Transmission Of SH Waves Research Articles

Reflection and transmission of SH waves at the interface of a V-notch and a piezoelectric/piezomagnetic half-space

Reflection and transmission of SH waves at the interface of a V-notch and a piezoelectric/piezomagnetic half-space

Homogenization of very rough three-dimensional interfaces for the poroelasticity theory with Biot's model

In this paper, we carry out the homogenization of a very rough three-dimensional interface separating two dissimilar generally anisotropic poroelastic solids modeled by the Biot theory. The very rough interface is assumed to be a cylindrical surface that rapidly oscillates between two parallel planes, and the motion is time-harmonic. Using the homogenization method with the matrix formulation of the poroelasicity theory, the explicit homogenized equations have been derived. Since the obtained homogenized equations are totally explicit, they are very convenient for solving various practical problems. As an example proving this, the reflection and transmission of SH waves at a very rough interface of tooth-comb type is considered. The closed-form analytical expressions of the reflection and transmission coefficients have been derived. Based on them, the effect of the incident angle and some material parameters on the reflection and transmission coefficients are examined numerically.

Homogenization of very rough two-dimensional interfaces separating two dissimilar poroelastic solids with time-harmonic motions

The homogenization of a very rough three-dimensional interface separating two dissimilar isotropic poroelastic solids with time-harmonic motions was considered by Gilbert and Ou (Acoustic wave propagation in a composite of two different poroelastic materials with a very rough periodic interface: A homogenization approach. Int J Multiscale Comput Eng 2003; 1(4): 431–440). The homogenized equations have been derived; however, they are still in implicit form. In this paper, the homogenization of a very rough two-dimensional interface separating two dissimilar generally anisotropic poroelastic solids with time-harmonic motions is investigated. The main aim of the investigation is to derive homogenized equations in explicit form. By employing the homogenization method, along with the matrix formulation of the poroelasticity theory, the explicit homogenized equations have been derived. Since these equations are totally explicit, they are very useful in solving practical problems. As an example proving this, the reflection and transmission of SH waves at a very rough interface of the tooth-comb type is considered. The closed-form analytical expressions of the reflection and transmission coefficients are obtained. Based on these expressions, the dependence of the reflection and transmission coefficients on some parameters is examined numerically.

Reflection, refraction, and transmission of SH waves at a micropolar layer separating two elastic media

In this paper, we study the reflection, refraction, and transmission of SH-waves in media separated by a layer whose behavior is described by a simplified model of Cosserat (micropolar) elasticity. The effect of a micropolar medium on the reflection and refraction of SH-waves is obtained. The amplitude ratios and energy fluxes of reflected and transmitted waves are graphically represented.

Reflection and transmission of SH waves at a very rough interface and its band gaps

This paper deals with the reflection and transmission of SH waves at a very rough interface separating two dissimilar isotropic elastic solids. The interface oscillates between two straight lines. By means of homogenization, the domain containing the very rough interface is replaced by an effective material layer whose elastic constants depend on the thickness variable. The reflection and transmission of SH waves at the very rough interface is then reduced to the ones at a FGM layer. The exact analytical formulas for the reflection and transmission coefficients have been derived. Based on them, the dependence of the reflection and transmission coefficients on the incident angle, the wave frequency, the material constants and the geometry of the rough interface are examined. Remarkably, it has been shown that a very rough interface of comb-type with the comb-tooth width varying periodically can produce band-gaps to SH waves. With this fact, many potential applications can be expected coming from very rough interfaces of comb-type with periodic comb-tooth width. It is also shown that the width and the location of band-gaps depend strongly on the contrast of rigidities of two half-spaces, the amplitude of the variation of the comb-tooth width, the incident angle of SH waves and the number of periods of comb-tooth.

Reflection and transmission of SH-waves at a corrugated interface between two semi-infinite anisotropic magnetoelastic half-spaces

An analysis has been carried out for reflection and transmission of a plane SH-wave incident at a corrugated interface between two anisotropic magnetoelastic half-spaces. Rayleigh’s method of approximation is applied to derive the reflection and transmission coefficients for first order approximation of corrugation. The expressions for reflection and transmission coefficients for first order approximation of corrugation are obtained in closed form for a special type of interface. It is found that these coefficients are proportional to the amplitude of corrugation and are functions of magnetoelastic properties of materials of the half-spaces as well as the angle of incidence. Special cases are deduced for anisotropic and isotropic materials for particular case of corrugation. Numerical computations are performed for a specific model of two different anisotropic magnetoelastic media. The effects of anisotropic magnetoelastic coupling parameter, the angle at which wave crosses the magnetic field, frequency factor, wave length of corrugation, and the amplitude of corrugation are shown through figures.

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.

