Reflection and Refraction of SH-Waves at a Corrugated Interface between Two-Dimensional Transversely Isotropic Half-Spaces.

Tomar, S. K.; Saini, Sohan Lal

doi:10.4294/jpe1952.45.347

Cited by 30 publications

(26 citation statements)

References 20 publications

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“…Rayleigh used this method, in his paper "On the dynamical theory of grating" [1907], and later, researchers in various fields applied his method to explain reflection and transmission phenomena of waves from irregular boundary surfaces. Using different techniques, many problems of reflection and refraction of elastic waves from irregular boundary surfaces have appeared in the open literature, such as [Abubakar 1962;Asano 1960;1961;1966;Dunkin and Eringen 1962;Tomar and Saini 1997;Okamoto and Takenaka 1999;Tomar et al 2002;Gupta 1987;Kumar et al 2003;Tomar and Kaur 2003;Kaur and Tomar 2004;Kaur et al 2005].…”

Section: Introductionmentioning

confidence: 99%

Shear waves at a corrugated interface between two dissimilar fiber-reinforced elastic half-spaces

Singh

Tomar

2007

JOMMS

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A problem of reflection and transmission of shear waves (SH waves) at a corrugated interface between two distinct fiber-reinforced elastic half-spaces has been analyzed. Rayleigh's method of approximation is used to determine the reflection and transmission coefficients. We find that (i) these coefficients are functions of the angle of incidence and the elastic parameters of the media, (ii) the coefficients corresponding to irregularly reflected and transmitted waves are proportional to the amplitude of the corrugated interface, and (iii) reflection and transmission coefficients of the regularly reflected and transmitted waves are greater than those of irregularly reflected and transmitted waves. The energy ratios of reflected and transmitted waves are also presented. Numerical computations are performed and the results obtained are presented graphically. Some earlier results by other workers are recovered by our treatment.

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Section: Introductionmentioning

confidence: 99%

Shear waves at a corrugated interface between two dissimilar fiber-reinforced elastic half-spaces

Singh

Tomar

2007

JOMMS

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“…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. …”

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confidence: 99%

“…The problems of wave propagation from plane boundaries in anisotropic media have also been studied by Musgrave (1960), Keith and Crampin (1977), Mandal (1991), Ruger (1997) among others. Tomar and Saini (1997) studied the reflection and refraction of SH-waves at a corrugated interface between two transversely isotropic elastic half spaces. Recently, Tomar et al (2002) investigated the reflection and transmission coefficients of SH-waves at corrugated interface between transversely isotropic and visco-elastic solid half-spaces.…”

Section: Introductionmentioning

confidence: 99%

“…Tomar and Saini (1997) studied the reflection and refraction of SH-waves at a corrugated interface between two transversely isotropic elastic half spaces. Recently, Tomar et al (2002) investigated the reflection and transmission coefficients of SH-waves at corrugated interface between transversely isotropic and visco-elastic solid half-spaces.…”

Section: Introductionmentioning

confidence: 99%

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

Tomar

Kaur

2014

Earth Planet Sp

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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.

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“…Singh and Kumar [12,13] studied the reflection and refraction of waves in micropolar elastic solid. Tomar et al [14], studied the reflection and refraction of SH waves at corrugated interface between transversely isotropic and visco-elastic solid half space. Kumar and Sarthi [15] studied the reflection and refraction of thermo elastic plane waves at an interface between two thermo elastic media without energy dissipation.…”

Section: Introductionmentioning

confidence: 99%

Reflection and Transmission at the Boundary Surface of Thermoelastic Swelling Porous Media

Kumar¹

2012

J Appl Mech Eng

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The present investigation is concerned with the propagation of waves and their reflection and transmission from a plane interface between two different swelling porous thermo elastic half-spaces in welded contact. It is shown that there exist two dilatational waves, thermal wave and two transverse waves propagating with different velocities. The amplitude ratios of various reflected and transmitted waves are computed and presented graphically. It is found that amplitude ratios of reflected and transmitted waves are functions of angle of incidence, frequency and swelling porosity of the media. A particular case has also been deduced from the present investigation. The present investigation has immense application in geophysics and manufactured materials.

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Reflection and Refraction of SH-Waves at a Corrugated Interface between Two-Dimensional Transversely Isotropic Half-Spaces.

Cited by 30 publications

References 20 publications

Shear waves at a corrugated interface between two dissimilar fiber-reinforced elastic half-spaces

Shear waves at a corrugated interface between two dissimilar fiber-reinforced elastic half-spaces

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

Reflection and Transmission at the Boundary Surface of Thermoelastic Swelling Porous Media

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