Scattering of Surface Waves by the Edge of a Floating Elastic Plate

The diffraction of plane surface waves by a semiinfinite floating plate in a fluid of finite depth is studied. An explicit analytical solution of the problem is obtained using the Wiener–Hopf technique. Simple exact formulas for reflection and transmission coefficients and their asymptotic expressions are derived. Results of numerical calculations using the obtained formulas are presented.     

Wave reflection by a submerged cycloidal breakwater in presence of a beach with different depth profiles

In this work, formulas for the reflection and transmission coefficients of one-dimensional linear water waves propagating over a submerged structure with a cycloidal cross section in presence of a sloping beach are determined. In the specialized literature, the previous coefficients are obtained mainly for the limit of linear water waves, considering that the water depth upstream and downstream of the structure is flat. For the analysis, we have obtained an approximate analytical solution to the dimensionless Modified Mild-Slope Equation, which models the interactions of a wide range of water waves, from short waves to long waves. The results shown that the presence of small breakwaters not always generate increments on the reflection coefficients, but on the contrary case they contribute to the reflection of the waves decreasing, which is due to the interference of energy that exists between the inclined beach and the structure. To validate the approximate analytical solution, we present a comparison against analytical solutions reported in the specialized literature, obtained with the aid of linear long wave theory, and a numerical solution, all the solutions adjust properly. Results of this study are expected to be used by coastal engineers for preliminary feasibility and desk design of submerged cycloidal breakwaters.     

含单排周期微裂纹平板结构中的弹性波传播

受损伤固体中含有的微裂纹或微孔洞往往具有周期性，对含周期性缺陷结构中的弹性波分析是力学研究中的重要课题，它直接关系到结构的强度和使用寿命。目前对损伤固体中弹性波散射与透射研究结果主要是弹性动力学平面问题。1995年。Scarpetta和Sumbatyan采用解析法研究了平面波在双周期裂纹弹性介质中的传播问题。并推出显式分析结果。本文基于弹性动力学理论，分析研究了含有单排横向周期裂纹的平板中弯曲波的反射与透射问题。给出了含单排裂纹时反射波与透射波系数的数值结果。对于多排裂纹情况，可采用具有退化核第一类Fredholm积分方程方法分析求解，在求解中给出相应的无量纲数，例如无量纲波数、裂纹尺寸比等。本文分析结果可望能在工程振动控制中应用。     

Surface Wave Diffraction on a Floating Elastic Plate

Plane surface wave diffraction by a floating semi-infinite plate is studied. An analytic solution of the problem is constructed by the Wiener-Hopf technique. Analytic formulas for the reflection and transmission coefficients and their shortwave and longwave asymptotics are obtained. An explicit representation for the fluid velocity potential is found. The displacement, strain, and pressure distributions over the plate are investigated as functions of a dimensionless parameter, namely, the reduced rigidity of the plate, and the asymptotic distribution is studied for long and short waves.     

弹性波在准饱和土和弹性土界面的反射与透射

考虑土颗粒和孔隙流体的压缩性,根据准饱和土体的变形连续条件和平衡条件,推导了P1波(快压缩波)、P2波(慢压缩波)和S波的计算公式．根据Snell定理,研究了平面P1波从准饱和土体入射到弹性土层时在界面上的反射和透射,并绘制了反射系数、透射系数和界面应力、位移随入射角的变化曲线,结果表明:饱和度是影响界面效应的一个重要因素,当饱和度低于99％时,反射和透射系数以及应力和位移基本相等,变化不大,但当饱和度为100％时,虽然饱和度比99％提高了1％,但反射和透射系数以及应力和位移值比饱和度为99％时明显降低．     

Shock-Induced Borehole Waves and Fracture Effects

We perform wave experiments using a vertical shock tube setup. Shock waves are generated by the rupture of a thin membrane. In the test section, the incident pressure waves generate borehole-guided waves along water-saturated samples. The tube is equipped with side wall gages and a mobile pressure probe, so that the attenuation and reflection of the wave can be measured. The computation for a single horizontal fracture intersecting a vertical borehole gives a quantitative prediction of reflection and transmission of borehole-guided waves. Three different fracture apertures are used for the calculation. Fracture aperture significantly affects both reflection and transmission coefficients. Large fractures increase reflectivity and decrease transmissivity. In the experiment, we found that both pressures above and below the fracture are influenced by the fracture aperture indeed, thus indicating the potential for fracture detection by borehole waves.     

Shock-Induced Borehole Waves and Fracture Effects

We perform wave experiments using a vertical shock tube setup. Shock waves are generated by the rupture of a thin membrane. In the test section the incident pressure waves generate borehole-guided waves along water-saturated samples. The tube is equipped with side wall gages and a mobile pressure probe, so that the attenuation and reflection of the wave can be measured. The computation for a single horizontal fracture intersecting a vertical borehole gives a quantitative prediction of reflection and transmission of borehole-guided waves. Three different fracture apertures are used for the calculation. Fracture aperture significantly affects both reflection and transmission coefficients. Large fractures increase reflectivity and decrease transmissivity. In the experiment, we found that both pressures above and below the fracture are influenced by the fracture aperture indeed, thus indicating the potential for fracture detection by borehole waves.     