Reflection and transmission of SH-waves at a corrugated interface between two laterally and vertically heterogeneous anisotropic elastic solid half-spaces

This paper is concerned with the reflection and transmission coefficients of SH-waves at a corrugated interface between two anisotropic heterogeneous elastic solid half spaces. Both the half spaces are taken transversely isotropic and laterally and vertically heterogeneous. The Rayleigh’s method of approximation is adopted and expressions for reflection and transmission coefficients are obtained in closed form for the first-order approximation of the corrugation. In Rayleigh’s method, expressions in boundary conditions containing the function defining the corrugated boundary are expanded in Fourier series and unknown coefficients in the solutions are determined to any given order of approximation in terms of a small parameter characteristic of the boundary. The analytical expressions of these coefficients show that they depend upon corrugation of the interface and are strongly influenced by the anisotropy and heterogeneity of the half-spaces. Numerical computations are performed for the case of a particular corrugated interface: ζ =c cos k* x showing that the effect of heterogeneity on the reflection and transmission coefficients is minimum near the normal incidence and dominance of this effect increases with the angle of incidence. For incident wave striking at 45°, the effect of the corrugation is found significant on the reflection and transmission coefficients. The maximum effect of transverse isotropy on the reflection and transmission coefficients is observed at normal incidence when the values of the anisotropy parameters are 0.5 and 0.8 for the upper and lower half-spaces, respectively. The effect of frequency of the incident wave is observed on all reflected and refracted waves. The analytical expressions derived by Tomar and Saini (1997), Gupta (1987) and Asano (1960) are obtained as particular cases with our formulation.

Reflection/refraction of SH-waves at a corrugated interface between two different anisotropic and vertically heterogeneous elastic solid half-spaces

AbstractWe investigate the reflection and transmission of SH-waves at a corrugated interface between two different anisotropic, heterogeneous elastic solid half-spaces. Both the media are assumed to be transversely isotropic and vertically heterogeneous. Rayleigh's method is followed and expressions for the reflection and transmission coefficients are obtained in closed form for the first-order approximation of the corrugation. It is found that these coefficients depend on corrugation and are affected by the anisotropy and heterogeneity of the media. Numerical computations for a particular model have been performed.

Transmission of SH Waves Through an Elastic Layer Between Two Solids With Frictional Contact Interfaces

The propagation of SH waves in a three-layered medium containing an interlayer between two semi-infinite solids with frictional contact interfaces is studied. The incident wave, which propagates through the layer from one half-space to another with subcritical angle, is assumed to be strong enough so that friction may be broken, and the local slip may take place at the interfaces. The mixed boundary conditions involving inequalities and unknown intervals lead to a set of recurrence relations. Special examples are given for the case of identical materials to illustrate the mathematical procedure to obtain final results. The interface tractions and relative slip velocities are presented. The interaction between the two interfaces is discussed. It is shown that the slip of the interface near the incident wave may restrain the slip of the interface far from the incident wave, while that the latter may facilitate the former. We also find the instability of the system for similar values of the two interface friction coefficients. Finally, the energy transmitted through the interlayer and dissipated by the friction of the two interfaces are examined.

Reflection and transmission ofSH waves in an initially stressed medium consisting of a sandy layer lying over a fluid-saturated porous solid

Biot's theory is employed to study the reflection and transmission ofSH waves in a sandy layer lying over a fluid-saturated porous solid half-space. The entire medium is considered under constant initial stress. Effects of sandiness, initial stress, anelasticity and viscosity of the interstitial fluid on the partitioning of energy are studied. In the presence of initial stress the incident wave starts attenuating when incider beyond a certain angle (depending upon the amount of initial stress), even if the medium is perfectly clastic. Anelasticity of the solid layer results in the dissipation of energy during transmission. The direction of attenuation vector of incident wave affects the dissipation energy to a large extent. Effect on partitioning of energy reverse at incidence after the critical angle. A complete account of energy returmed back to the underlying half-space and that which is dissipated in the overlying layer has been discussed analytically as well as numerically.

Transmission of SH Waves Through a Periodic Array of Elastic Cylinders

The reflection and transmission characteristics of a grating of identical, circular elastic cylinders, arranged periodically in an elastic slab, are investigated. Use is made of a simple approach synthesized from Fourier-Bessel expansions and the T-matrix method for the analysis of a two-dimensional problem involving SH waves only. It is observed that the nonspecular modes are generally very weak for such gratings in contrast with those for gratings made of periodic bimaterial interfaces. The presented analysis may be easily extened to the case of diffraction of incident P-and/or SV-waves, and should be useful for noise control applications.

Propagation, reflection and transmission of waves under initial shear stresses

The paper deals with the study of propagation of Love waves and reflection as well as transmission of SH waves under initial shear stresses. The results have been computed taking two real media and presented graphically to compare with the initial stress-free cases.