Wave reflection in slightly compressible, finitely deformed elastic media

Summary  In this paper, the reflection of a plane wave at an incrementally traction-free boundary of a half-space composed of nearly incompressible elastic material is considered. It is shown that two distinct cases exist, these being dependent on the underlying primary deformation. In the first case, the appropriate slowness sections are each approximately elliptical, and the corresponding reflection phenomena closely mirrors that associated with the corresponding linear isotropic theory. Specifically, an angular range of direction of incident wave exists, for which both a quasi-longitudinal and quasi-shear wave are reflected, the former being replaced by a surface wave outside this angular range. In the second case, the outer slowness section is re-enrant and, in addition to the scenarios previously mentioned, it is possible for two quasi-shear waves to be reflected. Numerical illustrations of reflection coefficients are presented in respect of a modified Varga material and the case of increasing bulk modulus is investigated. Received 17 January 2000; accepted for publication 22 February 2000     

Response of moving load due to irregularity in slightly compressible,finitely deformed elastic media

The present paper has been framed to study the stresses produced on the rough surface of a slightly compressible, finitely deformed half space due to a normal moving load. The surface of the medium is irregular with parabolic type of irregularity. The perturbation method is applied to find the displacement field. The normal and shear stresses have been obtained in closed form and discussed numerically by means of figures. It has been observed that the shear stress developed at different depths below the surface depends on the irregularity depth, frictional coefficient and irregularity factor of the rough surface of the medium. Also, surface plots have been drawn to analyze the combined variation of non-dimensional stresses and irregularity factor against depth.     

Stresses produced in slightly compressible,finitely deformed elastic media due to a normal moving load

In this paper, the stresses developed in slightly compressible, finitely deformed half-space due to normal moving load has been discussed. It has been observed that this type of media have much effect on the existing normal and shearing stresses due to the load. The numerical calculations have been done for developed stresses at different depths. It has been observed that the stresses increase significantly in case of slightly compressible, deformed media.     

Exact solution of sound reflection on infinite laminated plate and transmission through it

An exact solution is proposed in this paper based on the elasticity theory for sound reflection from an infinite laminated plate and transmission through it, and some phenomena of sound propagation in an isotropic media are also discussed. Some examples given here could be used to test approximate models of laminated plates.     

Propagation of plane P-waves at interface between elastic solid and unsaturated poroelastic medium

A linear viscoporoelastic model is developed to describe the problem of reflection and transmission of an obliquely incident plane P-wave at the interface between an elastic solid and an unsaturated poroelastic medium, in which the solid matrix is filled with two weakly coupled fluids (liquid and gas). The expressions for the amplitude reflection coefficients and the amplitude transmission coefficients are derived by using the potential method. The present derivation is subsequently applied to study the energy conversions among the incident, reflected, and transmitted wave modes. It is found that the reflection and transmission coefficients in the forms of amplitude ratios and energy ratios are functions of the incident angle, the liquid saturation, the frequency of the incident wave, and the elastic constants of the upper and lower media. Numerical results are presented graphically. The effects of the incident angle, the frequency, and the liquid saturation on the amplitude and the energy reflection and transmission coefficients are discussed. It is verified that in the transmission process, there is no energy dissipation at the interface.     

Response of loose bonding on reflection and transmission of elastic waves at interface between elastic solid and micropolar porous cubic crystal

The problem of reflection and transmission of plane periodic waves incident on the interface between the loosely bonded elastic solid and micropolar porous cubic crystal half spaces is investigated. This is done by assuming that the interface behaves like a dislocation, which preserves the continuity of traction while allowing a finite amount of slip. Amplitude ratios of various reflected and transmitted waves have been depicted graphically. Some special cases of interest have been deduced from the present investigation.     

Propagation of electromagnetic wave in the three phases soil media

IntroductionItisofparamountimportancetogetgeotechnicalparameterssuchasmoisture ,compactness,andshearstrengthforgeotechnicalengineeringtransaction .Butthemethodtofetchthesoilsamplesforlaboratorytestcannotavoidbringingthedisturbance ,andmakethetestresultsinconsistenttotheactualstatusofsoil.Inrecentyears,theapplicationofEMwaveinthedetectinghiddentroublesindamsandundergroundfoundationsdevelopedrapidly .Buttherearestillsomefactorsthatrestricttheadvanceofapplication .Firstly ,thesoilconstitutesthr…     

固-固有限周期声子晶体中SH波全反射隧穿的机理

利用边界条件推导出SH波在一维固-固有限周期声子晶体中的转移矩阵,并用倏逝波的概念和多波束干涉理论,从理论上解释了一维固-固有限周期声子晶体全反射隧穿效应产生的物理机理,得出了全反射隧穿峰带波长满足的解析公式。利用解析公式和转移矩阵研究了一维固-固有限周期声子晶体中SH波的全反射隧穿效应,结果发现两种方法得出的结论是吻合的。     

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.     

