Propagation Of Torsional Surface Waves Research Articles

Effect of Non-Homogeneity and Initial Stress on Torsional Surface Wave Propagation in Initially Stressed Poroelastic Medium Bounded by a Heterogeneous Layer and Half-Space

Effect of Non-Homogeneity and Initial Stress on Torsional Surface Wave Propagation in Initially Stressed Poroelastic Medium Bounded by a Heterogeneous Layer and Half-Space

An investigation of torsional surface wave in a piezoelectric fiber-reinforced composite layer imperfectly bonded to a functionally graded half-space

This article presents a comprehensive study of torsional surface wave propagation in a piezoelectric fiber-reinforced composite (PFRC) layer bonded to functionally graded (FG) half-space considering electrically short and open boundary conditions. The Strength of Materials (SM) and Rule of Mixtures (ROM) approaches have been adopted to determine the effective properties of the PFRC. The non-ideal mechanical and electrical interfacial boundary has been considered for the problem which appears in various realistic scenarios. For the torsional surface wave propagation through PFRC bonded to FG half-space, the dispersion equation has been derived analytically using Whittaker function. The obtained results are validated and matched with existing results by considering special cases. The variation of phase velocity due to the influence of fiber volume fraction, interfacial imperfection parameters and functionally grading parameters have been analyzed and illustrated by means of graphs. Furthermore, the distribution of the field variables, stress and electric displacements across the composite are presented through surface plots. The model holds potential applications in designing and manufacturing transducers, actuators and sensors. The use of PFRC can be found in a wide range of cutting-edge technology, including vibration-canceling gadgets, energy harvesters, and pressure sensors.

Analysis of integrated effect of irregularity and corrugated interfaces of doubly layered half space on torsional surface wave propagation

Present geophysical model analyzes the propagation characteristics of torsional wave in an inhomogeneous viscoelastic fiber‐reinforced layer sandwiched between superior porous layer and transversely isotropic piezoelectric subspace with imperfect interfaces. Porous layer and intermediate reinforced layer are endowed with initial stress and corrugated interfaces, whereas the lower piezoelectric half space possesses rectangular cavity at the welded contact. Earth's adjacent layers near mountainous region often endowed with initial stresses resemble the present geological setup. The material properties of intermediate layer are considered to be varying exponentially. Particular cases have been deduced for electrically open and short condition for validation with the standard Love wave expressions. Effects of the relevant parameters on resultant torsional velocity have been explored through numerical simulation and depicted for electrically short and open conditions. Findings of present model may be utilized in the field of signal testing, sensors design, seismic acoustic wave (SAW) devices, and geophysical application concerned with torsional wave based on non‐destructive evaluation.

Influence of gravity on torsional surface waves in a dissipative medium

The present paper deals with the possibilities of propagation of torsional surface waves in a viscoelastic medium under gravity field. During the study it will observe that the increase in gravity parameter will increase the velocity of the wave, the increase in viscoelastic parameter, decrease the velocity of the wave until the product of angular frequency and viscoelastic parameter is less than unity. It also notes that as the velocity increases, the curve becomes asymptotic in nature when the period of oscillation increases. In fact the maximum damping in velocity has been identified at this cut off point which may be considered as the point where a viscoelastic material becomes a viscous medium.The absorption coefficients have also been calculated for different values of the viscoelastic parameter and gravity field.

Propagation of Torsional Surface Waves in Heterogeneous Half-Space with Irregular Free Surface

This study is an attempt to show the impacts of free surface irregularity on the torsional surface waves propagating in heterogeneous, elastic half-space. The surface irregularity is taken in the parabolic form at the surface of the half-space. The governing equation and corresponding closed form solutions are derived. Then, the phase velocity of torsional surface waves is obtained analytically and the influences of surface irregularity are studied in detail. Numerical results analyzing the torsional surface waves propagation are discussed and presented graphically. The analytical solutions and numerical results reveal that, the surface irregularity and heterogeneity have notable effects on the torsional surface waves propagation in the elastic half-space. Since the Earth crust is heterogeneous medium with irregular surface, thus it is important to consider the effects of heterogeneity and surface irregularity on velocity of torsional surface waves propagating in the Earth medium.

