefficient frequency spectrum and directional spectrum for concrete face slope breakwaters and rubble mound breakwaters are investigated through physical model tests in the present study. The refl...The wave reflection coefficient frequency spectrum and directional spectrum for concrete face slope breakwaters and rubble mound breakwaters are investigated through physical model tests in the present study. The reflection coefficients of oblique irregular waves are analyzed by the Modified Two-Point Method (MTPM) proposed by the authors. The results show that the wave reflection coefficient decreases with increasing wave frequency and incident angle or decreasing structure slope. The reflection coefficient frequency spectrum and its variation with Iribarren number are given in this paper. The paper also suggests an empirical 3-dimensional reflection coefficient spectrum, i.e. reflection coefficient directional spectrum, which can be used to illustrate quantitatively the variation of reflection coefficient with the incident angle and the Iribarren number for oblique irregular waves.展开更多
In this study,we focus on the numerical modelling of the interaction between waves and submerged structures in the presence of a uniform flow current.Both the same and opposite senses of wave propagation are considere...In this study,we focus on the numerical modelling of the interaction between waves and submerged structures in the presence of a uniform flow current.Both the same and opposite senses of wave propagation are considered.The main objective is an understanding of the effect of the current and various geometrical parameters on the reflection coefficient.The wave used in the study is based on potential theory,and the submerged structures consist of two rectangular breakwaters positioned at a fixed distance from each other and attached to the bottom of a wave flume.The numerical modeling approach employed in this work relies on the Boundary Element Method(BEM).The results are compared with experimental data to validate the approach.The findings of the study demonstrate that the double rectangular breakwater configuration exhibits superior wave attenuation abilities if compared to a single rectangular breakwater,particularly at low wavenumbers.Furthermore,the study reveals that wave mitigation is more pronounced when the current and wave propagation are coplanar,whereas it is less effective in the case of opposing current.展开更多
The seismic reflection and transmission characteristics of a single layer sandwiched between two dissimilar poroelastic solids saturated with two immiscible viscous fluids are investigated. The sandwiched layer is mod...The seismic reflection and transmission characteristics of a single layer sandwiched between two dissimilar poroelastic solids saturated with two immiscible viscous fluids are investigated. The sandwiched layer is modeled as a porous solid with finite thickness. The propagation of waves is represented with potential functions. The displacements of particles in different phases of the aggregate are defined in terms of these potential functions. Due to the presence of viscosity in pore fluids, the reflected and transmitted waves are inhomogeneous in nature, i.e., with different directions of propagation and attenuation. The closed-form analytical expressions for reflection and transmission coefficients are derived theoretically for appropriate boundary conditions. These expressions are calculated as a non-singular system of linear algebraic equations and depend on the various parameters involved in this non-singular system. Hence,numerical examples are studied to determine the effects of various properties of the sandwich layer on reflection and transmission coefficients. The essential features of layer thickness, incident direction, wave frequency, liquidsaturation and capillary pressure of the porous layer on reflection and transmission coefficients are depicted graphically and discussed. The analysis shows that reflection and transmission coefficients are strongly associated with incident direction and various properties of the porous layer.展开更多
A set of experiments is carried out in a towing tank to study the effects of the curvature of perforated plates on the wave reflection coefficient （Cr）. The curvature of a perforated plate can be changed by rotating...A set of experiments is carried out in a towing tank to study the effects of the curvature of perforated plates on the wave reflection coefficient （Cr）. The curvature of a perforated plate can be changed by rotating a reference perforated plate about its origin point according to the parabolic equation y=-x2 A plunger-type wave maker is used to generate regular waves. The reflection coefficients are calculated using Goda and Suzuki’s （1976） method. The results are compared with those of vertical or sloped passive wave absorbers. The comparison shows that a perforated plate with a curved profile is highly efficient in terms of reducing the wave reflection coefficient. A correlation is established to estimate the reflection coefficient of curved perforated plates as a function of both flow and geometry characteristics.展开更多
