Based on the modified Biot model for asturated soils, taking the compressibilities of the grains and the pore fluid as well as the viscous coupling into account, the reflection and transmission of seismic aves at an i...Based on the modified Biot model for asturated soils, taking the compressibilities of the grains and the pore fluid as well as the viscous coupling into account, the reflection and transmission of seismic aves at an interface between two saturated soils are studied in this paper. A formula is derived for calculation of the amplitude reflection and transmission coefficients of various waves. A aumerical investigation of the dependence of the coefficients on the angle of incidence and the frequency is performed. This study is of a value for seismological studies and geophysical exploration.展开更多
The reflection and transmission of elastic waves through a couple-stress elastic slab that is sandwiched between two couple-stress elastic half-spaces are studied in this paper. Because of the couple-stress effects, t...The reflection and transmission of elastic waves through a couple-stress elastic slab that is sandwiched between two couple-stress elastic half-spaces are studied in this paper. Because of the couple-stress effects, there are three types of elastic waves in the couple-stress elastic solid, two of which are dispersive. The interface conditions between two couple-stress solids involve the surface couple and rotation apart from the surface traction and displacement. The nontraditional interface conditions between the slab and two solid half-spaces are used to obtain the linear algebraic equation sets from which the amplitude ratios of reflection and transmission waves to the incident wave can be determined. Then,the energy fluxes carried by the various reflection and transmission waves are calculated numerically and the normal energy flux conservation is used to validate the numerical results. The special case, couple-stress elastic slab sandwiched by the classical elastic half-spaces, is also studied and compared with the situation that the classical elastic slab sandwiched by the classical elastic half-spaces. Incident longitudinal wave(P wave) and incident transverse wave(SV wave) are both considered. The influences of the couplestress are mainly discussed based on the numerical results.It is found that the couple-stress mainly influences the transverse modes of elastic waves.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
Based on angular spectrum expansion and 4 × 4 matrix theory, the reflection and transmission characteristics of a Laguerre Gaussian （LG） beam from uniaxial anisotropic multilayered media are studied. The reflec...Based on angular spectrum expansion and 4 × 4 matrix theory, the reflection and transmission characteristics of a Laguerre Gaussian （LG） beam from uniaxial anisotropic multilayered media are studied. The reflected and transmitted beam fields of an LG beam are derived. In the case where the principal coordinates of the uniaxial anisotropic media coincide with the global coordinates, the reflected and transmitted beam intensities from a uniaxial anisotropic slab and three-layered media are numerically simulated. It is shown that the reflected intensity components of the incident beam, especially the TM polarized incident beam, are smaller than the transmitted intensity components. The distortion of the reflected intensity component is more evident than that of the transmitted intensity component. The distortion of intensity distribution is greatly affected by the dielectric tensor and the thickness of anisotropic media. We finally extend the application of the method to general anisotropic multilayered media.展开更多
Wave reflection and transmission in a beam containing a semi-infinite crack are studied analytically based on Timoshenko beam theory., Two kinds of crack surface conditions： non-contact （open） and fully contact （c...Wave reflection and transmission in a beam containing a semi-infinite crack are studied analytically based on Timoshenko beam theory., Two kinds of crack surface conditions： non-contact （open） and fully contact （closed） cracks, are considered respectively for an isotropic beam. The analytical solution of reflection and transmission coefficients for a semi-infinite crack is obtained. The power reflection and transmission ratios depend on both the frequency and the position of the crack. Numerical results show the conservation of power transport. The transmitted energy among various wave modes is also investigated. A finite element method is used to verify the validity of the analytical results.展开更多
The propagation, reflection, and transmission of SH waves in slightly com- pressible, finitely deformed elastic media are considered in this paper. The dispersion relation for SH-wave propagation in slightly compressi...The propagation, reflection, and transmission of SH waves in slightly com- pressible, finitely deformed elastic media are considered in this paper. The dispersion relation for SH-wave propagation in slightly compressible, finitely deformed layer over- lying a slightly compressible, finitely deformed half-space is derived. The present paper Mso deals with the reflection and refraction （transmission） phenomena due to the SH wave incident at the plane interface between two distinct slightly compressible, finitely deformed elastic media. The closed form expressions for the amplitude ratios of reflection and refraction coefficients of the reflected and refracted SH waves are obtained from suit- able boundary conditions. For the numerical discussions, we consider the Neo-Hookean form of a strain energy function. The phase speed curves, the variations of reflection, and transmission coefficients with the angle of incidence, and the plots of the slowness sections are presented by means of graphs.展开更多