Torsional surface wave propagation in a transversely isotropic FG substrate with piezoelectric over-layer within surface/interface theory

Propagation of the torsional surface waves in a medium consisting of a functionally graded (FG) substrate bonded to a thin piezoelectric over-layer has been analytically formulated in the mathematical framework of surface/interface elasticity theory. In the cases where the wavelength and/or the thickness of the over-layer are comparable to the surface/interface characteristic length, then the surface/interface effects are not negligible. It is assumed that the over-layer is made of hexagonal 622 crystals with a single axis of rotational symmetry coinciding with the axis of polarization. The half-space is made of an FG transversely isotropic material in which the elasticity tensor and the mass density vary linearly with depth. Accounting for the surface/interface effects, the pertinent dispersion relation is derived analytically and verified for five different limiting cases of the proposed problem. The effect of the inhomogeneity parameters of the FG half-space and the surface/interface parameters on the dispersion relation is studied numerically, and the results are compared with those obtained from the classical theory.

Torsional Waves in a Fiber Composite Medium at a Loosely Bonded Interface Constrained Between Dry Sandy Layer and Gravitating Poroelastic Substrate

The objective of this paper is to study the effect of loosely bonded interface on torsional surface wave propagation in a fiber reinforced composite medium constrained between dry sandy layer and an anisotropic gravitating poroelastic substrate. All the media are assumed to be under initial stress. The dispersion relation on this proposed multilayer ground structure has been derived in closed form under certain boundary conditions, which contain Whittaker function and its derivative, which is further expanded asymptotically, retaining up to only the linear terms. The numerical solution for the limiting case of torsional surface waves is also discussed. As a special case of the problem, when the entire medium is isotropic and one of the upper layer vanishes and removing the initial stress and gravity, the dispersion relation obtained is in agreement with the classical Love type wave equation. The influence of various technical constants, such as sandy parameter, reinforcement parameter, porosity parameter, Biot’s gravity parameter, loosely bonded parameters, initial stress of both the layers and half spaces on the phase velocity of torsional surface wave has been pointed out by means of graphs.

Propagation of Torsional Surface Waves in a Nonhomogeneous Half-Space With Circular Irregularity in Free Surface

The present paper studies the effect of circular regularity on propagation of torsional surface waves in an elastic non-homogeneous half-space. Both rigidity and density of the half-space are assumed to vary inversely linearly with depth. Separation of variable method has been used to get the analytical solutions for the dispersion equation of the torsional surface waves. Also, the effects of non-homogeneity and irregularity on the phase velocity of torsional surface waves have shown graphically.

Analysis of Torsional Waves in a Prestressed Composite Structure with Loosely Bonded and Corrugated Boundaries

A mathematical model is presented to describe the propagation of torsional surface waves in a corrugated loosely bonded orthotropic layer sandwiched between two initially stressed viscoelastic half-spaces. The dispersion relation in a closed form is obtained for the analytical model. It is found that the initial stress, hydrostatic stress, viscoelasticity, and the bonding and flatness parameters have a great effect on the phase velocity of torsional surface waves. The method of separation of variables is employed to obtain an analytical solution in the present study. Some particular cases are discussed, and it is found that the results obtained well agree with the classical Love wave equation. Numerical simulations have also been performed to show results of the present analytical study graphically.

Effect of Irregularity on Torsional Surface Waves in an Initially Stressed Porous Layer Sandwiched Between Two Non-homogeneous Half-Spaces

The present work deals with the possibility of propagation of torsional surface waves in fluid saturated porous layer lying between two non-homogeneous half-spaces. It has been assumed directional rigidities and density vary hyperbolically in the upper half-space whereas rigidity and density are assumed to vary exponentially in the lower half-space. The irregularity is taken in the form of a triangle at the lower interface. The velocity equation has been derived and the results have been discussed. The study reveals that the torsional waves propagate in the assumed medium and the irregularity, initial stress, porosity, non-homogeneity parameter, anisotropy and ratio of directional rigidities have a pronounced influence on the propagation of torsional wave. Further it has been observed that neglecting the lower or upper half-space, the velocity equation of torsional surface waves for a homogeneous layer over or below a homogeneous half-space coincides with that of Love waves.

