M.L. Gogna

Reflection and refraction of a longitudinal microrotational wave at an interface between two micropolar elastic solids in welded contact

Abstract In this paper a longitudinal microrotational wave impinging at a plane discontinuity between two micropolar elastic solids in welded contact is discussed. The reflection and refraction coefficients of the longitudinal microrotational wave striking against the plane discontinuity have been calculated numerically and plotted as a function of angle of emergence for a specific model. The amplitude ratio have also been plotted as a function of frequency. The results of Parfitt and Eringen [ J. Acoust. Soc. Am . 45 (5), 1258–1272 (1969)] have been reduced as a special case.

Seismic wave propagation in a viscoelastic porous solid saturated by viscous liquid

A general solution is deduced of the differential equations describing the propagation of elastic waves in a dissipative liquid-filled viscoelastic porous solid. The velocities of three existing waves have been expressed in convenient form using the moduli of the solid phase and by introducing the frequency-dependent equivalent mass densities. The solution is then used to examine some of the phenomena which arise when each of the three-body waves, in turn, are incident on a traction-free plane boundary. Analytic expressions for the reflection coefficients are obtained. Numerical calculations have been made, for a particular model, in case of incidentPI wave. Effect of viscoelasticity and viscosity on the reflection coefficients has also been exhibited.

Reflection and refraction of coupled transverse and micro-rotational waves at an interface between two different micropolar elastic media in welded contact

Abstract The problem of reflection and refraction of coupled transverse shear and micro-rotation waves at an interface between two micropolar elastic solids with different elastic properties in welded contact, is discussed. Various reflection and refraction coefficients for incident coupled waves impinge obliquely at the plane interface have been calculated numerically and plotted against the angle of emergence for a specific model. The results of Parfitt and Eringen [1] have been obtained as a special case.

Surface wave propagation in a liquid-saturated porous layer overlying a homogeneous transversely isotropic half-space and lying under a uniform layer of liquid

Abstract Dispersion of Rayleigh-type surface waves is studied in a liquid-saturated porous solid layer under a uniform layer of homogeneous liquid, and lying over a transversely isotropic elastic half-space. Special cases have been deduced by reducing the depth of the layer to zero and by changing the transversely isotropic solid to an isotropic elastic solid. A frequency equation in the form of a tenth-order determinant is obtained. For numerical calculations, a particular model consisting of a water-saturated sandstone layer lying over a beryl solid and under a uniform layer of water is considered. To observe the effects of the depths of the layers on the phase velocity, dispersion curves for the phase velocity have been plotted for different values of the ratio of the depths of two layers.

Surface wave propagation in a transversely isotropic elastic layer overlying a liquid saturated porous solid half-space and lying under the uniform layer of liquid

Dispersion of Rayleigh-type surface wave is studied in a homogeneous transversely isotropic elastic layer overlying a nondissipative liquid-saturated porous solid half-space and lying under a uniform layer of homogeneous liquid. The frequency equation in the form of ninth-order determinant is obtained.Special cases have been deduced by reducing the depth of the layers to zero and by changing the transverse isotropic layer to an isotropic layer. Dispersion curves for the phase velocity have been plotted for a particular model.

Reflection and refraction of plane harmonic waves at an interface between elastic solid and porous solid saturated by viscous liquid

A general solution of Biots field equations governing small motions of a porous solid saturated by viscous liquid is employed to study the reflection and refraction at the interface between an elastic solid and a liquid-saturated porous solid. The incident wave is assumed to be plane and homogeneous, propagating through the isotropic elastic solid. The poroelastic solid is considered to be a dissipative one. Amplitude and energy ratios are computed numerically for a particular model. With first-order corrections for the porosity of solid and viscosity of liquid, the limiting cases of low and high frequencies are computed.

Steady-state response to moving loads in micropolar elastic medium with stretch

Abstract The present paper is concerned with the steady-state response to moving loads on the free plane boundary of a semi-infinite micropolar elastic medium with stretch. The displacement components, microrotation, force stress, couple stress and vector first moment are determined for the cases of supersonic, subsonic and transonic velocities. It is shown that the results of this analysis reduce to those without stretch.

Rayleigh wave dispersion equation for a layered spherical earth with exponential function solutions in each shell

We consider the second-order differential equations ofP-SV motion in an isotropic elastic medium with spherical coordinates. We assume that in the medium Lamés parameters λ, μ ∞rp and compressional and shear-wave velocities α, β ∞r, wherer is radial distance. With this regular heterogeneity both the radial functions appearing in displacement components satisfy a fourth-order differential equation which provides solutions in terms of exponential functions. We then consider a layered spherical earth in which each layer has heterogeneity as specified above. The dispersion equation of the Rayleigh wave is obtained using the Thomson-Haskel method. Due to exponential function solutions in each layer, the dispersion equation has similar simplicity, as in a flat-layered earth. The dispersion equation is further simplified, whenp=−2. We obtain numerical results which agree with results obtained by other methods.

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

Biots 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.

Propagation of waves in a micropolar elastic layer with stretch immersed in an infinite liquid

The effect of liquid on the propagation of waves in a micropolar elastic layer with stretch has been investigated. The frequency and wave velocity equations for symmetric and antisymmetric vibrations are derived. Propagation of monochromatic waves in a micropolar elastic layer with stretch is discussed. Results of this analysis reduce to those without stretch.