Based on the modified Biot＇s theory of two-phase porous media, a study was presented on seismic reflection and transmission coefficients at an air-water interface of saturated porous soil media. The major differences...Based on the modified Biot＇s theory of two-phase porous media, a study was presented on seismic reflection and transmission coefficients at an air-water interface of saturated porous soil media. The major differences between air-saturated soils and water-saturated soils were theoretically discussed, and the theoretical formulas of reflection and transmission coefficients at an air-water interface were derived. The characteristics of propagation and attenuation of elastic waves in air-saturated soils were given and the relations among the frequency, the angle of incidence and the reflection, transmission coefficients were analyzed by using numerical methods. Numerical results show that the propagation characteristic of the wave in air-saturated soils is great different from that in water-saturated soils. The frequency and the angle of incidence can have great influences on the reflection and transmission coefficients at interface. Some new cognition about the wave propagation is obtained and the study suggests that we may carefully pay attention to the influence of air on the dynamic analysis of seismic wave.展开更多
The reflection and transmission of a finite-power Airy beam incident on a dielectric slab are investigated by an analytical method.Based on the plane-wave angular spectrum expansion and Fresnel approximation,the analy...The reflection and transmission of a finite-power Airy beam incident on a dielectric slab are investigated by an analytical method.Based on the plane-wave angular spectrum expansion and Fresnel approximation,the analytical expressions of the reflected field,internal field as well as transmitted field in each region are obtained.Through numerical simulations,the intensity distributions of the incident beam,reflected beam,internal beam as well as transmitted beam are presented at oblique incidence.Besides,we also compare the intensity distributions of the geometrical-optics beam field,the first order beam mode field and the actual beam field,which indicates that the contribution of each order beam mode field to the actual beam field is related to the refractive index of the dielectric slab.Meanwhile,the reflection characteristics of the Airy beams in the special cases of Brewster incidence and total reflection are investigated.Finally,the effects of the optical thickness and refractive index of the dielectric slab on the peak intensity distributions and beam shifts of the reflected and transmitted beams are also discussed in detail.The analytical and numerical results will be useful to analyze the propagation dynamics of Airy beam in the dielectric slab and provide some theoretical supports to the design of optical film.展开更多
The study done in this paper brings out the effect of the viscoelasticity on the reflection/transmission coefficients. The knowledge of this effect can be useful for several applications, such as enhancing the resolut...The study done in this paper brings out the effect of the viscoelasticity on the reflection/transmission coefficients. The knowledge of this effect can be useful for several applications, such as enhancing the resolution of the seismic sections, fluid and fracture detection. It can also have other applications different from the geophysical domain, as the study of the bonding between the materials in the civil engineering domain. We use the complex Lame coefficients in the continuity equations at the boundary layers to get the analytical expressions of the reflection/transmission coefficients in viscoelastic media. The coefficients can be divided into two parts, the first part is independent from the quality factor, and it corresponds to the elastic reflection/transmission coefficients. The second part is dependent on the quality factor contrast and it represents the contribution of the viscoelasticity on the reflection/transmission coefficients. From the numerical study it appears that the effect of the viscoelasticity is significant near to the critical angles. This effect is not clear and it is difficult to interpret and we do not know if it has a physical meaning or it is only a mathematical artifact that is why it is better to be far from the critical angles for seismic investigation.展开更多
The reflection and transmission properties of thermo-elastic waves at five possible interfaces between two different strain gradient thermo-elastic solids are investigated based on the generalized thermo-elastic theor...The reflection and transmission properties of thermo-elastic waves at five possible interfaces between two different strain gradient thermo-elastic solids are investigated based on the generalized thermo-elastic theory without energy dissipation （the GN theory）. First, the function of free energy density is postulated and the constitutive relations are defined. Then, the temperature field and the displacement field are obtained from the motion equation in the form of displacement and the thermal transport equation without energy dissipation in the strain gradient thermo-elastic solid. Finally, the five types of thermo-elastic interracial conditions are used to calculate the amplitude ratios of the reflection and transmission waves with respect to the incident wave. Further, the reflection and transmission coefficients in terms of energy flux ratio are calculated and the numerical results are validated by the energy conservation along the normal direction. It is found that there are five types of dispersive waves, namely the coupled longitudinal wave （the CP wave）, the coupled thermal wave （the CT wave）, the shear wave, and two evanescent waves （the coupled SP wave and SS wave）, that become the surface waves at an interface. The mechanical interfacial conditions mainly influence the coupled CP waves, SV waves, and surface waves, while the thermal interracial conditions mainly influence the coupled CT waves.展开更多