Taking the joint matching coefficient(JMC) which represents the contact area ratio of the joint in rock masses as the key parameter, a one-dimensional contacted interface model(CIM-JMC) was established in this study t...Taking the joint matching coefficient(JMC) which represents the contact area ratio of the joint in rock masses as the key parameter, a one-dimensional contacted interface model(CIM-JMC) was established in this study to describe the wave propagation across a single joint. According to this model, the reflected and transmitted waves at the joint were obtained, and the energy coefficients of reflection and transmission were calculated. Compared with the modified Split Hopkinson pressure bar(SHPB) experiment, it was validated by taking the incident wave of the SHPB test as the input condition in the CIM-JMC, and the reflected and transmitted waves across the joint were calculated by the model. The effects of four sets of JMCs(0.81, 0.64, 0.49, and 0.36) on the transmission and reflection of the stress wave propagation across the joint were analyzed and compared with the experimental results. It demonstrated that the values of CIM-JMC could represent both the transmission and reflection of the stress wave accurately when JMC > 0.5, but could relatively accurately represent the reflection rather than the transmission when JMC < 0.5. By contrasting energy coefficients of joints with different JMCs, it was revealed that energy dissipated sharply along the decrease of JMC when JMC > 0.5.展开更多
The propagation of elastic waves is studied in a porous solid saturated with two immiscible viscous fluids. The propagation of three longitudinal waves is represented through three scalar potential functions. The lone...The propagation of elastic waves is studied in a porous solid saturated with two immiscible viscous fluids. The propagation of three longitudinal waves is represented through three scalar potential functions. The lone transverse wave is presented by a vector potential function. The displacements of particles in different phases of the aggregate are defined in terms of these potential functions. It is shown that there exist three longitudinal waves and one transverse wave. The phenomena of reflection and refraction due to longitudinal and transverse waves at a plane interface between an elastic solid half-space and a porous solid half-space saturated with two immiscible viscous fluids are investigated. For the presence of viscosity in pore-fluids, the waves refracted to the porous medium attenuate in the direction normal to the interface. The ratios of the amplitudes of the reflected and refracted waves to that of the incident wave are calculated as a non- singular system of linear algebraic equations. These amplitude ratios are used to further calculate the shares of different scattered waves in the energy of the incident wave. The modulus of the amplitude and the energy ratios with the angle of incidence are computed for a particular numerical model. The conservation of the energy across the interface is verified. The effects of variations in non-wet saturation of pores and frequencies on the energy partition are depicted graphically and discussed,展开更多
Phenomena of reflection and refraction of plane harmonic waves at a plane interface between an elastic solid and doubleporosity dual-permeability material are investigated. The elastic solid behaves non-dissipatively,...Phenomena of reflection and refraction of plane harmonic waves at a plane interface between an elastic solid and doubleporosity dual-permeability material are investigated. The elastic solid behaves non-dissipatively, while double-porosity dual-permeability materials behave dissipatively to wave propagation due to the presence of viscosity in pore fluids. All the waves(i.e., incident and reflected) in an elastic medium are considered as homogeneous(i.e., having the same directions of propagation and attenuation), while all the refracted waves in double-porosity dual-permeability materials are inhomogeneous(i.e., having different directions of propagation and attenuation). The coefficients of reflection and refraction for a given incident wave are obtained as a non-singular system of linear equations. The energy shares of reflected and refracted waves are obtained in the form of an energy matrix. A numerical example is considered to calculate the partition of incident energy among various reflected and refracted waves. The effect of incident direction on the partition of the incident energy is analyzed with a change in wave frequency, wave-induced fluid-flow, pore-fluid viscosity and double-porosity structure.It has been confirmed from numerical interpretation that during the reflection/refraction process, conservation of incident energy is obtained at each angle of incidence.展开更多
The present work deals with the reflection of plane seismic waves at the stress-free plane surface of double-porosity dualpermeability material. The incidence of two main waves（i.e., P1 and SV） is considered. As a r...The present work deals with the reflection of plane seismic waves at the stress-free plane surface of double-porosity dualpermeability material. The incidence of two main waves（i.e., P1 and SV） is considered. As a result of the incident waves,four reflected（three longitudinal and one shear） waves are found in the medium. The expressions of reflection coefficients for a given incident wave are obtained as a non-singular system of linear equations. The energy shares of reflected waves are obtained in the form of an energy matrix. A numerical example is considered to calculate the partition of incident energy for fully closed as well as perfectly open pores. Effect of incident direction on the partition of the incident energy is analyzed with the change in wave frequency, wave-induced fluid-flow, pore-fluid viscosity and double-porosity structure. It has been confirmed from the numerical interpretation that during the reflection process, conservation of incident energy is obtained at each angle of incidence.展开更多