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。     

带隔板装药爆轰波马赫反射理论研究和数值模拟

基于三波理论和Whitham方法对带隔板装药爆轰波相互作用后发生的正规反射和非正规反射进行了理论分析,给出了爆轰波发生马赫反射时临界入射角和马赫杆增长角等参数的变化规律,提出了马赫杆高度的计算模型。基于凝聚炸药爆轰Jones-Wilkins-Lee(JWL)模型和冲击起爆的Lee-Tarver模型,利用有限元计算软件对带隔板装药爆轰波的传播过程进行了数值模拟。结果表明,发生马赫反射后,随着爆轰波的传播,马赫杆的高度不断增加。数值模拟结果与理论计算结果吻合较好,说明本文中采用的理论模型和数值模拟方法能够较准确地描述带隔板装药爆轰波马赫反射的传播过程。     

The method of mixed boundary condition for a kion of linear and nonlinear composite structure

This paper deals with the axisymmetrical deformation of shallow shells in large deflection which are in conjunction with linear elastic structures at the boundary: A method of mixed boundary condition for this problem is introduced, then the problem of a composite structure is transformed into a problem of a single structure and the integral equations are given. The perturbation method is used to obtain the solutions and an example of composite structure consisting of a shallow spherical and a cylindrical shell is presented.Communicated by Yeh Kai-yuan     

两层流体中水波在垂直薄板上的反射与透射

研究在两层流体中表面波模态和内波模态的波浪与半潜式刚性垂直薄板 相互作用的问题. 基于特征函数展开理论,建立了两种模态入射波作用下,半潜式刚性垂直 薄板的反射与透射能量的计算方法,证明了对每一种模态的入射波,另一种模态波浪的反射 与透射能量是相等的. 对水面漂浮和座底半潜式薄板的反射与透射能量,以及作用在其上的 水平波浪力进行了数值计算分析,表明在某个频率范围内,流体的分层效应对这些水动力 量的影响是不可忽视的. 特别地,当薄板的一端位于两层流体的内界面上时,两种模态波浪 的能量转化是最大的.     

Propagation of acoustic waves in porous media and their reflection and transmission at a pure-fluid/porous-medium permeable interface

We find a sufficient condition of hyperbolicity for a differential system governing the motion of a one-dimensional porous-medium, so ensuring the existence of a solution for the associated Cauchy problem. We study propagation of linear waves impacting at a pure-fluid/porous-medium interface and we deduce novel expressions for the reflection and transmission coefficients in terms of the spectral properties of the governing differential system. We show three-dimensional plots drawing reflection and transmission coefficients as functions of Biot’s parameters. In such a way we propose an indirect method for measuring Biot’s parameters when the measurement of the reflection and transmission coefficients associated to the traveling waves is possible.     

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.     

Study of anomalous wave propagation and reflection in semi-infinite elastic metamaterials

Elastic metamaterials have been investigated to achieve negative effective properties, which cannot be found in the conventional elastic medium. In this paper, plane wave propagation and reflection in semi-infinite elastic metamaterials with doubly or triply negative material properties are studied analytically and numerically. The unique negative refractions for the longitudinal (P) wave and transverse (S) wave are captured by the proposed generalized Snell’s law. Attention is paid to quantitative characterization of the effects of different negative property combinations on the anomalous wave propagation. The effects of different angles of incidence are also investigated for both double-negative and triple-negative transmitted media and some unusual wave propagation phenomena such as complete wave mode conversion are numerically demonstrated. This study can serve as the theoretical foundation for engineering and designing general metamaterial-based elastic wave devices.     

PMN-PT夹层弹性半空间结构中SH波的传播Propagation of SH waves in sandwich structures consisting of PMN-PT single crystal layer and elastic half-spaces

分析了弹性上下半空间和PMN‐PT单晶层组成的夹层结构中SH波的传播性质,PMN‐PT单晶沿[011]c方向极化,宏观上呈mm2对称,且晶体沿角度θ方向切割。基于正交各向异性压电材料和各向同性弹性材料的基本方程,得到了夹层结构中SH波传播时行列式形式的频散方程。通过对数值算例进行分析可以看出,PMN‐PT单晶的切割角度和弹性材料属性对结构中的相速度有很大影响,因此波的某些传播性能可以通过材料的设计以及晶体切割的方向来实现,这些结论为声表面波器件的开发和应用提供了理论依据。     

Propagation of wave at the boundary surface of transversely isotropic thermoelastic material with voids and isotropic elastic half-space

The purpose of this research is to study the effect of voids on the surface wave propagation in a layer of a transversely isotropic thermoelastic material with voids lying over an isotropic elastic half-space. The frequency equation is derived after developing a mathematical model for welded and smooth contact boundary conditions. The dispersion curves giving the phase velocity and attenuation coefficient via wave number are plotted graphically to depict the effects of voids and anisotropy for welded contact boundary conditions. The specific loss and amplitudes of the volume fraction field, the normal stress, and the temperature change for welded contact are obtained and shown graphically for a particular model to depict the voids and anisotropy effects. Some special cases are also deduced from the present investigation.