For the boundary between transversely isotropic media with a vertical axis of symmetry (VTI media), the interface between a liquid and a VTI medium, and the free-surface of an elastic half-space of a VTI medium, an ac...For the boundary between transversely isotropic media with a vertical axis of symmetry (VTI media), the interface between a liquid and a VTI medium, and the free-surface of an elastic half-space of a VTI medium, an accurately fast algorithm was presented for calculating reflection/transmission (R/T) coefficients. Specially, the case of post-critical angle incidence was considered. Although we only performed the numerical calculation for the models of the VTI media, the calculated results can be extended to the models of transversely isotropic media with a horizontal axis of rotation symmetry (HTI media). Compared to previous work, this algorithm can be used not only for the calculation of R/T coefficients of the boundary between ellipsoidally anisotropic media, but also for that between generally anisotropic media, and the speed and accuracy of this algorithm are faster and higher. According to the anisotropic parameters of some rocks given by the published literature, we performed the calculation of R/T coefficients by using this algorithm and analyzed the effect of the rock anisotropy on R/T coefficients. We used Snell's law and the energy balance principle to perform verification for the calculated results.展开更多
Chen＇s technique of computing synthetic seismograms, which decomposes every vector with a set of basis of orthogonality and completeness before applying the Luco-Apsel-Chen （LAC） generalized reflection and transmis...Chen＇s technique of computing synthetic seismograms, which decomposes every vector with a set of basis of orthogonality and completeness before applying the Luco-Apsel-Chen （LAC） generalized reflection and transmission coefficients method, is confirmed to be efficient in dealing with elastic waves in multi-layered media and accurate in any frequency range. In this article, we extend Chen＇s technique to the computation of coupled seismic and electromagnetic （EM） waves in layered porous media. Expanding the involved mechanical and electromagnetic fields by a set of scalar and vector wave-function basis, we obtain the fundamental equations which are subsequently solved by using a recently developed version of the LAC generalized reflection and transmission coefficients method. Our approach and corresponding program is validated by reciprocity tests. We also show a numerical example of a two-layer model with an explosion source. The P-to-EM conversion waves radiated from the interface may have potential application.展开更多
Currently, scant attention has been paid to the theoretical analysis on dynamic response mechanism of the ＂Dualistic＂ structure roek slope. The analysis presented here provides insight into the dynamic response of t...Currently, scant attention has been paid to the theoretical analysis on dynamic response mechanism of the ＂Dualistic＂ structure roek slope. The analysis presented here provides insight into the dynamic response of the ＂Dualistie＂ structure rock slope. By investigating the principle of energy distribution, it is shown that the effect of a joint plays a significant role in slope stability analysis. A dynamic reflection and transmission model （RTM） for the ＂Dualistic＂ structure rock slope and explicit dynamic equations are established to analyze the dynamic response of a slope, based on the theory of elastic mechanics and the principle of seismic wave propagation. The theoretical simulation solutions show that the dynamic response of the ＂Dualistic＂ structure rock slope （soft-hard） model is greater than that of the ＂Dualistic＂ strueture rock slope （hard-soft） model, especially in the slope crest. The magnifying effect of rigid foundation on the dynamic response is more obvious than that of soft foundation. With the amplitude increasing, the cracks could be found in the right slope （soft-hard） crest. The crest failure is firstly observed in the right slope （soft-hard） during the experimental process. The reliability of theoretical model is also investigated by experiment analysis. The conclusions derived in this paper could also be used in future evaluations of Multi-layer rock slopes.展开更多
In this study, the propagation of electromagnetic waves in one-dimensional plasma photonic crystals （PPCs）, namely, superlattice structures consisting alternately of a homogeneous unmagnetized plasma and dielectric ...In this study, the propagation of electromagnetic waves in one-dimensional plasma photonic crystals （PPCs）, namely, superlattice structures consisting alternately of a homogeneous unmagnetized plasma and dielectric material, is simulated numerically using the finite-difference time-domain （FDTD） algorithm. A perfectly matched layer （PML） absorbing technique is used in this simulation. The reflection and transmission coefficients of electromagnetic （EM） waves through PPCs are calculated. The characteristics of the photonic band gap （PBG） are discussed in terms of plasma density, dielectric constant ratios, number of periods, and introduced layer defect. These may provide some useful information for designing plasma photonic crystal devices.展开更多