Torsional Wave Propagation in a Pre-Stressed Structure with Corrugated and Loosely Bonded Surfaces

AbstractAn analytical model is presented to study the behaviour of propagation of torsional surface waves in initially stressed porous layer, sandwiched between an orthotropic half-space with initial stress and pre-stressed inhomogeneous anisotropic half-space. The boundary surfaces of the layer and halfspaces are taken as corrugated, as well as loosely bonded. The heterogeneity of the lower half-space is due to trigonometric variation in elastic parameters of the pre-stressed inhomogeneous anisotropic medium. Expression for dispersion relation has been obtained in closed form for the present analytical model to observe the effect of undulation parameter, flatness parameter and porosity on the propagation of torsional surface waves. The obtained dispersion relation is found to be in well agreement with classical Love wave equation for a particular case. The cases of ideally smooth interface and welded interface have also been analysed. Numerical example and graphical illustrations are made to demonstrate notable effect of initial stress, wave number, heterogeneity parameter and initial stress on the phase velocity of torsional surface waves.

Study of torsional wave in a poroelastic medium sandwiched between a layer and a half-space of heterogeneous dry sandy media

In this article, the propagation of torsional surface wave in an anisotropic poroelastic layer of finite thickness sandwiched between two heterogeneous dry sandy media is investigated. The first uppermost dry sandy medium is considered as a layer of finite thickness and the second one is considered as a lower half-space. The heterogeneities in both dry sandy media are assumed to arise due to quadratic variations in elastic moduli and mass densities. Whittaker’s functions and variable separable techniques have been taken into the application to calculate the interior deformations inside the assumed model; consequently, we obtain a closed form dispersion relation for the torsional wave using effective boundary conditions. Moreover, casewise dispersion equations for some particular aspects of the problem have been studied, which serve as the focal theme of the study. Some significant observations have been made by detailed numerical calculations and graphical visuals related to the effects of tensile and compressive initial stresses, sandy parameters, heterogeneity parameters, porosity parameter, and thickness ratio parameter on the phase velocity of the torsional wave.

Mathematical Modeling of Torsional Surface Wave Propagation in a Non-Homogeneous Transverse Isotropic Elastic Solid Semi-Infinite Medium Under a Layer

The present paper deals with the mathematical modeling of the propagation of torsional surface waves in a non-homogeneous transverse isotropic elastic half-space under a rigid layer. Both rigidities and density of the half-space are assumed to vary inversely linearly with depth. Separation of variable method has been used to get the analytical solutions for the dispersion equation of the torsional surface waves. Also, the effects of nonhomogeneities on the phase velocity of torsional surface waves have been shown graphically. Also, dispersion equations have been derived for some particular cases, which are in complete agreement with some classical results.

Dispersion Study of Propagation of Torsional Surface Wave in a Layered Structure

AbstractThis paper presents the feasibility of torsional surface wave propagation in an anisotropic layer sandwiched between two anisotropic inhomogeneous media. The anisotropy considered in the upper layer and the lower half-space is of transversely isotropic kind while the sandwiched anisotropic layer is a porous layer. The directional rigidities and density have been considered linearly and exponentially varying in the half-space and in the upper layer respectively, while it is taken as a variable in the sandwiched layer. The compact form of dispersion equation governing the propagation of the torsional surface wave has been derived by using the Whittaker function under appropriate boundary conditions. The dispersion of the torsional wave and the effects of inhomogeneity parameters, initial stress and poroelastic constant have been calculated numerically and demonstrated through graphs.

Effect of Gravity and Initial Stresses on Torsional Surface Waves in Dry Sandy Medium Under Rigid Layer

The Present Paper devoted to investigate the effect of presence of rigid boundary on the propagation of torsional surface waves in a gravitating earth with a dry sandy medium under initial stress. The mathematical analysis of the problem has been dealt with the Whittaker function. Assuming the expansion of the Whittaker function up to linear term, it is concluded that the gravity field will always allow torsional waves to propagate in elastic and sandy medium under initial stress and rigid layer. Finally, it reveals that the sandy medium without support of a gravity field can not allow the propagation of torsional surface waves in presence of initial stress under rigid layer, where as the presence of a gravity field always supports the propagation of torsional surface waves regardless of whether the medium is elastic or dry sandy under rigid layer.

