P. C. Pal

Reflection and Transmission of Plane SH-Waves Through an Anisotropic Magnetoelastic Layer Sandwiched Between Two Semi-Infinite Inhomogeneous Viscoelastic Half-Spaces

Reflection and transmission coefficients due to incident plane SH-waves at an anisotropic magnetoelastic layer sandwiched between two inhomogeneous viscoelastic half-spaces are obtained. The inhomogeneity in viscoelastic coefficients of the lower half-space is considered as quadratic, while that of the upper half-space is considered as exponential. The solutions for the layer and half-spaces are obtained analytically. The formulae for reflection and transmission coefficients are obtained for viscoelastic half-spaces subjected to continuity conditions of interfaces of an anisotropic magnetoelastic layer with viscoelastic half-spaces and Snell’s law. These coefficients are found to be the function of phase velocity, wave number, inhomogeneity, thickness of layer, and angle of incidence. Two special cases are considered. In case I, the problem is reduced to reflection and transmission in two viscoelastic half-spaces, whereas case II considers two isotropic half-spaces. Numerical computations are carried out for a specific model. The graphs are plotted for reflection and transmission coefficients against the angle of incidence and non-dimensional wave number for inhomogeneity parameters, the angle at which the wave crosses the magnetic field, the thickness of the layer, and frequency. In general, as the inhomogeneity parameter increases, the reflection and transmission coefficients decrease, while the angle at which the wave crosses the magnetic field, the thickness of the layer and frequency have systematic effects. The effect of angle of incidence on the reflection and transmission coefficients is not monotonic, but converges for an angle of incidence for all the parameters. Also, graphs are plotted for phase shift versus angle of incidence. The effects of inhomogeneity, the angle at which the wave crosses the magnetic field, thickness of the layer and frequency are considered. The phase shift exhibits a similar nature for these parameters.

Wave Propagation in an Inhomogeneous Anisotropic Generalized Thermoelastic Solid

The plane wave propagation in an inhomogeneous anisotropic thermally conducting elastic solid is studied with two thermal relaxation times. Three types of plane waves—quasi-P, quasi-S, and thermal waves—are shown to exist. The analytical expressions for their velocities of propagation are obtained. The inhomogeneity drastically affects the velocity of these waves and also depends on the angle of propagation and frequency. The effects of these parameters are shown graphically.

Generation of SH-type waves due to shearing stress discontinuity in a sandy layer overlying an isotropic and inhomogeneous elastic half-space

The generation of SH-type waves due to sudden application of a stress discontinuity which moves after creation at the sandy layer of finite thickness overlying an isotropic and inhomogeneous elastic half-space is considered. The displacements are obtained in exact form by the method due to Cagniard modified by De Hoop. The numerical calculations are obtained. Two cases of shearing stress discontinuities are considered for different sandiness parameters. The graphs are drawn to show the effect of sandiness in the displacement components.

Love waves in a layered functionally graded piezoelectric structure under initial stress

Abstract To study the effect of initial stress on the propagation behavior of Love waves in a layered functionally graded piezoelectric structure, a mathematical model is established. The piezoelectric layer is taken as exponentially graded material where as half-space is taken as simply elastic substratum. The coupled electromechanical field equations are solved analytically to obtain the mechanical displacements and electrical potential functions for the piezoelectric layer and elastic substrate. The dispersion relations are obtained for electrically open and short cases. The higher mode Love wave propagation has been considered. For numerical interpretation of the results, four sets of piezoelectric layer and elastic substrate have been taken into consideration. Graphical representation reveals about the effect of initial stress and the effect of inhomogeneity parameter on the phase velocity against wave number for electrically open and electrically short cases, respectively.

Surface wave propagation in sandy layer overlying a liquid saturated porous half-space and lying under a uniform liquid layer

ABSTRACT Dispersion of Rayleigh-type surface waves is studied in a sandy layer under a uniform layer of homogeneous liquid lying over liquid-saturated porous solid half-space. The frequency equation in the form of a ninth-order determinant is obtained and evaluated. Special cases have been deduced and dispersion curves for the phase velocity and wave number have been plotted for a particular model.

Effect of dynamic visco-elasticity on vertical and torsional vibrations of a half-space

By expressing the dynamic visco-elastic characteristic of a material in terms of the complex shear modulus, the vertical vibrations of a visco-elastic half-space as well as that of a mass in visco-elastic half-space are considered here. Torsional vibrations of a visco-elastic half-space is also considered. Numerical results are derived for two cases and shown graphically.

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

Abstract 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.

Torsional Body Forces in a Kelvin-Voigt-Type Visco-Elastic Half Space

An analysis is presented to consider the problem of torsional body forces within a Kelvin-Voigt type visco- elastic material half space. Hankel & Fourier transform are used to calculate the disturbance for a body force located at a constant depth from the free surface. Numerical results are obtained and the natures are shown graphically.