SH-type Waves Research Articles

Defects and waves in anisotropic and layered media: Stroh formalism in terms of the Cartesian system of vector functions

ABSTRACT When waves propagate through anisotropic elastic media, P- and SV-type waves (Rayleigh waves) are generally coupled with SH-type waves (Love waves). In contrast, in isotropic elastic media, SH/Love waves are decoupled and separate from other body/surface waves. However, the conditions under which these waves in anisotropic media may be decoupled remain unclear. In this paper, we introduce a Cartesian vector function system, named as the Cartesian LMN vector system, and derive solutions using this system within the Stroh formalism. This approach inherently accounts for both coupling and decoupling cases. Various source functions based on the Cartesian LMN vector system are derived. The Cartesian LMN system further enables a straightforward reduction to two-dimensional wave problems, including simplified source functions for line forces and lattice dislocations.

Vibrations analysis of propagation of SH-type wave influenced by a point source in a porous piezoelectric layered structure by Green’s function approach

Vibrations analysis of propagation of SH-type wave influenced by a point source in a porous piezoelectric layered structure by Green’s function approach

Effect of SH-type waves and shear stress discontinuity on a moving loaded composite structure

Effect of SH-type waves and shear stress discontinuity on a moving loaded composite structure

SH-type wave motion in a geophysical model with monoclinic and heterogeneous media due to a point source at the interface

SH-type wave motion in a geophysical model with monoclinic and heterogeneous media due to a point source at the interface

Site dependent and spatially varying response spectra

The goal of this study is to provide a stochastic method to investigate the effects of the randomness of soil properties due to their natural spatial variability on the response spectra spatial variation at sites with varying conditions. For this purpose, Monte Carlo Simulations are used to include the variability of both incident ground motion and soil parameters in the response spectra by mean of an appropriate coherency loss function and a site-dependent transfer function, respectively. The approach is built on the assumption of vertical propagation of SH type waves in soil strata with uncertain parameters. The response spectra are obtained by numerical integration of the governing equation of a single-degree-of-freedom (SDOF) system under non-stationary site-dependent and spatially varying ground motion accelerations simulated with non-uniform spectral densities and coherency loss functions. Numerical examples showed that randomness of soil properties significantly affects the amplitudes of the response spectra, indicating that as the heterogeneity induced by the randomness of the parameters of the medium increases, the spectral ordinates attenuate.

The study of reflection/transmission phenomena in a corrugated interface between two magnetoelastic transversely isotropic media

In this paper, an integrated approach has been carried out with an intent to study the reflection and transmission phenomena of plane SH-type wave on a corrugated interface separating two magnetoelastic transversely isotropic half-space. Closed form expressions for reflection and transmission coefficients have been derived for both plane and corrugated surface. Rayleigh’s method of approximation have been incorporated to deduce equations for the first- and second-order approximation of corrugation. Analytical solutions for both the half-spaces have been worked out. All possible cases have been apprehended specially for anisotropic and an isotropic medium. The effects of magnetoelastic coupling parameter, angle at which the wave crosses the magnetic field, corrugation amplitude, frequency factor and wave number have been explained by collaborating with graphical analysis.

Generation of SH-type waves due to shearing stress discontinuity in an anisotropic layer overlying an initially stressed elastic half-space

Generation of SH-type waves due to shearing stress discontinuity in an anisotropic layer overlying an initially stressed elastic half-space

Detection of Fundamental Shear Horizontal Guided Waves Using a Surface-Bonded Chirped Fiber-Bragg-Grating Fabry–Perot Interferometer

In this paper, detection of the fundamental shear horizontal (SH0) guided wave mode in a plate using a surface-bonded Fabry–Perot interferometer formed by a pair of tandem chirped fiber-Bragg-gratings (CFBG-FPI) has been investigated both theoretically and experimentally. Using the developed theory, the underlying mechanism that governs the sensor's response to SH0 mode is explored in detail. Then, the dependence on both the incident angle and frequency (or wavelength) of the SH0 wave is investigated. Owing to the pure shear strain induced by the SH0 mode, the fiber sensor shows a significantly different response in comparison to other ultrasonic waves, such as Lamb-type guided waves. Our results show that 1) the sensor is most sensitive to SH-type waves at an incident angle of around 45° and nonsensitive at the incident angles of 0° and 90° and 2) a minimum sensitivity is reached when the equivalent ultrasonic wavelength impinged on the fiber axis is equal to the effective length of the CFBG-FPI sensor; this effective length is close to the length of each CFBG.