In this work,an enriched model describing the longitudinal wave propagation is established based on Mindlin’s Second Strain Gradient(SSG)theory,which can describe the heterogeneity caused by the micro-structure inter...In this work,an enriched model describing the longitudinal wave propagation is established based on Mindlin’s Second Strain Gradient(SSG)theory,which can describe the heterogeneity caused by the micro-structure interactions in the frame of continuum mechanics.The governing equation and associated boundary conditions are derived based on Hamilton’s principle,then the dispersion relation of non-classical longitudinal wave together with the extra-waves appearing exclusively in SSG theory model are investigated.The investigations are based on the modal density,energy flow,and forced response of the rod.Wave transmission and reflection through planar interfaces based on the proposed model have been calculated.Finally,the results of the enriched model are well interpreted by comparing with the classical theory results,and some useful conclusions are derived on the SSG theory based model in the wave propagation characterization.展开更多
Scattering of surface waves by the edge of a small undulation on a porous bed in an ocean of finite depth, where the free surface has an ice-cover being modelled as an elastic plate of very small thickness, is investi...Scattering of surface waves by the edge of a small undulation on a porous bed in an ocean of finite depth, where the free surface has an ice-cover being modelled as an elastic plate of very small thickness, is investigated within the framework of linearized water wave theory. The effect of surface tension at the surface below the ice-cover is neglected. There exists only one wave number propagating at just below the ice-cover. A perturbation analysis is employed to solve the boundary value problem governed by Laplace＇s equation by a method based on Green＇s integral theorem with the introduction of appropriate Green＇s function and thereby evaluating the reflection and transmission coefficients approximately up to first order. A patch of sinusoidal ripples is considered as an example and the related coefficients are determined.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
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
Two problems of scattering of surface water waves involving a semi-infinite elastic plate and a pair of semi-infinite elastic plates,separated by a gap of finite width,floating horizontally on water of finite depth,ar...Two problems of scattering of surface water waves involving a semi-infinite elastic plate and a pair of semi-infinite elastic plates,separated by a gap of finite width,floating horizontally on water of finite depth,are investigated in the present work for a two-dimensional time-harmonic case.Within the frame of linear water wave theory,the solutions of the two boundary value problems under consideration have been represented in the forms of eigenfunction expansions.Approximate values of the reflection and transmission coefficients are obtained by solving an over-determined system of linear algebraic equations in each problem.In both the problems,the method of least squares as well as the singular value decomposition have been employed and tables of numerical values of the reflection and transmission coefficients are presented for specific choices of the parameters for modelling the elastic plates.Our main aim is to check the energy balance relation in each problem which plays a very important role in the present approach of solutions of mixed boundary value problems involving Laplace equations.The main advantage of the present approach of solutions is that the results for the values of reflection and transmission coefficients obtained by using both the methods are found to satisfy the energy-balance relations associated with the respective scattering problems under consideration.The absolute values of the reflection and transmission coefficients are presented graphically against different values of the wave numbers.展开更多
The present study is concerned with the reflection and transmission of plane waves at an interface between homogenous invisicid liquid half space and a micropolar liquid-saturated porous solid half space. The reflecti...The present study is concerned with the reflection and transmission of plane waves at an interface between homogenous invisicid liquid half space and a micropolar liquid-saturated porous solid half space. The reflection and transmission coefficients of various reflected and transmitted waves with the angle of incident have been obtained. Numerical calculation has been performed for amplitude ratios of various reflected and transmitted waves. Micropolarity and porosity effects on the reflection and transmission coefficients have been depicted graphically. Some particular cases have been deduced from the present formulation.展开更多
文摘Based on the modified Biot model for asturated soils, taking the compressibilities of the grains and the pore fluid as well as the viscous coupling into account, the reflection and transmission of seismic aves at an interface between two saturated soils are studied in this paper. A formula is derived for calculation of the amplitude reflection and transmission coefficients of various waves. A aumerical investigation of the dependence of the coefficients on the angle of incidence and the frequency is performed. This study is of a value for seismological studies and geophysical exploration.
