Reflection and refraction of plane waves under initial stresses at an interface

The paper deals with the phenomena of reflection and refraction of plane elastic waves at a plane interface between two semi-infinite elastic solid media in contact, when both the media are initially stressed. It has been shown analytically that both reflected and refracted P and SV waves depend on initial stresses present in the media. The numerical values of reflection and refraction coefficients for different initial stresses and the angle of incidence have been calculated by computer and the results are given in the form of graphs. Many results are found in the paper which are not seen in initially stress-free media.     

Effects of initial stress on the reflection and transmission waves at the interface between two piezoelectric half spaces

The effects of initial stress on the reflection and transmission waves at the interface between two piezoelectric half spaces are studied in this paper. First, the secular equations in the traverse isotropic piezoelectric half space are derived from the general dynamic equation with initial stress taken into consideration. Then, the interface conditions that displacement, stress, electric potential, and electric displacement are continuous across interface are required to be satisfied by three sets of coupled waves, namely, quasi-longitudinal wave, quasi-transverse wave and the electric–acoustic wave. The algebraic equations resulting from the interface conditions are solved to obtain the amplitude ratio of various waves and furthermore the energy reflection and transmission coefficients of various waves. The numerical results are shown graphically and the effects of initial stress are discussed.     

Reflection and refraction of plane waves on the interface of two anisotropic media

We use generalized functionally invariant solutions [1] of the equations of motion to obtain and analytically study solutions of the plane problem of reflection and refraction of plane waves on the interface of two anisotropic media with four elastic constants depending on the angles of incidence of primary waves for various relations between the elastic constants of the contacting media. For the primary waves, we find the ranges of incidence angles for which real and complex secondary waves are excited. We study all possible combinations of the distribution of phase velocities and reflection and refraction angles in detail and obtain conditions characterizing the directions of the energy flux vectors for the primary and secondary waves depending on the incidence angles of the primary waves for different relations between the elastic constants of the contacting media, which satisfy the necessary and sufficient conditions for the elastic energy form to be positive definite.     

Reflection and transmission of plane waves at an imperfectly bonded interface between piezoelectric and piezomagnetic media

The paper analyzes the reflection and transmission of plane waves at an imperfect interface between piezoelectric (PE) and piezomagnetic (PM) media. The materials are assumed to be transversely isotropic. The linear spring model is used to describe the imperfection of bonding behavior at the interface. According to this model, the properties of the interface can be characterized by the normal and tangential interfacial stiffnesses. Numerial examples are performed for BaTiO₃/CoFe₂O₄ material combination. Four cases, a perfect, slip, normal weak bonding and unbonding interfaces for the coupled quasi-pressure (QP) wave incidence from BaTiO₃ medium are compared in detail. Numerical results of the reflection and transmission coefficients (RTCs) varying with incident angle for different interfacial stiffnesses are presented. Results show that the transmitted QP/reflected QSV waves are the strongest in the perfect/unbonded cases, respectively. The scattered waves in the slip and normal weak bonding cases are between those of the perfect and unbonded cases generally. Critial angles have noticeable effect on the RTCs and energy coefficients for the coupled scattered waves of the perfect and slip cases but have a little/no effect on those of the normal weak bonding/unbonded cases. It is found that the sum of the energy carried by the transmitted/reflected QP and QSV waves is less than unit for the imperfect bonding between BaTiO₃/CoFe₂O₄ solids. These results may provide some useful reference datum for the imperfection measurment at the PE and PM interface.     

