Initial stress and heterogeneity effects on torsional waves in dry sand half-space between reinforced half-space and poroelastic medium

PurposeThe purpose of this paper is to investigate the effect of initial stress and heterogeneity on the propagation of torsional waves in dissipative medium. The problem consists of dry sand poroelastic half-space embedded between heterogeneous self-reinforced half-space and poroelastic medium. The frequency equation is derived in the framework of Biot's theory with some variants.Design/methodology/approachTorsional wave propagation in dry sand poroelastic half-space embedded between self-reinforced half-space and poroelastic medium. All the constituents here are assumed to be dissipative, heterogeneous and initial stressed.FindingsPhase velocity and attenuation are computed against wavenumber for various values of self-reinforcement parameter, inhomogeneity parameter and initial stress. Particular cases are discussed in absence of dissipation. The numerical results are presented graphically.Originality/valueInitial stress and heterogeneity effects on torsional waves in dry sand half-space between reinforced half-space and poroelastic medium are investigated. The frequency equation is derived, and which intern gives the phase velocity and attenuation coefficient for various values of initial stress, self-reinforcement parameter and heterogeneity parameter. From the numerical results, it is clear that as wavenumber varies phase velocity and attenuation are periodic in nature for all the cases. Particular cases are discussed in absence of dissipation. This kind of analysis can be extended to any elastic solid by taking magnetic, thermo and piezoelectric effects into account.

FDTD analysis of ELF radio wave propagation in the spherical Earth-ionosphere waveguide and its validation based on analytical solutions

The FDTD model of electromagnetic wave propagation in the Earth-ionosphere cavity was developed under assumption of axisymmetric system, solving the reduced Maxwell’s equations in a 2D spherical coordinate system. The model was validated on different conductivity profiles for the electric and magnetic field components for various locations on Earth along the meridian. The characteristic electric and magnetic altitudes, the phase velocity and attenuation rate were calculated. We compared the results of numerical and analytical calculations and found good agreement between them. The undertaken FDTD modeling enables us to analyze the Schumann resonances and the propagation of individual lightning discharges occurring at various distances from the receiver. The developed model is particularly useful when analyzing ELF measurements.

Method for determining the intrinsic parameters of strip transmission lines

The features of the propagation of electromagnetic waves in strip transmission lines have been studied. Methods for measuring the phase velocity and attenuation coefficient of an electromagnetic wave in strip transmission lines are considered. The problem of the lack of methods for measuring their wave impedance is analyzed. A method is proposed for determining the intrinsic parameters of strip lines from the results of measurements by a vector analyzer of S-parameter circuits of electrically long and short lines in a coaxial channel. The intrinsic parameters of the strip lines are determined by the proposed method in the frequency range 0.01–26.50 GHz.

Influence of mechanical imperfection on the transference of Love-type waves in viscoelastic substrate overloaded by visco-micropolar composite structure

Purpose This mathematical analysis has been accomplished for the purpose of understanding the propagation behaviour like phase velocity and attenuation of Love-type waves through visco-micropolar composite Earth’s structure. Design/methodology/approach The considered geometry of this problem involves a micropolar Voigt-type viscoelastic stratum imperfectly bonded to a heterogeneous Voigt-type viscoelastic substratum. With the aid of governing equations of motion of each individual medium and method of separation of variable, the components of micro-rotation and displacement have been obtained. Findings The boundary conditions of the presumed geometry at the free surface and at the interface, together with the obtained components of micro-rotation, displacement and mechanical stresses give rise to the determinant form of the dispersion relation. Moreover, some noteworthy cases have also been extrapolated in detail. Graphical interpretation irradiating the impact of viscoelasticity, micropolarity, heterogeneity and imperfectness on the phase velocity and attenuation of Love-type waves is the principal highlight of the present study. Practical implications In this study, the influence of the considered parameters such as micropolarity, viscoelasticity, heterogeneity, and imperfectness has been elucidated graphically on the phase velocity and attenuation of Love-type waves. It has been noticed from the graphs that with the rising magnitude of micropolarity and heterogeneity, the attenuation curves shift upwards, that is the loss of energy of these waves takes place in a rapid way. Hence, from the outcomes of the present analysis, it can be concluded that heterogeneous micropolar stratified media can serve as a helpful tool in increasing the attenuation or in other words, loss of energy of Love-type waves, thus reducing the devastating behaviour of these waves. Originality/value Till date, the mathematical modelling as well as vibrational analysis of Love-type waves in a viscoelastic substrate overloaded by visco-micropolar composite Earth’s structure with mechanical interfacial imperfection remain unattempted by researchers round the globe. The current analysis is an approach for studying the traversal traits of surface waves (here, Love-type waves) in a realistic stratified model of the Earth’s crust and may thus, serves as a dynamic paraphernalia in various domains like earthquake and geotechnical engineering; exploration geology and soil mechanics and many more, both in a conceptual as well as pragmatic manner.