基金supported by the Fundamental Research Funds for the Central Universities (Grant FRF-BR-15026A)the National Natural Science Foundation of China (Grant 10972029)
文摘The reflection and transmission of elastic waves through a couple-stress elastic slab that is sandwiched between two couple-stress elastic half-spaces are studied in this paper. Because of the couple-stress effects, there are three types of elastic waves in the couple-stress elastic solid, two of which are dispersive. The interface conditions between two couple-stress solids involve the surface couple and rotation apart from the surface traction and displacement. The nontraditional interface conditions between the slab and two solid half-spaces are used to obtain the linear algebraic equation sets from which the amplitude ratios of reflection and transmission waves to the incident wave can be determined. Then,the energy fluxes carried by the various reflection and transmission waves are calculated numerically and the normal energy flux conservation is used to validate the numerical results. The special case, couple-stress elastic slab sandwiched by the classical elastic half-spaces, is also studied and compared with the situation that the classical elastic slab sandwiched by the classical elastic half-spaces. Incident longitudinal wave(P wave) and incident transverse wave(SV wave) are both considered. The influences of the couplestress are mainly discussed based on the numerical results.It is found that the couple-stress mainly influences the transverse modes of elastic waves.
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.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61475123,61571355,and 61308025)the Natural Science Basic Research Plan in Shaanxi Province,China(Grant No.2016JQ4015)the Overseas Training Program for Young Backbones Teachers Sponsored by China Scholarship Council and Xidian University
文摘Based on angular spectrum expansion and 4 × 4 matrix theory, the reflection and transmission characteristics of a Laguerre Gaussian （LG） beam from uniaxial anisotropic multilayered media are studied. The reflected and transmitted beam fields of an LG beam are derived. In the case where the principal coordinates of the uniaxial anisotropic media coincide with the global coordinates, the reflected and transmitted beam intensities from a uniaxial anisotropic slab and three-layered media are numerically simulated. It is shown that the reflected intensity components of the incident beam, especially the TM polarized incident beam, are smaller than the transmitted intensity components. The distortion of the reflected intensity component is more evident than that of the transmitted intensity component. The distortion of intensity distribution is greatly affected by the dielectric tensor and the thickness of anisotropic media. We finally extend the application of the method to general anisotropic multilayered media.
基金the National Natural Science Foundation of China(Nos.50478037 and 10572058)the Research Foundation for the Doctoral Program of Higher Education(No.20050287016).
文摘Wave reflection and transmission in a beam containing a semi-infinite crack are studied analytically based on Timoshenko beam theory., Two kinds of crack surface conditions： non-contact （open） and fully contact （closed） cracks, are considered respectively for an isotropic beam. The analytical solution of reflection and transmission coefficients for a semi-infinite crack is obtained. The power reflection and transmission ratios depend on both the frequency and the position of the crack. Numerical results show the conservation of power transport. The transmitted energy among various wave modes is also investigated. A finite element method is used to verify the validity of the analytical results.
文摘The propagation, reflection, and transmission of SH waves in slightly com- pressible, finitely deformed elastic media are considered in this paper. The dispersion relation for SH-wave propagation in slightly compressible, finitely deformed layer over- lying a slightly compressible, finitely deformed half-space is derived. The present paper Mso deals with the reflection and refraction （transmission） phenomena due to the SH wave incident at the plane interface between two distinct slightly compressible, finitely deformed elastic media. The closed form expressions for the amplitude ratios of reflection and refraction coefficients of the reflected and refracted SH waves are obtained from suit- able boundary conditions. For the numerical discussions, we consider the Neo-Hookean form of a strain energy function. The phase speed curves, the variations of reflection, and transmission coefficients with the angle of incidence, and the plots of the slowness sections are presented by means of graphs.