This study examines the reflection of regular and irregular waves from a partially perforated caisson breakwater located on a step bed. The step bed is treated as an idealized rubble mound foundation. Based on the lin...This study examines the reflection of regular and irregular waves from a partially perforated caisson breakwater located on a step bed. The step bed is treated as an idealized rubble mound foundation. Based on the linear potential theory, an analytical solution is developed to calculate the reflection coefficient of the structure subjected to regular waves. The matched eigenfunction expansion method is used for the solution. The regular wave method is also extended to irregular waves using a linear transfer function. The calculated results obtained for limiting cases are exactly the same as corresponding results given by the previous researchers. The present predictions also agree well with experimental data in the published literatures. Numerical experiments are conducted to examine the variations of the reflection coefficient versus its main effect factors, and some interesting results are presented.展开更多
The governing equations of a transversely isotropic dissipative medium are solved analytically to obtain the speeds of plane waves. The appropriate solutions satisfy the required boundary conditions at the stress-free...The governing equations of a transversely isotropic dissipative medium are solved analytically to obtain the speeds of plane waves. The appropriate solutions satisfy the required boundary conditions at the stress-free surface to obtain the expressions of the reflection coefficients of reflected quasi-P (qP) and quasi-SV (qSV) waves in closed form for the incidence of qP and qSV waves. A particular model is chosen for numerical computation of these reflection coefficients for a certain range of the angle of incidence. The numerical values of these reflection coefficients are shown graphically against the angle of incidence for different values of initial stress parameter. The impact of initial stress parameter on the reflection coefficients is observed significantly.展开更多
The reflection of regular and irregular waves from a partially perforated caisson breakwater with a rock-filled core is examined. The present mathematical model is developed by means of the matched eigenfunction metho...The reflection of regular and irregular waves from a partially perforated caisson breakwater with a rock-filled core is examined. The present mathematical model is developed by means of the matched eigenfunction method. Numerical results of the present model are compared with the experimental data of different researchers. Numerical examples are given to examine the effect of rock fill on the reflection coefficient. The differences between regular and irregular waves are also investigated by means of theoretical and experimental results. It is found that the minimum reflection coefficient of irregular waves is larger than that of corresponding regular waves, but the contrary is the case for the maximum reflection coefficient.展开更多
This investigation examines long wave reflection and transmission induced by a sloping step. Bellman and Kalaba's (1959) invariant imbedding is introduced to find wave reflection. An alternative method matching bo...This investigation examines long wave reflection and transmission induced by a sloping step. Bellman and Kalaba's (1959) invariant imbedding is introduced to find wave reflection. An alternative method matching both the surface elevation and its surface slope of each region at the junction is applied to the determination of wave reflection and transmission. The proposed methods are compared with the accurate numerical results of Porter and Porter (2000) and those of Mei (1983) for a vertical step. The wave reflection obtained for a mildly sloping step differs significantly from the result of Mei. The wave reflection is found to fluctuate owing to wave trapping for the mild sloping step. The height and the face slope of the step are important for determining wave reflection and transmission coefficients.展开更多
Based on nonlocal thermoelastic theory, this article studies the reflection of waves in nanometersemi-conductor media. Firstly, the governing equations are established based on couplednonlocal elasticity theory, pl...Based on nonlocal thermoelastic theory, this article studies the reflection of waves in nanometersemi-conductor media. Firstly, the governing equations are established based on couplednonlocal elasticity theory, plasma diffusion equation, and moving equation. Then, using theharmonic method, the solution of the dissipation equation and the analytic expression of thereflection coefficient rate are obtained. Finally, the influences of nonlocal parameters on wavevelocities are showed graphically. It is found that after the introduction of nonlocal effect, thephase and group velocities all show the attenuation, and as the frequency increases, the nonlocalparameter is bigger, and the decay rate is faster. The reflection coefficient rate varies greatly withdifferent theories, with different reflection coefficient rates depending on the incident angle.展开更多
The governing equations of an initially stressed rotating orthotropic dissipative medium are solved analytically to obtain the velocity equation which indicates the existence of two quasi-planar waves. The appropriate...The governing equations of an initially stressed rotating orthotropic dissipative medium are solved analytically to obtain the velocity equation which indicates the existence of two quasi-planar waves. The appropriate particular solutions in the half-space satisfy the required boundary conditions at the stress-free surface to obtain the expressions of the reflec-tion coefficients of the reflected quasi-P (qP) and reflected quasi-SV (qSV) waves in closed form for the incidence of qP and qSV waves. A particular model is chosen for numerical computation of these reflection coefficients for a certain range of the angle of incidence. The numerical values of these reflection coefficients are shown graphically against the angle of incidence for different values of initial stress parameter and rotation parameter. The impact of initial stress and rotation parameters on the reflection coefficients is observed significantly.展开更多