The influence of the viscosity and the magnetic field on reflection and transmission of waves at interface between magneto-viscoelastic materials

The influence of the viscosity on reflection and refraction of plane shear elastic waves in two magnetized semi-infinite media is investigated. The numerical results for the absolute values of the reflection and refraction coefficients and their relative changes for a particular choice of the media are presented graphically. The relative changes of these coefficients are calculated for two special orientations of the magnetic field. It is found that the absolute values of these coefficients are not only functions of the angle of incidence but they are also functions of both the large primary magnetic field and the viscosity of the media. They also vary with the orientation of the magnetic field. Finally, we show that the results of earlier works could be obtained here as particular cases. Finally, this study is regarded an attempt to accommodate magnetic field in visco-elastic media where reflection and refraction of plane shear waves are considered. Results which are obtained in this investigation useful for practical applications or for understanding some aspects of physical acoustic.     

Transmission and reflection of acoustic waves by an obstacle in a waveguide

By an extension of the null field approach introduced by Waterman the transmission and reflection of acoustic waves by an obstacle in a waveguide are considered. The waveguide is assumed to have a constant cross section but otherwise the geometry is left arbitrary. The scattered field is obtained as a complicated mode sum containing the transition matrix of the obstacle, the reflection matrix of the waveguide wall and the transformation relations between the cylindrical and spherical basis functions. For a circular cross section of the waveguide relatively explicit expressions are given for the transmission and reflection coefficients, and numerical results are shown for spherical and spheroidal obstacles in rotationally symmetric configurations. Several natural extensions of the present results are finally recognized.     

Reflection and refraction of plane quasi-P waves at a corrugated interface between distinct triclinic elastic half spaces

The reflection and refraction pattern of elastic waves at a corrugated interface between two triclinic half-spaces is discussed. The incident wave is taken to be the cause of the interface disturbance and the reflected and refracted waves are effects. This leads to the causality requirement that the reflected and refracted waves must propagate away from the interface. Closed form expressions of reflection and transmission coefficients are derived using Rayleigh’s method of approximation. The formulae of reflection and transmission coefficients are derived in closed form for the first-order approximation of the corrugation. The analytical expressions of all the three phase velocities of qP, qSV and qSH waves have been derived. The variation of reflection and refraction coefficients with the angle of incidence and also with the corrugation parameter is shown. In this paper we have developed Graphical User Interface (GUI) Software in MATLAB which shows the variation of reflection and refraction coefficients with respect to incident angle and corrugation parameter. This software can be generalized to show the variation of reflection and refraction coefficients. Numerical computations are performed for a scientific model and the results obtained are shown graphically.     

Propagation,reflection, and transmission of SH-waves in slightly compressible,finitely deformed elastic media

The propagation, reflection, and transmission of SH waves in slightly compressible, finitely deformed elastic media are considered in this paper. The dispersion relation for SH-wave propagation in slightly compressible, finitely deformed layer overlying a slightly compressible, finitely deformed half-space is derived. The present paper also 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 suitable 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.     

Quasi-P-waves at a corrugated interface between two dissimilar monoclinic elastic half-spaces

In this paper we have derived reflection and transmission coefficients of qP-waves at a corrugated interface between two different elastic half-spaces of monoclinic type. Using Rayleigh’s method, the expressions for reflection and transmission coefficients are derived in closed form for a specific interface and for the first order approximation of the corrugation. Numerical computations are performed for a specific model and the results obtained have been shown graphically. The variation of the modulus of reflection and transmission coefficients with the angle of incidence, frequency and corrugation of the interface are shown separately. These coefficients are found to be strongly influenced by the angle of incidence, frequency, elastic parameters and amplitude of the corrugation of the interface. It is found that (i) the modulus of reflection and transmission coefficients at the plane interface are independent of corrugation of the interface and that of frequency of the incident wave, (ii) the reflection and transmission coefficients of regularly reflected and transmitted waves are found to be greater than that of irregularly reflected and transmitted waves, (iii) the coefficients of irregularly reflected and transmitted waves are found to increase and decrease with increase of corrugation and frequency parameters respectively. The results of Singh and Khurana [Singh, S.J., Khurana, S., 2001. Reflection and transmission of P- and SV-waves at the interface two between monoclinic elastic half-spaces. Proc. Natl. Acad. Sci. India 71(A) (IV), 305–319] have been reduced from the present problem.     

On theory of generalized thermoelastic solids with voids and diffusion

Governing equations of thermoelastic diffusion material with voids are modified with the help of Lord and Shulman theory of generalized thermoelasticity. These governing equations are then solved in two-dimension to show the existence of four coupled longitudinal waves and a shear wave. The complex absolute values of the speeds of the coupled longitudinal waves are computed numerically against the frequency for Magnesium material. The reflection of these plane waves from a stress free thermally insulated boundary is also studied, where the dependence of the reflection coefficients on angle of incidence is shown graphically for the incidence of coupled longitudinal wave only. The speeds and reflection coefficients of plane waves are also computed numerically in the absence of voids and diffusion parameters, which are shown graphically to observe the effects of voids and diffusion.     