Reflection and transmission of quasi-plane waves at the interface of piezoelectric semiconductors with initial stresses

We examine the reflection and transmission phenomena of quasi-longitudinal plane(QP) waves in an AlN-ZnO laminated composite structure. The structure is designed under the influence of the initial stresses in which one carrier piezoelectric semiconductor(PSC) half-space is in welded contact with another PSC half-space.The secular equations in the transversely isotropic PSC material are derived from the general dynamic equation, taking the initial stresses into consideration. It is shown that the incident quasi-longitudinal wave(QP-mode) at the interface generates four types of reflected and transmitted waves, namely, QP wave, quasi-transverse(QSV) wave,electric-acoustic(EA) wave, and carrier plane(CP) wave. The algebraic equations are obtained by imposing the boundary conditions on the common interface of the laminated structure. Reflection and transmission coefficients of waves are obtained by implementing Cramer's rule. Profound impacts of the initial stresses and exterior electric biasing field on the reflection and transmission coefficients of waves are investigated and presented graphically.     

Reflection and refraction of attenuated waves at boundary of elastic solid and porous solid saturated with two immiscible viscous fluids

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 nonsingular 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.     

两微极磁热弹性固体分界面上波的反射与折射

给出了磁场、热场和弹性场多场耦合作用下微极广义热弹性固体的一般控制方程.该方 程既包含了磁场、热场和弹性场的耦合作用,又在其广义热传导方程中涵盖了耦合热弹理论 (C-D)及其5类推广(L-S理论,G-L理论,G-N(II,III)理论和C-T理论).运用该微极广义磁热 弹性控制方程,研究了在定常磁场作用下, 具有均匀初始温度的两理想接触微极弹性介质平面分界面上磁热弹性波的反射和折射现象.给出了分别在缺少磁场、热场作用或不同广义热传 导理论下反射或折射热波、纵向位移波、耦合横向和微旋转波与入射纵向位移波的振幅比随 入射角变化的关系曲线.对缺少磁、热和微极性以及热松弛时间时对应的反射、折射系数进 行了对比.结果表明磁、热和微极性以及热松弛时间对振幅比均有不同程度的影 响,与磁、热和微极性一样,热松弛时间对不同类型波的影响能力差别明显,但对同 一类型的反射波和折射波的影响相似.     

Reflection and refraction of plane waves at the interface of an elastic solid and microstretch thermoelastic solid with microtemperatures

The problem of reflection and refraction of waves at the interface of an elastic solid and microstretch thermoelastic solid with microtemperatures has been investigated. It is shown that due to incidence of P-wave or SV-wave at the interface, the waves are reflected and refracted. The amplitude ratios of these various reflected and refracted waves have been computed numerically, and graphical representation of their variations is made with the angle of incidence. Effect of microrotation on these amplitude ratios has been shown graphically. Some particular cases of interest have also been discussed.     

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.     

Influence of imperfect bonding on the reflection and transmission of QP-wave at the interface of two functionally graded piezoelectric materials

This paper studies the reflection and transmission of two dimensional quasi P wave incident at an imperfect interface between two dissimilar Functionally Graded Piezoelectric Materials (FGPM) half-spaces. The imperfect bonding behavior between the two considered half-spaces is described by the interfacial imperfections. The imperfection is characterized by the normal stiffness and tangential stiffness using the linear spring model. These interface parameters (i.e normal stiffness and tangential stiffness) are dependent on the elastic properties of interphase. Secular equations have been derived analytically for both the half-spaces. Different cases of imperfect interfaces namely perfect interface, slip interface, weak bonding interface and unbounded interface have been assumed and discussed. Influence of material gradients on the reflection and transmission coefficients (RTC’s) have been inflicted graphically for all the four considered interface conditions. Further, a comparative study of the RTC’s with respect to the incident angle has been carried out for the different cases of imperfections. The obtained results may be useful for measuring imperfection at the interface and designing of SAW devices.     

波在双孔隙与单孔隙介质界面上的反射与透射

基于Biot理论和双重孔隙介质理论研究了弹性波在双重孔隙介质与流体饱和单一孔隙介质 界面的反射和透射问题,在界面上假定裂缝孔隙流体相对于固体骨架的位移为零,推导了反 射系数和透射系数的计算公式,数值讨论了反射系数和透射系数随入射角和频率的变化关 系. 同时,讨论了双重孔隙介质中3种压缩波(P-1, P-2和P-3波)和一种剪切波(S波) 的频散和衰减特性.