Mathematical study of Rayleigh waves in piezoelectric microstretch thermoelastic medium

This paper is concerned with the study of propagation of Rayleigh waves in a homogeneous isotropic piezo-electric microstretch-thermoelastic solid half-space. The medium is subjected to stress-free, isothermal boundary. After developing a mathematical model, the dispersion curve in the form of polynomial equation is obtained. Phase velocity and attenuation coefficient of the Rayleigh wave are computed numerically. The numerically simulated results are depicted graphically. Some special cases have also been derived from the present investigation.

Effects of Soil Parameters Uncertainties on the Behaviour of Anisotropic Porous Media to Shear Waves

In the present study, the wave equations for shear waves propagating in anisotropic fluid-saturated porous media are established in order to obtain the solutions in terms of displacements and dispersion equation. The wave velocities in the vertical and horizontal directions are derived. The uncertainties of the soil parameters due to their spatial variability are taken into account via Monte Carlo Simulations. The results are restricted to the effects of the porosity and permeability uncertainties on the phase velocity and attenuation for SH wave in addition to the anisotropy for Love wave. Results show that the mean velocities are more sensitive to the random variations of the permeability than to that of the porosity, but both phase velocity and attenuation decrease as the uncertainties increase. On the other hand, the anisotropy level and the randomness significantly affect the dispersion of Love waves. The present approach which converts a deterministic solution in a probabilistic one may be used as an everyday tool for practical applications of shear wave propagation in random media.

Stoneley and Rayleigh waves in thermoelastic materials with voids

The present paper deals with the propagation of surface waves (Stoneley and Rayleigh waves) in thermoelastic materials with voids. The frequency equations of the Stoneley waves at the bonded and unbonded interfaces between two dissimilar half-spaces of thermoelastic materials with voids are obtained. The numerical values of the determinant for bonded and unbonded interface are calculated for a particular model. We also derived the frequency equation of the Rayleigh wave in thermoelastic materials with voids. The phase velocity and attenuation coefficients have shown that there are two modes of vibration. These two modes are computed and they are depicted graphically. The effect of thermal parameters in these surface waves is discussed.

Analytical solutions of thermo-piezoelectric interactions in a solid fiber of polygonal cross-sections immersed in fluid

Purpose The purpose of this paper is to study the analytical solutions of transversely isotropic thermo-piezoelectric interactions in a polygonal cross-sectional fiber immersed in fluid using the Fourier expansion collocation method. Design/methodology/approach A mathematical model is developed for the analytical study on a transversely isotropic thermo-piezoelectric polygonal cross-sectional fiber immersed in fluid using a linear form of three-dimensional piezothermoelasticity theories. After developing the formal solution of the mathematical model consisting of partial differential equations, the frequency equations have been analyzed numerically by using the Fourier expansion collocation method (FECM) at the irregular boundary surfaces of the polygonal cross-sectional fiber. The roots of the frequency equation are obtained by using the secant method, applicable for complex roots. Findings From the literature survey, it is evident that the analytical formulation of thermo-piezoelectric interactions in a polygonal cross-sectional fiber contact with fluid is not discussed by any researchers. Also, in this study, a polygonal cross-section is used instead of the traditional circular cross-sections. So, the analytical solutions of transversely isotropic thermo-piezoelectric interactions in a polygonal cross-sectional fiber immersed in fluid are studied using the FECM. The dispersion curves for non-dimensional frequency, phase velocity and attenuation coefficient are presented graphically for lead zirconate titanate (PZT-5A) material. The present analytical method obtained by the FECM is compared with the finite element method which shows a good agreement with present study. Originality/value This paper contributes the analytical model to find the solution of transversely isotropic thermo-piezoelectric interactions in a polygonal cross-sectional fiber immersed in fluid. The dispersion curves of the non-dimensional frequency, phase velocity and attenuation coefficient are more prominent in flexural modes. Also, the surrounding fluid on the various considered wave characteristics is more significant and dispersive in the hexagonal cross-sections. The aspect ratio (a/b) of polygonal cross-sections is critical to industry or other fields which require more flexibility in design of materials with arbitrary cross-sections.