Wave propagation in liquid-saturated porous solid with micropolar elastic skelton at boundary surface

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.     

Reflection and transmission of elastic waves at five types of possible interfaces between two dipolar gradient elastic half-spaces

Reflection and transmission of an incident plane wave at five types of possible interfaces between two dipo-lar gradient elastic solids are studied in this paper. First, the explicit expressions of monopolar tractions and dipolar trac-tions are derived from the postulated function of strain energy density. Then, the displacements, the normal derivative of displacements, monopolar tractions, and dipolar tractions are used to create the nontraditional interface conditions. There are five types of possible interfaces based on all possible combinations of the displacements and the normal derivative of displacements. These interfacial conditions with consid-eration of microstructure effects are used to determine the amplitude ratio of the reflection and transmission waves with respect to the incident wave. Further, the energy ratios of the reflection and transmission waves with respect to the incident wave are calculated. Some numerical results of the reflection and transmission coefficients are given in terms of energy flux ratio for five types of possible interfaces. The influences of the five types of possible interfaces on the energy parti-tion between the refection waves and the transmission waves are discussed, and the concept of double channels of energy transfer is first proposed to explain the different influences of five types of interfaces.     

Wave propagation in an orthotropic micropolar elastic solid

Two-dimensional plane wave propagation in an orthotropic micropolar elastic solid is studied. There exist three types of coupled waves in xy-plane, whose velocities depend upon the angle of propagation and material parameters. A problem on reflection of these plane waves from a stress-free boundary is considered. The reflection coefficients of various reflected waves are computed numerically for a particular model of the solid. The effects of anisotropy upon the velocities and reflection coefficients are depicted graphically for different angles of propagation.     

Interaction of interfacial and internal waves *

Reflection of internal waves at an interface between the mixed layer and a stratified fluid under the layer is investigated experimentally. Reflection coefficients of the internal waves and transmission coefficients of interfacial waves are obtained for the case in which the interfacial waves propagate along the interface. In order to reveal the energy budget of the two kinds of waves, the above reflection and transmission coefficients are employed in consideration of dissipation of the waves. These coefficients are investigated for different values of a ratio of the frequencies of the interfacial and internal waves. When the ratio is , 1 or 2 at the same horizontal wavenumber, overreflection takes place (i.e., reflection coefficient > 1), while under the same condition the transmission coefficient of the interfacial wave is less than unity. This indicates that the energy source of the overreflection of the internal wave is the interfacial wave. Overreflection also takes place when the two waves have the same frequencies and are in phase. On the other hand, the interfacial wave overtransmits the energy (i.e., transmission coefficient > 1) when the two waves are out of phase.     

Reflection for three-dimensional plane waves in triclinic crystalline medium

The propagation of three-dimensional plane waves at a traction free boundary of a half-space composed of triclinic crystalline material is discussed.A method has been developed to find the analytical expressions of all the three phase velocities of quasi-P (qP),quasi-SV(qSV)and quasi-SH(qSH)in three dimensions.Closed form expressions in three dimensions for the amplitude ratios of reflection coefficients of qP,qSV and qSH waves in a triclinic medium are obtained.These expressions are used for numerically studying the variation of the reflection coefficients with the angle of incidence.The graphs are drawn for different polar angle and azimuth.Numerical results presented indicate that the anisotropy affect the reflection coefficients significantly in the three dimensional case compared to the two-dimensional case.     

Scattering of water waves by a submerged thin vertical elastic plate

The problem of water wave scattering by a thin vertical elastic plate submerged in infinitely deep water is investigated here assuming linear theory. The boundary condition on the elastic plate is derived from the Bernoulli–Euler equation of motion satisfied by the plate. This is converted into the condition that the normal velocity of the plate is prescribed in terms of an integral involving the difference in velocity potentials (unknown) across the plate multiplied by an appropriate Green’s function. The reflection and transmission coefficients are obtained in terms of integrals involving combinations of the unknown velocity potential on the two sides of the plate and its normal derivative on the plate, which satisfy three simultaneous integral equations, solved numerically. These coefficients are computed numerically for various values of different parameters and are depicted graphically against the wave number for different situations. The energy identity relating these coefficients is also derived analytically by employing Green’s integral theorem. Results for a rigid plate are recovered when the parameters characterizing the elastic plate are chosen negligibly small.     

Scattering of water waves by thin vertical plate submerged below ice-cover surface

The present paper is concerned with scattering of water waves from a vertical plate, modeled as an elastic plate, submerged in deep water covered with a thin uniform sheet of ice. The problem is formulated in terms of a hypersingular integral equation by a suitable application of Green's integral theorem in terms of difference of potential functions across the barrier. This integral equation is solved by a collocation method using a finite series involving Chebyshev polynomials. Reflection and transmission coefficients are obtained numerically and presented graphically for various values of the wave number and ice-cover parameter.