Effect of Rigid Boundary on the Propagation of Torsional Surface Waves in Heterogeneous Earth Media

The present paper has been framed to study the influence of rigid boundary on the propagation of torsional surface waves in an inhomogeneous crustal layer over an inhomogeneous half space. In the layer the rigidity and density vary linearly along the depth whereas the inhomogeneous half space exhibits inhomogeneity of exponential type. The dispersion equation is derived in a closed form. For a homogeneous layer over a homogeneous half space the dispersion equation turns into the dispersion equation of the propagation of Love type wave under rigid boundary. The effects of inhomogeneity factor on the phase velocity are depicted by means of graphs.

Torsional Wave Propagation in an Initially Stressed Anisotropic Heterogeneous Crustal Layer Lying Over a Viscoelastic Half-space

The present paper is concerned with the study of propagation of torsional surface waves in a non-homogeneous crustal layer under initial stress overlying a viscoelastic half-space. In the layer directional rigidities and density are considered to vary quadratically with depth. The dispersion equation is derived in closed form by means of separation of variables. As a special case when the layer is homogeneous, the dispersion relation coincides with the classical torsional wave equation. To show the nature of torsional waves, dispersion curves have been plotted by taking variation in initial stress, inhomogeneity and viscoelastic parameters. The substantial influence of initial stress, heterogeneity and viscoelastic parameter on the phase velocity are elucidated by means of graphs. This problem may find its applications in the field of earthquake engineering and geophysical prospects.

Influence of Loosely-Bonded Sandwiched Initially Stressed Visco-Elastic Layer on Torsional Wave Propagation

AbstractAssumption that the common interfaces of the media are perfectly bonded may not be always true. Situation may arise that composition of the two medium may be responsible for weakening the contact between them. So, it becomes obligatory to consider a loosely bonded interface in such cases which may affect the propagation of elastic waves through them. This paper thrashes out the propagation of torsional surface wave in an initially stressed visco-elastic layer sandwiched between upper and lower initially stressed dry-sandy Gibson half-spaces, theoretically. Both the upper and lower dry-sandy Gibson half-spaces are considered to be loosely-bonded with the sandwiched layer. Mathematical model is proposed and solution in terms of Whittaker's and Bessel's function is obtained. Velocity equation is obtained in closed form, its real part deals with the dispersion phenomenon whereas its imaginary part provides the damping characteristics. Influence of heterogeneities, sandiness, gravity parameters, initial-stresses, loose-bonding and internal-friction on the phase and damped velocities of torsional wave are computed numerically and depicted graphically. Deduced dispersion equation and damped velocity equation matches with classical Love-wave equation and vanishes identically for the isotropic case respectively.

Effects of Anisotropy, Initial Stress, Heterogeneity, and Gravity on Torsional Wave Propagation

AbstractThe present paper provides the results of a study of the propagation of torsional surface waves in an initially stressed self-reinforced layer lying over a dry sandy Gibson half-space in the presence of initial stress and gravity. The closed-form dispersion relation was obtained analytically. The influences of initial stress, reinforcement, inhomogeneity, gravity, and sandy parameter on the torsional wave were investigated by plotting the dispersion curves. It was observed that the rigidities, initial stress, and sandy parameter of the half-space have a favoring effect on the phase velocity, whereas gravity has the reverse effect on the velocity of the torsional surface wave. It also was noted that as reinforcement increased in the medium, the phase velocity also increased significantly.

Influence of corrugated boundary surface and reinforcement of fibre-reinforced layer on propagation of torsional surface wave

These days fibre-reinforced materials are frequently used in construction sector for example in dams, bridges etc. Also the earth structure and artificial structure made by human may contain irregularity or corrugation, therefore, propagation of waves and vibrations through these structures gets affected by them. Motivated by these facts the present problem aims to study the propagation of torsional surface wave in a fibre-reinforced layer with corrugated boundary surface overlying an initially stressed transversely isotropic half-space. The closed form of the dispersion equation has been deduced and the notable effect of reinforcement, undulatory parameter of corrugated boundary surfaces of the layer, corrugation parameter of upper and lower boundary surfaces of the layer, initial stress acting in half-space and wave number on the phase velocity of torsional surface wave has been exhibited. The numerical computation along with graphical illustration has been carried out for fibre-reinforced layer of carbon fibre-epoxy resin and T300/5208 graphite/epoxy material for the transversely isotropic half-space. As a special case of the problem, deduced dispersion equation is found in well-agreement with the classical Love wave equation. Comparative study for reinforced and reinforced free layer has been performed and also depicted graphically. Moreover some analysis is made to highlight the important peculiarities of the problem.