Reflection and transmission of random waves from submerged ohstacles under various conditions are investigated in this study by means of the boundary element method. The algorithm is based on the Lagrangian descriptio...Reflection and transmission of random waves from submerged ohstacles under various conditions are investigated in this study by means of the boundary element method. The algorithm is based on the Lagrangian description with finite difference adopted for the approximation of time derivative. The accuracy of the model is confirmed by a previous study of the transmission of irregular waves in a water tank without any obstacle, under which sets of submerged breakwaters are located. To reduce the effect of reflection from the wall, a sponge zone is employed at the other end of the flume as an artificial absorbing beach. The power spectrum of Bretschneider-Mitsuyasu type defined by significant wave height, H1/3, and period, T1/3, is employed for the condition of incident waves chosen for the generation of irregular waves. Time histofies of water elevations are measured with numerous pseudo wave gages on the free water surface. With reference to the method for the estimation of irregular incident and reflected waves in random sea presented by Goda and Suzuki （1976）, the dissipation efficiency of the breakwaters is investigated. Gauges in different positions are tested for their suitability for the estimation of reflection coefficients for irregular waves. The present results demonstrate the effectiveness of the estimation of reflection coefficient for random waves, and indicate the feasibility of the numerical model.展开更多
基金the National "973" Project (No.2007CB209603) the "863" Project (No.2006AA06Z108)
文摘We introduce the Thomsen anisotropic parameters into the approximate linear reflection coefficient equation for P-SV wave in weakly anisotropic HTI media. From this we get a new, more effective, and practical reflection coefficient equation. We performed forward modeling to AVO attributes, obtaining excellent results. The combined AVO attribute analysis of PP and PS reflection data can greatly reduce ambiguity, obtain better petrophysical parameters, and improve parameter accuracy.
基金The present work was financially supported by the Joint Fund of the National Natural Science Foundation of China the Hong Kong Science Research Bureau under contract No.49910161985 the Research Fund for the Development of Harbor Engineering Desig
文摘The reflection coefficient and the total horizontal forces of regular waves acting on theperforated caisson are experimentally investigated. The empirical relationship between reflection coefficient and the ratio of the total horizontal forces acting on the perforated caisson to those on solid vertical walls with the relative chamber width, relative water depth and porosity of perforated wall, etc. are given. Moreover, the results of the ratio of the total horizontal forces are also compared with formulas given by Chinese Harbour Design Criteria and Takahashi, which may be useful for the practical engineering application.
基金Project 40574058 Supported by the National Natural Science Foundation of China
文摘Although the Zoeppritz equation is suitable for a single interface in a thick deposit, it has some limitations for composite reflection waves from both the floor and the roof of coal seams. Based on the ray model, the relationship of the overall reflection coefficient of composite reflection P waves, from coal seam versus incidence angle (AVO), is dis- cussed. The result shows that: 1) the overall reflection coefficient of composite reflection waves from coal seams is a negative value and is determined mainly by the lithology of roof and floor, which is different from the reflection coeffi- cient of a single interface; 2) if the incidence angle ranges from 0° to 6°, the reflection coefficient of composite waves of a coal seam does not change with the incidence angle and 3) if the incidence angle ranges from 6–60° , the reflection coefficient increases monotonically.
文摘The hollow-pipe perforated breakwater is of low reflection. In this paper the functions of reflection coefficients of both regular and random waves are theoretically derived, based on the concept of linear superimposition of reflected and incident waves and with the total flow rate continuity of integral form instead of the non-continuity of the boundary condition, and based on the concept of linear wave spectrum theory. Comparisons between theoretical results presented here and measurements of model tests show reasonable agreement.
基金The work reported in this paper is financially supported by both the National Natural Science Foundation of China (No.59909001) the Research Fund for the Doctoral Program of Ministry of Education of China (No.98014118)
文摘In this paper, the modified Bayesian method for the analysis of directional wave spectra and reflection coefficients is verified by numerical and physical simulation of waves. The results show that the method can basically separate the incident and reflected directional spectra. In addition, the effect of the type of wave gage arrays, the number of measured wave properties, and the distance between the wave gage array and the reflection line on the resolution of the method are investigated. Some suggestions are proposed for practical application.
