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In the context of the triple-phase lag model, comparison studies are conducted between the memory-dependent derivative and fractional order derivative on the propagation of plane waves in a half-space of initially stressed transversely isotropic piezothermoelastic material. The coupled governing equations of the considered model involving relaxation time, time delay, fractional order parameter, and kernel function are selected according to specific problems and solved using the normal mode analysis technique and obtaining the analytical expression. The non-dimensional temperature, displacement, electrical displacements, and stresses at different values of the fractional order parameter and time delay factor are obtained graphically. [ABSTRACT FROM AUTHOR]

AbstractThis paper investigates Love-type wave propagation in a multilayered, elastic, prestressed solid half-space with voids. Using the Haskell matrix method, the dispersion relation is derived for a stress-free boundary surface. Two distinct dispersive fronts of Love-type waves, propagating at different speeds, are identified. One behaves like waves in a prestressed elastic half-space, while the other is novel due to voids. Analytical expressions for three-layered and two-layered models are provided. Graphical representations compare the dispersion curves, highlighting differences and dependencies. The study explores how void parameters, initial stress, and layer thickness influence phase velocity, with applications in various engineering fields. [ABSTRACT FROM AUTHOR]

This manuscript addresses a significant research gap in the study by employing a mathematical model of photo thermoelastic wave propagation in a rotator semiconductor medium under the effect of a magnetic field and initial stress, as well as ramp-type heating. The considered model is formulated during the photothermal theory and in two-dimensional (2D) electronic-elastic deformation. The governing equations represent the interaction between the primary physical parameters throughout the process of photothermal transfer. Computational simulations are performed to determine the temperature, carrier density, displacement components, normal stress, and shear stress using the application of Lame's potential and normal mode analysis. Numerical calculations are carried out and graphically displayed for an isotropic semiconductor like silicon (Si) material. Furthermore, comparisons are made with the previous results obtained by the others, as well as in the presence and absence of magnetic field, rotation, and initial stress. The obtained results illustrate that the rotation, initial stress, magnetic field, and ramp-type heating parameter all have significant effects. This investigation provides valuable insights into the synergistic dynamics among a magnetization constituent, semiconducture structures, and wave propagation, enabling advancements in nuclear reactors' construction, operation, electrical circuits, and solar cells. [ABSTRACT FROM AUTHOR]

The purpose of this study is to analyze the features of a moving Griffith crack in an initially stressed infinitely long and finitely thick isotropic strip with moving parallel punches of constant load acting on its boundaries owing to plane wave propagation under point loading. Coupled singular integral equations and singularities of the Cauchy-type are used to formulate the present model, Dirac delta function is employed to analyze point load located at the moving crack edge, and Hilbert transformation properties are used for obtaining stress intensity factor (SIF) with constant point loading. Numerical simulations and graphical illustrations are performed to analyze the influences of the prevalent parameters, viz. initial stresses, punch pressure, distinct positions of point load, length and speed of the crack on the SIF for the considered isotropic material strip. [ABSTRACT FROM AUTHOR]

Purpose: The aim of this work is to study the wave propagation in a rotating fiber-reinforced thermo-viscoelastic solid. Methods: The analytical technique used to obtain the ordinary differential equations was normal mode analysis. In this article using the modified Green-Lindsay (MGL) theory and the Green-Lindsay (G-L) theory. Results: The numerical calculations have been completed, and the physical fields have been determined using the proper boundary conditions. The effects of rotation, viscosity, and magnetic field are discussed. Conclusion: Overall, the research on the rotation and magnetic field effect on fiber-reinforced thermo-viscoelastic have a significant influence on all the physical variables and several potential practical implications and engineering applications in various fields such as environmental, chemical, and energy engineering. [ABSTRACT FROM AUTHOR]

