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.     

Effective amplification of optical solitons in high power transmission systems

Nonlinear Dynamics - We study the effective amplification of optical solitons in high power transmission systems based on a nonlinear Schrödinger equation with variable coefficients. Three...     

Explicit formulas for the reflection and transmission coefficients of one-component waves through a stack of an arbitrary number of layers

The transmission and reflection of one-component elastic, acoustic, optical waves on a stack of arbitrary number of different homogeneous layers have been intensively studied in the literature. However, all obtained formulas for the reflection and transmission coefficients are in implicit form. In this paper, we provide the explicit formulas for them. From these formulas we immediately arrive at the explicit formulas for the reflection and transmission coefficients of one-component waves through an FGM layer. Based on the obtained exact formulas, approximate formulas for the reflection and transmission coefficients are established for a stack of thin layers and for a thin FGM layer. It is numerically shown that they are good approximations. Since the obtained formulas are totally explicit, they are useful in evaluating, not only numerically but also analytically, the transmission and reflection coefficients of one-component waves.     

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.     

Acoustic wave incidence on a multilayer medium containing a bubbly fluid layer

The problem of acoustic wave reflection and transmission through a multilayer medium containing a bubbly fluid layer is considered. For the water-water with air bubbles-water model the wave reflection and transmission coefficients are calculated and compared with the experimental data. The problem parameters, at which these coefficients take extremum values, are determined. The influence of vapor within the bubbles on the acoustic wave transmission through a layer of a fluid with the vapor-gas bubbles is shown.     

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．     

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.     

Propagation and localization of Rossby waves over random topography (two-layer model)

We study propagation of Rossby waves over randomly stratified bottom topography in a two-layer system. The problem is reduced to coupled stochastic wave equations in latitudinal variable with suitable boundary conditions. When the two-dimensional system is broken into its basic barotropic and baroclinic modes, each one is scattered by the medium, and generates the like-wise and the cross-wise components. We study statistics of the reflection and transmission coefficients for both types of generated modes, and show localization for the like-wise components, and propagation for the cross-wise components. The localization lengths and the transmission rates are estimated in terms of the basic parameters of the system and the correlation-function of topographic fluctuations.     

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.     

Reflection and refraction of SH-waves at a corrugated interface between two laterally and vertically heterogeneous viscoelastic solid half-spaces

Reflection and transmission coefficients due to incident plane SH-waves at a corrugated interface between two isotropic, laterally and vertically heterogeneous visco-elastic solid half spaces are obtained. The density and complex rigidity of each medium are considered to vary along horizontal and vertical directions. Closed form expressions of reflection and transmission coefficients are derived using Rayleigh’s method of approximation. These coefficients are found to be the function of corrugation, heterogeneity, angle of incidence, angle between propagation and attenuation vectors and visco-elasticity of the media. Numerical computations are made for a specific model to study the nature of dependence of these coefficients. Variations of reflection and transmission coefficients for the first order of approximation of the corrugation versus angle of incidence, corrugation and angle between propagation and attenuation vectors are computed and depicted graphically. Comparison is made between these coefficients in viscoelastic media and in uniform elastic media. The problems investigated earlier by Asano [Bull. Earthq. Res. Inst. 38 (1960) 177], Singh et al. [Acta Geophys. Pol. XXVI (1978) 209], Kaushik and Chopra [Geophys. Res. Bull. 18 (1980) 111] and Gupta [Geophys. Trans. 33 (1987) 89] have been reduced as particular cases.     

Numerical estimation of the influence of joint stiffness on free vibrations of frame structures via the scattering of waves at elastic joints

In the structural design of mechanical products, natural frequencies must be controlled to reduce noise and vibration. In particular, the stiffness of the joints which assemble the structural components affects the natural frequencies. Therefore, it is important to predict the influence of joint stiffness on natural frequencies. Generally, these effects are determined by iterative finite element analyses of assembled structural models. Because this results in high computational costs, the sensitivity of natural frequencies to joint stiffness should be determined by a different approach to make the structural design process more efficient. Therefore, this paper proposes the use of reflection and transmission coefficients of elastic joints to predict the dependency of natural frequencies on joint stiffness. First, we formulate the reflection and transmission coefficients of joint stiffness, and then organize the coefficients using a ray tracing method. These formulations enable us to discuss the mechanisms which determine the natural frequency of a structure based on a wave approach using the phase-closure principle. Therefore, by applying the phase-closure principle to the frame structure, we investigate the formation of bending modes, which suggests that the effects of joint stiffness on natural frequencies correspond to the dependence of the reflection and transmission coefficients on joint stiffness. Therefore, these coefficients are useful indicators for estimating the influence of joint stiffness.     