文摘The wave reflection coefficient frequency spectrum and directional spectrum for concrete face slope breakwaters and rubble mound breakwaters are investigated through physical model tests in the present study. The reflection coefficients of oblique irregular waves are analyzed by the Modified Two-Point Method (MTPM) proposed by the authors. The results show that the wave reflection coefficient decreases with increasing wave frequency and incident angle or decreasing structure slope. The reflection coefficient frequency spectrum and its variation with Iribarren number are given in this paper. The paper also suggests an empirical 3-dimensional reflection coefficient spectrum, i.e. reflection coefficient directional spectrum, which can be used to illustrate quantitatively the variation of reflection coefficient with the incident angle and the Iribarren number for oblique irregular waves.
文摘In this study,we focus on the numerical modelling of the interaction between waves and submerged structures in the presence of a uniform flow current.Both the same and opposite senses of wave propagation are considered.The main objective is an understanding of the effect of the current and various geometrical parameters on the reflection coefficient.The wave used in the study is based on potential theory,and the submerged structures consist of two rectangular breakwaters positioned at a fixed distance from each other and attached to the bottom of a wave flume.The numerical modeling approach employed in this work relies on the Boundary Element Method(BEM).The results are compared with experimental data to validate the approach.The findings of the study demonstrate that the double rectangular breakwater configuration exhibits superior wave attenuation abilities if compared to a single rectangular breakwater,particularly at low wavenumbers.Furthermore,the study reveals that wave mitigation is more pronounced when the current and wave propagation are coplanar,whereas it is less effective in the case of opposing current.
文摘The seismic reflection and transmission characteristics of a single layer sandwiched between two dissimilar poroelastic solids saturated with two immiscible viscous fluids are investigated. The sandwiched layer is modeled as a porous solid with finite thickness. The propagation of waves is represented with potential functions. The displacements of particles in different phases of the aggregate are defined in terms of these potential functions. Due to the presence of viscosity in pore fluids, the reflected and transmitted waves are inhomogeneous in nature, i.e., with different directions of propagation and attenuation. The closed-form analytical expressions for reflection and transmission coefficients are derived theoretically for appropriate boundary conditions. These expressions are calculated as a non-singular system of linear algebraic equations and depend on the various parameters involved in this non-singular system. Hence,numerical examples are studied to determine the effects of various properties of the sandwich layer on reflection and transmission coefficients. The essential features of layer thickness, incident direction, wave frequency, liquidsaturation and capillary pressure of the porous layer on reflection and transmission coefficients are depicted graphically and discussed. The analysis shows that reflection and transmission coefficients are strongly associated with incident direction and various properties of the porous layer.
文摘A set of experiments is carried out in a towing tank to study the effects of the curvature of perforated plates on the wave reflection coefficient （Cr）. The curvature of a perforated plate can be changed by rotating a reference perforated plate about its origin point according to the parabolic equation y=-x2 A plunger-type wave maker is used to generate regular waves. The reflection coefficients are calculated using Goda and Suzuki’s （1976） method. The results are compared with those of vertical or sloped passive wave absorbers. The comparison shows that a perforated plate with a curved profile is highly efficient in terms of reducing the wave reflection coefficient. A correlation is established to estimate the reflection coefficient of curved perforated plates as a function of both flow and geometry characteristics.
基金financially supported by the China Postdoctoral Science Foundation (No. 2017M620620)the Beijing Natural Science Foundation (No. 2184108)+2 种基金the Fundamental Research Funds for the Central Universities (No. FRF-TP-16-073A1)the National Science Foundation for Distinguished Young (No. 41525009)the State Key Research Development Program of China (Nos. 2016YFC0600703 and 2017YFC0804609)
文摘Taking the joint matching coefficient(JMC) which represents the contact area ratio of the joint in rock masses as the key parameter, a one-dimensional contacted interface model(CIM-JMC) was established in this study to describe the wave propagation across a single joint. According to this model, the reflected and transmitted waves at the joint were obtained, and the energy coefficients of reflection and transmission were calculated. Compared with the modified Split Hopkinson pressure bar(SHPB) experiment, it was validated by taking the incident wave of the SHPB test as the input condition in the CIM-JMC, and the reflected and transmitted waves across the joint were calculated by the model. The effects of four sets of JMCs(0.81, 0.64, 0.49, and 0.36) on the transmission and reflection of the stress wave propagation across the joint were analyzed and compared with the experimental results. It demonstrated that the values of CIM-JMC could represent both the transmission and reflection of the stress wave accurately when JMC > 0.5, but could relatively accurately represent the reflection rather than the transmission when JMC < 0.5. By contrasting energy coefficients of joints with different JMCs, it was revealed that energy dissipated sharply along the decrease of JMC when JMC > 0.5.