Purpose: This study analyzed the impact of initial stresses on the propagation of Love-type waves in a fiber-reinforced viscoelastic layer situated between an isotropic inhomogeneous half-space and an orthotropic viscoelastic layer. The aim of the purposed work is to investigate how various factors such as initial stresses, viscoelastic properties, thickness ratio, inhomogeneity, and reinforcement affect wave propagation in the layered structure. Methods: The separable variable method is used to obtain the displacement components for the considered layers and half-space. By applying suitable boundary conditions, the dispersion relation for Love-type wave propagation derived. The dispersion relation was then examined for different cases, considering factors such as initial stresses, viscoelastic properties, thickness ratio, inhomogeneity, and reinforcement equal to zero. Numerical computations were performed using the MATHEMATICA software, and the results were graphically depicted. Results: The study successfully obtained the dispersion curves, which illustrated the influence of various parameters on Love-type wave propagation. The results showed how initial stresses, viscoelastic properties, thickness ratio, inhomogeneity, and reinforcement affected the wave propagation behavior. Conclusion: The findings of the study confirmed the validity of the mathematical model developed in this study, as the derived dispersion relation simplified the pre-existing velocity wave equation for Love waves. The analysis of dispersion curves demonstrated the significant effects of initial stresses and other parameters on the phase and damping velocity of the Love-type wave in the fiber-reinforced viscoelastic layer. The study enhances our understanding of Love wave propagation and its practical applications in structural engineering, earthquake engineering, non-destructive testing, material science, and geophysics. [ABSTRACT FROM AUTHOR]

In this work, an analysis of the propagation of horizontally polarized magnetoelastic shear waves at a loosely bonded interface between two fiber-reinforced (FRC) media is performed. The assumption is that the upper layer is a heterogeneous FRC medium with initial stress, while the lower layer is an FRC half-space subject to gravity. A closed-form expression of the dispersion equation has been derived using Whittaker's function and its asymptotic expansion for both exponential and linear types of heterogeneous cases. The obtained dispersion equation matches well with previously existing results and the classical Love wave equation. In both cases, it was found that the magnetoelastic coupling parameters, horizontal compressive initial stresses, loosely bound, and Biot's gravity parameter of the layered structure all have a favoring effect on the phase velocity. It was also observed that in the linear heterogeneous case, the magnetoelastic coupling parameter has a detrimental influence on the speed of shear wave propagation, while in the exponential heterogeneous situation, it has a beneficial impact. The findings of this study can be used to improve analysis in the fields of geotechnical engineering and civil engineering. This study examines the characteristic behavior of horizontally polarized magnetoelastic shear wave propagation in an inhomogeneous fiber reinforced layer overlaying a fiber-reinforced half-space in the presence of initial stress and gravity. Reinforced materials are now one of the fundamental necessities of building projects of any significant magnitude. In addition, it is crucial to consider the impact of loose bonding at the common interface between the layer and the half-space while building the sensors to improve their efficacy and ultimately achieve high performance. This work is relevant to geotechnical and civil engineering applications and is innovative. Examining the effect of various nondimensional parameters' responses to wave motion is of great interest to researchers due to the immense practical and economic potential of composite structures made from such materials. The present article may have numerous applications in the disciplines of space exploration, aviation, construction, geophysics, geomechanics, and so on. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The purpose of this study is to investigate SH wave in the periodic cement-based piezoelectric layered barrier to meet the needs of vibration control in complex engineering environments and improve the application of periodic vibration isolation barrier in civil engineering. The governing equation of SH wave in periodic barrier is established based on the periodic theory of phononic crystals. The band structures are calculated by plane wave expansion method, the transmission characteristics are computed by transfer matrix method, and the attenuation effect of the periodic barrier is verified by finite element method. The effects of geometric parameters, material parameters and initial stress on band structures are analyzed in details. The numerical results show that the number of unit cells, initial stress and material parameters of the periodic barrier have significant effects on the band gap. As the lattice constant of the structure increases and the equivalent elastic modulus decreases, the lower boundary and the width of the band gap decrease. With the increase of tensile stresses, whether the lower and upper boundary or the width of the band gap will all increase, while they are decrease with the increase of compressive stresses. This work provides an alternative avenue for the design of periodic layers as wave barriers. [ABSTRACT FROM AUTHOR]