Diffraction of a mode close to its cut-off by a transversal screen in a planar waveguide

The problem of diffraction of a waveguide mode by a thin Neumann screen is considered. The incident mode is assumed to have frequency close to the cut-off. The problem is reduced to a propagation problem on a branched surface and then is considered in the parabolic approximation. Using the embedding formula approach, the reflection and transmission coefficients are expressed through the directivities of the edge Green’s function of the propagation problem. The asymptotics of the directivities of the edge Green’s functions are constructed for the case of small gaps between the screen and the walls of the waveguide. As the result, the reflection and transmission coefficients are found. The validity of known asymptotics of these coefficients is studied.     

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.     

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.     

Wave propagation and reflection-transmission in a stratified viscoelastic solid

The paper investigates time-harmonic wave propagation in continuously stratified solids and provides the results of a reflection-transmission process generated by a layer sandwiched between homogeneous half-spaces. The layer is continuously stratified and allows for jump discontinuities at a finite number of planes. The dissipative effects are accounted for through the classical Boltzmann law of viscoelasticity. By using displacement and traction as convenient vector variables, the governing equations are considered in a vector Volterra integral equation and the solution is determined by means of a matricant. Next the matricant is applied to determine the reflection and transmission coefficients of a layer, with a generic piecewise continuous profile of the material properties. The reflection-transmission process produced by an obliquely incident wave, is considered for horizontally-polarized waves. The low-frequency approximation is derived for the reflection and transmission coefficients. Next, the high-frequency approximation is investigated by a WKB-like procedure which involves a complex valued frequency-dependent shear modulus. The displacement solution is obtained for the forward- and the backward-propagating waves in the layer along with the reflection and transmission coefficients.     

三角形格构式塔身体型系数及屏蔽特性研究Study on shape coefficient and shielding effects of triangular latticed tower body

为满足高压／特高压输电铁塔风致倒塌问题对铁塔体型系数的精准度需求,研究了完全结构化多块网格对格构式三角形输电塔塔身流场的模拟能力,探讨了不同规范体型系数对某铁塔的适用性,并分析了塔身杆件复杂流动干扰作用下的屏蔽特性。结果表明,数值模拟与风洞试验的体型系数吻合很好;完全结构化网格能高保真、高度正交地对铁塔塔身这类复杂空间桁架流场进行离散;《英国杆塔荷载规范》的规定结果虽偏于保守,但其趋势最为接近真实值;在塔身桁架结构各个杆件之间流动干扰作用下,角钢弯折角朝向来流比背向来流的屏蔽作用更强;斜材弯折角背向气流和竖向辅助材弯折角朝向气流的组合之间的流动干扰,使得其对气流的屏蔽作用最强。     

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.     

Interfacial imperfection on reflection and transmission of plane waves in anisotropic micropolar media

This study is concerned with the reflection and transmission of plane waves at an imperfectly bonded interface between two orthotropic micropolar elastic half-spaces with different elastic and micropolar properties. There exist three types of coupled waves in xy-plane. The reflection and transmission coefficients of quasi-longitudinal (QLD) wave, quasi-coupled transverse microrotational (QCTM) wave and quasi-coupled transverse displacement (QCTD) wave have been derived for different incidence waves and deduced for normal force stiffness, transverse force stiffness, transverse couple stiffness and perfect bonding. The numerical values of modules of the reflection and transmission coefficients are presented graphically with the angle of incidence for orthotropic micropolar medium (MOS) and isotropic micrpolar medium (MIS). Some particular cases of interest have been deduced from the present investigation.     

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.