基金National Natural Science Foundation of China (59808011).
文摘Based on the modified Biot＇s theory of two-phase porous media, a study was presented on seismic reflection and transmission coefficients at an air-water interface of saturated porous soil media. The major differences between air-saturated soils and water-saturated soils were theoretically discussed, and the theoretical formulas of reflection and transmission coefficients at an air-water interface were derived. The characteristics of propagation and attenuation of elastic waves in air-saturated soils were given and the relations among the frequency, the angle of incidence and the reflection, transmission coefficients were analyzed by using numerical methods. Numerical results show that the propagation characteristic of the wave in air-saturated soils is great different from that in water-saturated soils. The frequency and the angle of incidence can have great influences on the reflection and transmission coefficients at interface. Some new cognition about the wave propagation is obtained and the study suggests that we may carefully pay attention to the influence of air on the dynamic analysis of seismic wave.
基金the National Natural Science Foundation of China(Grant Nos.62071359,61975158,62001377,and 61801349)China Postdoctoral Science Foundation(Grant No.2016M602770)+3 种基金Natural Science Basic Research Plan in Shaanxi Province of China(Grant Nos.2019JQ405,2019JM-238,2020JM-192,and 2021JM-135)Natural Science Basic Research Program of Shaanxi,China(Grant No.2020JQ-331)Postdoctoral Science Foundation in Shaanxi Province and the Fundamental Research Funds for the Central Universities,Scientific Research Program Funded by Shaanxi Provincial Education Department(Grant No.20JS059)the Open Foundation of Laboratory of Pinghu,Pinghu,China。
文摘The reflection and transmission of a finite-power Airy beam incident on a dielectric slab are investigated by an analytical method.Based on the plane-wave angular spectrum expansion and Fresnel approximation,the analytical expressions of the reflected field,internal field as well as transmitted field in each region are obtained.Through numerical simulations,the intensity distributions of the incident beam,reflected beam,internal beam as well as transmitted beam are presented at oblique incidence.Besides,we also compare the intensity distributions of the geometrical-optics beam field,the first order beam mode field and the actual beam field,which indicates that the contribution of each order beam mode field to the actual beam field is related to the refractive index of the dielectric slab.Meanwhile,the reflection characteristics of the Airy beams in the special cases of Brewster incidence and total reflection are investigated.Finally,the effects of the optical thickness and refractive index of the dielectric slab on the peak intensity distributions and beam shifts of the reflected and transmitted beams are also discussed in detail.The analytical and numerical results will be useful to analyze the propagation dynamics of Airy beam in the dielectric slab and provide some theoretical supports to the design of optical film.
文摘The study done in this paper brings out the effect of the viscoelasticity on the reflection/transmission coefficients. The knowledge of this effect can be useful for several applications, such as enhancing the resolution of the seismic sections, fluid and fracture detection. It can also have other applications different from the geophysical domain, as the study of the bonding between the materials in the civil engineering domain. We use the complex Lame coefficients in the continuity equations at the boundary layers to get the analytical expressions of the reflection/transmission coefficients in viscoelastic media. The coefficients can be divided into two parts, the first part is independent from the quality factor, and it corresponds to the elastic reflection/transmission coefficients. The second part is dependent on the quality factor contrast and it represents the contribution of the viscoelasticity on the reflection/transmission coefficients. From the numerical study it appears that the effect of the viscoelasticity is significant near to the critical angles. This effect is not clear and it is difficult to interpret and we do not know if it has a physical meaning or it is only a mathematical artifact that is why it is better to be far from the critical angles for seismic investigation.