Effect of Body Forces on the Propagation of SH-Type Waves in a Semi-infinite Anisotropic Elastic Medium

Effect of Body Forces on the Propagation of SH-Type Waves in a Semi-infinite Anisotropic Elastic Medium

Effect of Body Forces on the Propagation of SH-Type Waves in a Semi-infinite Visco-elastic Medium

The effect of time dependent body forces on the propagation of SH-type wave motion in visco-elastic half space is considered in this paper. The surface displacement component is obtained in a closed form. Numerical results are obtained for a particular case of time dependent body force at different distances from the source for the different values of the non-dimensional time. The results are shown graphically.

Impact of inhomogeneity on SH-type wave propagation in an initially stressed composite structure

The present analysis has been made on the influence of distinct form of inhomogeneity in a composite structure comprised of double superficial layers lying over a half-space, on the phase velocity of SH-type wave propagating through it. Propagation of SH-type wave in the said structure has been examined in four distinct cases of inhomogeneity viz. when inhomogeneity in double superficial layer is due to exponential variation in density only (Case I); when inhomogeneity in double superficial layers is due to exponential variation in rigidity only (Case II); when inhomogeneity in double superficial layer is due to exponential variation in rigidity, density and initial stress (Case III) and when inhomogeneity in double superficial layer is due to linear variation in rigidity, density and initial stress (Case IV). Closed-form expression of dispersion relation has been accomplished for all four aforementioned cases through extensive application of Debye asymptotic analysis. Deduced dispersion relations for all the cases are found in well-agreement to the classical Love-wave equation. Numerical computation has been carried out to graphically demonstrate the effect of inhomogeneity parameters, initial stress parameters as well as width ratio associated with double superficial layers in the composite structure for each of the four aforesaid cases on dispersion curve. Meticulous examination of distinct cases of inhomogeneity and initial stress in context of considered problem has been carried out with detailed analysis in a comparative approach.

Remarks on impact of irregularity on SH-type wave propagation in micropolar elastic composite structure

The present study investigates the propagation characteristics of SH-type wave and a new type of dispersive surface wave in an irregular composite structure comprised of a layer overlying a half-space, both constituted by distinct homogeneous micropolar isotropic elastic materials. At the common interface of the composite structure, two types of irregularities viz. rectangular and parabolic shaped, are studied in two distinct cases. Closed-form of frequency equations of SH-type wave associated with these cases have been obtained and matched with the classical Love wave equation in the isotropic case of the composite structure without irregularity at the common interface. Existence of new type of dispersive surface wave along with its dispersion relation has been deduced in the closed-form by adopting a distinct mathematical treatment for various cases concerned with the presence and absence of microrotational components in the composite structure. It is also examined that the dispersion equation of new type of dispersive surface wave vanishes identically in isotropic case of the composite structure. To unravel the effect of irregularity at the common interface and micropolarity associated with micropolar composite structure on SH-type and new type of dispersive surface wave, numerical computation and graphical demonstrations have been carried out in a comparative manner which serves as a salient feature of the study.

Generation of SH-type waves in a poroelastic layer sandwiched between prestressed orthotropic and nonhomogeneous mantles

ABSTRACTThe present work is concerned with a detailed illustration on the study of horizontally polarized shear waves (SH-type) propagation in a prestressed fluid saturated anisotropic porous layer sandwiched by prestressed orthotropic medium and nonhomogeneous mantles. The frequency equation for the assumed model is derived and their medium characteristics, such as porosity, prestress, anisotropy, and nonhomogeneity, are discussed. Numerical treatment is given to analyze these effects on phase velocities of SH-type waves and is plotted in various graphs. The parametric study divulges that the magnitude of wave velocities increases with the increase of nonhomogeneity parameter and prestress parameter.