基金Project supported by the Council of Scientific and Industrial Research (CSIR) of New Delhi(Nos. 09/105(0169)/2008-EMR-I and 09/105(0185)/2009-EMR-I)
文摘The propagation of elastic waves is studied in a porous solid saturated with two immiscible viscous fluids. The propagation of three longitudinal waves is represented through three scalar potential functions. The lone transverse wave is presented by a vector potential function. The displacements of particles in different phases of the aggregate are defined in terms of these potential functions. It is shown that there exist three longitudinal waves and one transverse wave. The phenomena of reflection and refraction due to longitudinal and transverse waves at a plane interface between an elastic solid half-space and a porous solid half-space saturated with two immiscible viscous fluids are investigated. For the presence of viscosity in pore-fluids, the waves refracted to the porous medium attenuate in the direction normal to the interface. The ratios of the amplitudes of the reflected and refracted waves to that of the incident wave are calculated as a non- singular system of linear algebraic equations. These amplitude ratios are used to further calculate the shares of different scattered waves in the energy of the incident wave. The modulus of the amplitude and the energy ratios with the angle of incidence are computed for a particular numerical model. The conservation of the energy across the interface is verified. The effects of variations in non-wet saturation of pores and frequencies on the energy partition are depicted graphically and discussed,
文摘Phenomena of reflection and refraction of plane harmonic waves at a plane interface between an elastic solid and doubleporosity dual-permeability material are investigated. The elastic solid behaves non-dissipatively, while double-porosity dual-permeability materials behave dissipatively to wave propagation due to the presence of viscosity in pore fluids. All the waves(i.e., incident and reflected) in an elastic medium are considered as homogeneous(i.e., having the same directions of propagation and attenuation), while all the refracted waves in double-porosity dual-permeability materials are inhomogeneous(i.e., having different directions of propagation and attenuation). The coefficients of reflection and refraction for a given incident wave are obtained as a non-singular system of linear equations. The energy shares of reflected and refracted waves are obtained in the form of an energy matrix. A numerical example is considered to calculate the partition of incident energy among various reflected and refracted waves. The effect of incident direction on the partition of the incident energy is analyzed with a change in wave frequency, wave-induced fluid-flow, pore-fluid viscosity and double-porosity structure.It has been confirmed from numerical interpretation that during the reflection/refraction process, conservation of incident energy is obtained at each angle of incidence.
文摘The present work deals with the reflection of plane seismic waves at the stress-free plane surface of double-porosity dualpermeability material. The incidence of two main waves（i.e., P1 and SV） is considered. As a result of the incident waves,four reflected（three longitudinal and one shear） waves are found in the medium. The expressions of reflection coefficients for a given incident wave are obtained as a non-singular system of linear equations. The energy shares of reflected waves are obtained in the form of an energy matrix. A numerical example is considered to calculate the partition of incident energy for fully closed as well as perfectly open pores. Effect of incident direction on the partition of the incident energy is analyzed with the change in wave frequency, wave-induced fluid-flow, pore-fluid viscosity and double-porosity structure. It has been confirmed from the numerical interpretation that during the reflection process, conservation of incident energy is obtained at each angle of incidence.
基金The Natural Science Foundation of Shandong Province under contract No Q2008F01the Specialized Research Fund for the Doctoral Program of Higher Education under contract No 200804231006the National Natural Science Foundation of China under contract Nos 40876047 and 50609001
文摘This study examines the reflection of regular and irregular waves from a partially perforated caisson breakwater located on a step bed. The step bed is treated as an idealized rubble mound foundation. Based on the linear potential theory, an analytical solution is developed to calculate the reflection coefficient of the structure subjected to regular waves. The matched eigenfunction expansion method is used for the solution. The regular wave method is also extended to irregular waves using a linear transfer function. The calculated results obtained for limiting cases are exactly the same as corresponding results given by the previous researchers. The present predictions also agree well with experimental data in the published literatures. Numerical experiments are conducted to examine the variations of the reflection coefficient versus its main effect factors, and some interesting results are presented.