基金supported by HeiLongJiang Natural Science Fund(No.B2015019)the National Natural Science Foundation of China(No.10972029)Basic Business Special in Heilongjiang Province Department of Education(135109232)
文摘The reflection and transmission properties of thermo-elastic waves at five possible interfaces between two different strain gradient thermo-elastic solids are investigated based on the generalized thermo-elastic theory without energy dissipation （the GN theory）. First, the function of free energy density is postulated and the constitutive relations are defined. Then, the temperature field and the displacement field are obtained from the motion equation in the form of displacement and the thermal transport equation without energy dissipation in the strain gradient thermo-elastic solid. Finally, the five types of thermo-elastic interracial conditions are used to calculate the amplitude ratios of the reflection and transmission waves with respect to the incident wave. Further, the reflection and transmission coefficients in terms of energy flux ratio are calculated and the numerical results are validated by the energy conservation along the normal direction. It is found that there are five types of dispersive waves, namely the coupled longitudinal wave （the CP wave）, the coupled thermal wave （the CT wave）, the shear wave, and two evanescent waves （the coupled SP wave and SS wave）, that become the surface waves at an interface. The mechanical interfacial conditions mainly influence the coupled CP waves, SV waves, and surface waves, while the thermal interracial conditions mainly influence the coupled CT waves.
基金the Natural Science Foundation of Shaanxi Province, China (Grant No. 2007D15)
文摘For the boundary between transversely isotropic media with a vertical axis of symmetry (VTI media), the interface between a liquid and a VTI medium, and the free-surface of an elastic half-space of a VTI medium, an accurately fast algorithm was presented for calculating reflection/transmission (R/T) coefficients. Specially, the case of post-critical angle incidence was considered. Although we only performed the numerical calculation for the models of the VTI media, the calculated results can be extended to the models of transversely isotropic media with a horizontal axis of rotation symmetry (HTI media). Compared to previous work, this algorithm can be used not only for the calculation of R/T coefficients of the boundary between ellipsoidally anisotropic media, but also for that between generally anisotropic media, and the speed and accuracy of this algorithm are faster and higher. According to the anisotropic parameters of some rocks given by the published literature, we performed the calculation of R/T coefficients by using this algorithm and analyzed the effect of the rock anisotropy on R/T coefficients. We used Snell's law and the energy balance principle to perform verification for the calculated results.
基金supported by the Natural R&D Special Fund for Public Welfare Industry(No.200808069)National Natural Science Foundation of China(Nos.40974038,40774028 and 40821062)
文摘Chen＇s technique of computing synthetic seismograms, which decomposes every vector with a set of basis of orthogonality and completeness before applying the Luco-Apsel-Chen （LAC） generalized reflection and transmission coefficients method, is confirmed to be efficient in dealing with elastic waves in multi-layered media and accurate in any frequency range. In this article, we extend Chen＇s technique to the computation of coupled seismic and electromagnetic （EM） waves in layered porous media. Expanding the involved mechanical and electromagnetic fields by a set of scalar and vector wave-function basis, we obtain the fundamental equations which are subsequently solved by using a recently developed version of the LAC generalized reflection and transmission coefficients method. Our approach and corresponding program is validated by reciprocity tests. We also show a numerical example of a two-layer model with an explosion source. The P-to-EM conversion waves radiated from the interface may have potential application.
基金financially supported by Project of the National Natural Science Foundation of China (Grant No. 41002126)Project of State Key Laboratory of Geohazard Prevention and Geoenvironment Protection (Grant No. SKLGP2009Z010)
文摘Currently, scant attention has been paid to the theoretical analysis on dynamic response mechanism of the ＂Dualistic＂ structure roek slope. The analysis presented here provides insight into the dynamic response of the ＂Dualistie＂ structure rock slope. By investigating the principle of energy distribution, it is shown that the effect of a joint plays a significant role in slope stability analysis. A dynamic reflection and transmission model （RTM） for the ＂Dualistic＂ structure rock slope and explicit dynamic equations are established to analyze the dynamic response of a slope, based on the theory of elastic mechanics and the principle of seismic wave propagation. The theoretical simulation solutions show that the dynamic response of the ＂Dualistic＂ structure rock slope （soft-hard） model is greater than that of the ＂Dualistic＂ strueture rock slope （hard-soft） model, especially in the slope crest. The magnifying effect of rigid foundation on the dynamic response is more obvious than that of soft foundation. With the amplitude increasing, the cracks could be found in the right slope （soft-hard） crest. The crest failure is firstly observed in the right slope （soft-hard） during the experimental process. The reliability of theoretical model is also investigated by experiment analysis. The conclusions derived in this paper could also be used in future evaluations of Multi-layer rock slopes.