This paper studies torsional wave propagation in a poro-viscoelastic medium of finite thickness. The considered medium is clamped between an inhomogeneous poro-elastic medium of finite thickness and a poro-elastic half-space. Both finite layers are initially stressed and the half-space is self-weighted. Classical dynamical coupled theories have been used to explore the problem. Interior deformations are calculated analytically. A complex frequency equation has been obtained with the aid of suitable boundary conditions. The decomposition of the complex frequency equation into real and imaginary parts provides dispersion and damping equations. These frequency equations exhibited their reliance on the variation of attenuation coefficient, dissipation factor, inhomogeneity, initial stresses, Biot's gravity, porosity and thickness ratio parameters. The impacts of the aforesaid parameters have been extensively studied and demonstrated graphically. [ABSTRACT FROM AUTHOR]

The effects of small length scale on the torsional surface waves propagating in a pre-stressed dissipative nanoplate were examined in this paper. Biot's incremental deformation principle as well as nonlocal elasticity theory were implemented to form the governing and frequency equations of torsional surface waves in nanoplate under considered conditions. In this work, we proposed a new approach to determine the phase velocity of torsional disturbances. Different categories are used to investigate the dispersion relations such as: wave number, scale coefficient, initial stress parameter, and dissipation coefficient. The results show that small length scale influences causes torsional dispersion of the wave propagation, which disappear in local elasticity theory. In addition, it is recognized that the torsional surface waves propagating in the pre-stressed dissipative nanoplates can be differentiated in a clear manner from those propagated in the absence of small length scale effects. The initial stress parameter can also be utilized to change the characteristics of the torsional surface wave's phase velocity in nanoplates. It is also observed that, the dissipation has a great effect on the phase velocity of torsional surface waves in propagating in the nanoplate. Therefore, this research is theoretically useful to convey information on nonlocal and dissipation properties of the nanomaterials: for example, through a precise measurement of the phase velocity of torsional surface wave propagates in a nanocomposite material by presence of the medium's dissipation. This work could be useful in understanding the way of designing the Nano devices and Nano resonators. [ABSTRACT FROM AUTHOR]

The objective of this study is to investigate the reflection phenomena of plane waves from the free surface of an initially stressed rotating nonlocal micropolar transversely isotropic generalized thermoelastic half-space considering Lord–Shulman (LS) and Green–Lindsay (GL) theory. Closed-form expressions for the phase velocities of reflected quasi-longitudinal displacement (qLD), quasi-transverse displacement (qTD), quasi-transverse microrotation (qTM) and quasi-thermal (qT) waves are derived, and boundary conditions yield a system of algebraic equations to determine reflection coefficients. Energy ratios of the reflected waves are also calculated, and it is observed that the law of conservation of energy holds good in the entire reflection phenomena. Numerical results for phase velocity and reflection coefficients are computed using MATLAB examining the effects of initial stress, rotation and nonlocal parameters. Comparisons between micropolar transversely isotropic thermoelastic (MTIT) and nonlocal micropolar transversely isotropic thermoelastic (NMTIT) media highlight the significant influence of these parameters on wave behavior. The model is validated by reducing the problem to a specific case and matching it with established results. The findings are graphically demonstrated providing new insights into wave propagation in anisotropic micropolar thermoelastic materials and significant influences of initial stress, rotation and nonlocal parameters on phase velocity and reflection coefficients offering insights for geophysical exploration. [ABSTRACT FROM AUTHOR]

In this paper, the propagation of interfacial waves at the joint boundary of two initially stressed compressible half-spaces is discussed. The materials are subject to pure homogeneous strain and the wave is assumed to travel along one of the principle axes. For mathematical formulation of the problem, non-linear theory of elasticity and theory of invariants are used. Boundary conditions at the interface are applied which lead to an implicit secular equation governing the wave speed. A prototype strain-energy function is used for specialized theoretical results to understand the physical behavior of waves at the interface. A special case of biaxial initial stress is considered and the results are presented theoretically and graphically for representative numerical values of parameters. It is observed that the wave speed is considerably affected by intrinsic properties, i.e., material parameters as well as the amount of initial stress. [ABSTRACT FROM AUTHOR]