Study of SH-type wave propagating in an anisotropic layer sandwiched between an orthotropic medium and an in-homogeneous half-space

The present paper investigates the effect of initial stress and the existence of SH- type wave in an initially stressed porous stratum sandwiched between an initially stressed orthotropic medium and an in-homogeneous half-space. Exponential variations of rigidity and density have been taken in the lower half-space. The dispersion equation has been derived in closed form. It is observed that the propagation of SH type wave is influenced by the medium characteristics such as porosity, initial stress, anisotropy and in-homogeneity parameter.

Reflection and transmission of plane SH-waves in two semi-infinite anisotropic magnetoelastic media

The reflection and transmission of SH-type waves have been considered. The closed form expressions are obtained for the reflection and transmission coefficients when plane SH-waves are incident at anisotropic magnetoelastic half-space. It is found that the reflection and transmission coefficients are strongly influenced by anisotropic magnetoelastic coupling parameter and the angle at which wave crosses the magnetic field. Special cases are considered. Numerical computations are performed for the different set of data for anisotropic magnetoelastic media. The effects of anisotropic magnetoelastic coupling parameter and the angle at which wave crosses the magnetic field are shown in figures by plotting graph between the reflection and transmission coefficients versus angle of incidence.

Propagation of SH-type waves in inhomogeneous anisotropic layer overlying an anisotropic viscoelastic half-space

An analysis has been carried out for the propagation of SH-type waves in inhomogeneous anisotropic layer overlying anisotropic viscoelastic half-space of higher order. The dispersion relation is obtained under certain boundary conditions. The effects of inhomogeneity in elastic coefficients and density for the layer are studied. The numerical results are discussed through figures for a particular model by plotting the graph between phase velocity and wave number for different values of inhomogeneity parameters and thickness of layer. Keywords : SH-type waves, Anisotropic layer, Inhomogeneity, Viscoelastic coefficient, Phase velocity.

Disturbance of SH-type waves due to moving stress discontinuity in an anisotropic soil layer overlying an inhomogeneous elastic half-space

The disturbance and propagation of SH-type waves in an anisotropic soil layer overlying an inhomogeneous elastic half-space by a moving stress discontinuity is considered. Stress discontinuity moves with non-uniform velocity and is impulsive in nature. The displacements are obtained in exact form by the method due to Cagniard modified by de Hoop. The numerical result is calculated for special cases and the natures are depicted graphically.

SH-type waves dispersion in an isotropic medium sandwiched between an initially stressed orthotropic and heterogeneous semi-infinite media

The present paper studies the propagation of shear waves (SH-type waves) in an homogeneous isotropic medium sandwiched between two semi infinite media. The upper half-space is considered as orthotropic medium under initial stress and lower half-space considered as heterogeneous medium. We have obtained the dispersion equation of phase velocity for SH-type waves. The propagation of SH-type waves are influenced by inhomogeneity parameters and initial stress parameter. The velocity of SH-type wave has been computed for different cases. We have also obtained the dispersion equation of phase velocity in homogeneous media in the absence of initial stress. The velocities of SH-type waves are calculated numerically as a function of kH (non-dimensional wave number) and presented in a number of graphs. To study the effect of inhomogeneity parameters and initial stress parameter we have plotted the velocity of SH-type wave in several figure. We have observed that the velocity of wave increases with the increase inhomogeneity parameters. We found that in both homogeneous and inhomogeneous media the velocity of SH-type wave increases with the increase of initial stress parameter. The results may be useful for the study of seismic waves propagation during any earthquake and artificial explosions.

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.

Shear waves in a piezoceramic layered structure

The propagation of SH-type wave is studied in a composite structure consisting of alternating polymeric layers and porous piezoelectric layers. The porous piezoelectric materials of the composite structure are assumed to have 6mm symmetry and their poling direction is along z-axis. Layers of the polymer are considered as isotropic dielectric elastic material. Solutions of the field equations for the porous piezoelectric material and for the polymeric material are obtained. Two cases, first when the direction of propagation of the SH-type wave is taken along the direction normal to the layering of the composite structure, and second when the propagation direction is taken along the layering, are considered for the derivation of the phase velocity. The dispersion and the stop-pass band behavior of the Floquet wave is also discussed. Numerical results for phase velocity and stop band effect are presented for a periodic system of alternating PZT-5H and polythene layers. The influence of volume fraction on phase velocity and stop band effect is discussed.