基金supported by the Program for New Century Excellent Talents in University(No.NCET-05-0575)the Education Science Foundation of Jiangxi Province(No.Z-03510)
文摘In this study, the propagation of electromagnetic waves in one-dimensional plasma photonic crystals （PPCs）, namely, superlattice structures consisting alternately of a homogeneous unmagnetized plasma and dielectric material, is simulated numerically using the finite-difference time-domain （FDTD） algorithm. A perfectly matched layer （PML） absorbing technique is used in this simulation. The reflection and transmission coefficients of electromagnetic （EM） waves through PPCs are calculated. The characteristics of the photonic band gap （PBG） are discussed in terms of plasma density, dielectric constant ratios, number of periods, and introduced layer defect. These may provide some useful information for designing plasma photonic crystal devices.
基金supported by the LabEx CeLyA (Centre Lyonnais d’Acoustique, ANR-10-LABX-0060) of Universitéde Lyon。
文摘In this work,an enriched model describing the longitudinal wave propagation is established based on Mindlin’s Second Strain Gradient(SSG)theory,which can describe the heterogeneity caused by the micro-structure interactions in the frame of continuum mechanics.The governing equation and associated boundary conditions are derived based on Hamilton’s principle,then the dispersion relation of non-classical longitudinal wave together with the extra-waves appearing exclusively in SSG theory model are investigated.The investigations are based on the modal density,energy flow,and forced response of the rod.Wave transmission and reflection through planar interfaces based on the proposed model have been calculated.Finally,the results of the enriched model are well interpreted by comparing with the classical theory results,and some useful conclusions are derived on the SSG theory based model in the wave propagation characterization.
文摘Scattering of surface waves by the edge of a small undulation on a porous bed in an ocean of finite depth, where the free surface has an ice-cover being modelled as an elastic plate of very small thickness, is investigated within the framework of linearized water wave theory. The effect of surface tension at the surface below the ice-cover is neglected. There exists only one wave number propagating at just below the ice-cover. A perturbation analysis is employed to solve the boundary value problem governed by Laplace＇s equation by a method based on Green＇s integral theorem with the introduction of appropriate Green＇s function and thereby evaluating the reflection and transmission coefficients approximately up to first order. A patch of sinusoidal ripples is considered as an example and the related coefficients are determined.
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.
基金NASI (National Academy of Sciences, India) for providing financial support
文摘Two problems of scattering of surface water waves involving a semi-infinite elastic plate and a pair of semi-infinite elastic plates,separated by a gap of finite width,floating horizontally on water of finite depth,are investigated in the present work for a two-dimensional time-harmonic case.Within the frame of linear water wave theory,the solutions of the two boundary value problems under consideration have been represented in the forms of eigenfunction expansions.Approximate values of the reflection and transmission coefficients are obtained by solving an over-determined system of linear algebraic equations in each problem.In both the problems,the method of least squares as well as the singular value decomposition have been employed and tables of numerical values of the reflection and transmission coefficients are presented for specific choices of the parameters for modelling the elastic plates.Our main aim is to check the energy balance relation in each problem which plays a very important role in the present approach of solutions of mixed boundary value problems involving Laplace equations.The main advantage of the present approach of solutions is that the results for the values of reflection and transmission coefficients obtained by using both the methods are found to satisfy the energy-balance relations associated with the respective scattering problems under consideration.The absolute values of the reflection and transmission coefficients are presented graphically against different values of the wave numbers.
文摘The present study is concerned with the reflection and transmission of plane waves at an interface between homogenous invisicid liquid half space and a micropolar liquid-saturated porous solid half space. The reflection and transmission coefficients of various reflected and transmitted waves with the angle of incident have been obtained. Numerical calculation has been performed for amplitude ratios of various reflected and transmitted waves. Micropolarity and porosity effects on the reflection and transmission coefficients have been depicted graphically. Some particular cases have been deduced from the present formulation.