文摘The governing equations of a transversely isotropic dissipative medium are solved analytically to obtain the speeds of plane waves. The appropriate solutions satisfy the required boundary conditions at the stress-free surface to obtain the expressions of the reflection coefficients of reflected quasi-P (qP) and quasi-SV (qSV) waves in closed form for the incidence of qP and qSV waves. A particular model is chosen for numerical computation of these reflection coefficients for a certain range of the angle of incidence. The numerical values of these reflection coefficients are shown graphically against the angle of incidence for different values of initial stress parameter. The impact of initial stress parameter on the reflection coefficients is observed significantly.
文摘The reflection of regular and irregular waves from a partially perforated caisson breakwater with a rock-filled core is examined. The present mathematical model is developed by means of the matched eigenfunction method. Numerical results of the present model are compared with the experimental data of different researchers. Numerical examples are given to examine the effect of rock fill on the reflection coefficient. The differences between regular and irregular waves are also investigated by means of theoretical and experimental results. It is found that the minimum reflection coefficient of irregular waves is larger than that of corresponding regular waves, but the contrary is the case for the maximum reflection coefficient.
文摘This investigation examines long wave reflection and transmission induced by a sloping step. Bellman and Kalaba's (1959) invariant imbedding is introduced to find wave reflection. An alternative method matching both the surface elevation and its surface slope of each region at the junction is applied to the determination of wave reflection and transmission. The proposed methods are compared with the accurate numerical results of Porter and Porter (2000) and those of Mei (1983) for a vertical step. The wave reflection obtained for a mildly sloping step differs significantly from the result of Mei. The wave reflection is found to fluctuate owing to wave trapping for the mild sloping step. The height and the face slope of the step are important for determining wave reflection and transmission coefficients.
基金supported by the National Natural Science Foundation of China (11672224)
文摘Based on nonlocal thermoelastic theory, this article studies the reflection of waves in nanometersemi-conductor media. Firstly, the governing equations are established based on couplednonlocal elasticity theory, plasma diffusion equation, and moving equation. Then, using theharmonic method, the solution of the dissipation equation and the analytic expression of thereflection coefficient rate are obtained. Finally, the influences of nonlocal parameters on wavevelocities are showed graphically. It is found that after the introduction of nonlocal effect, thephase and group velocities all show the attenuation, and as the frequency increases, the nonlocalparameter is bigger, and the decay rate is faster. The reflection coefficient rate varies greatly withdifferent theories, with different reflection coefficient rates depending on the incident angle.
文摘The governing equations of an initially stressed rotating orthotropic dissipative medium are solved analytically to obtain the velocity equation which indicates the existence of two quasi-planar waves. The appropriate particular solutions in the half-space satisfy the required boundary conditions at the stress-free surface to obtain the expressions of the reflec-tion coefficients of the reflected quasi-P (qP) and reflected quasi-SV (qSV) waves in closed form for the incidence of qP and qSV waves. A particular model is chosen for numerical computation of these reflection coefficients for a certain range of the angle of incidence. The numerical values of these reflection coefficients are shown graphically against the angle of incidence for different values of initial stress parameter and rotation parameter. The impact of initial stress and rotation parameters on the reflection coefficients is observed significantly.
文摘Reflection and transmission of random waves from submerged ohstacles under various conditions are investigated in this study by means of the boundary element method. The algorithm is based on the Lagrangian description with finite difference adopted for the approximation of time derivative. The accuracy of the model is confirmed by a previous study of the transmission of irregular waves in a water tank without any obstacle, under which sets of submerged breakwaters are located. To reduce the effect of reflection from the wall, a sponge zone is employed at the other end of the flume as an artificial absorbing beach. The power spectrum of Bretschneider-Mitsuyasu type defined by significant wave height, H1/3, and period, T1/3, is employed for the condition of incident waves chosen for the generation of irregular waves. Time histofies of water elevations are measured with numerous pseudo wave gages on the free water surface. With reference to the method for the estimation of irregular incident and reflected waves in random sea presented by Goda and Suzuki （1976）, the dissipation efficiency of the breakwaters is investigated. Gauges in different positions are tested for their suitability for the estimation of reflection coefficients for irregular waves. The present results demonstrate the effectiveness of the estimation of reflection coefficient for random waves, and indicate the feasibility of the numerical model.