Rocks in the upper mantle are extensively subjected to initial stress. The rock exhibits elastic anisotropy under the deviatoric stress, which affects the seismic response of underground structures. This paper aims to study the effect of stress‐induced anisotropy on the seismic source. The seismic moment tensor generated by a shear faulting in a homogeneous isotropic medium with initial stress is derived by using the motion description in the intermediate configuration, the constitutive relation of third‐order elasticity, and the boundary condition considering the effect of initial stress. Then the seismic moment tensor is decomposed to investigate seismic source characters quantitatively. Our results show that shear faulting in a stress‐induced anisotropic medium can produce significant non‐double‐couple (non‐DC) mechanisms, including compensated linear vector dipole (CLVD) and isotropic (ISO) components. ISO and CLVD components vary linearly with the initial shear stress on faults. In addition, stress‐induced anisotropy causes the double‐couple (DC) to deviate from the plane defined by the fault normal and slip direction. The initial stress not only affects the source intensity but also affects the propagation of seismic waves. The radiation patterns of longitudinal waves have non‐uniform lobes, which shows the characteristic of anisotropy. Stress‐induced anisotropic parameters are smaller than intrinsic anisotropy at high‐stress levels and a nearly linear function of the increased initial stress. These results underscore the importance of considering stress‐induced anisotropy in the inversion of focal mechanisms and provide a new perspective for monitoring underground stress. Plain Language Summary: Because of the Earth's gravity and crustal movement, underground rocks are subjected to three different principal stresses. The accumulation of tectonic stress is often associated with the occurrence of earthquakes. Getting a state of underground stress may help us determine whether an earthquake is likely to occur in a region. We use the third‐order elastic theory, in which the strain energy contains the cubic term of strain, and use Lagrangian boundary conditions to describe the seismic source modeled by a tangential sliding fault. The intensity of seismic sources caused by slipping faults can be characterized by seismic moment tensors. We decompose the tensors into isotropic, double‐couple, and compensated linear vector dipole components, and these components are closely related to the stress on the fault plane. Our results show that a shear faulting in stressed media may exhibit a tensile effect. The initial stress affects the source intensity and shape of radiation and affects the propagation of seismic waves. In addition, the symmetry of the stressed medium is also closely related to the initial stress. Future studies may use our work to obtain stress states in the focal region from the source information. Key Points: The incremental Piola‐Kirchhoff stress described in the intermediate state is discontinuous across the fault plane under initial stressNon‐double‐couple components generated by a shear fault in stressed media are linearly related to the initial shear stress on the fault planeThe initial stress causes the inhomogeneity of P‐wave radiation patterns and affects the travel time and amplitude of seismic waves [ABSTRACT FROM AUTHOR]

A mathematical model has been proposed for the analytical study of the propagation of Love-type wave in an initially stressed functionally graded piezoelectric material (FGPM) layer overlying an orthotropic fluid-saturated porous half-space. The expression of dispersion equation is derived in closed form for both electrically open and electrically short conditions. The impact of various affecting parameters viz. wave number, gradient parameter, tensile initial stress on the dispersion curve of Love-type wave has been revealed by means of graphical illustrations. Some remarkable observation has been made through numerical computation for different piezoelectric ceramics of BaTiO 3 , PZT-4 and PZT-5A, respectively. The outcomes of the present study are momentous for both theoretical and practical implication for the surface acoustic wave (SAW) devices. [ABSTRACT FROM AUTHOR]

Purpose: The 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/approach: Torsional 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. Findings: Phase 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/value: Initial 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. [ABSTRACT FROM AUTHOR]

This study investigates the influence of initial stress on the phase velocity and damping velocity of Rayleigh-type waves propagating in an anisotropic layer situated above a dry sandy half-space. The study employs the separation of variables method to determine displacement components for both the layer and half-space. By applying boundary conditions, the dispersion relation governing the propagation of Rayleigh-type waves is derived and analyzed across various scenarios. The validity of the mathematical model is confirmed by its ability to simplify the existing velocity wave equation for Rayleigh waves. Numerical computations are conducted using MATHEMATICA software to further explore the investigation, and the findings are visually represented through graphical illustrations. The study underscores the significant impact of initial stress, layer thickness, and sandiness parameters on the phase and damping velocities of Rayleigh waves, where increased initial stress accelerates wave propagation, thicker layers decelerate it, and higher sandiness values foster faster waves. The outcomes of this study not only deepen our comprehension of seismic wave propagation but also bear practical implications in the domains of earthquake engineering and geophysics. [ABSTRACT FROM AUTHOR]

In this paper, we studied the propagation of Love waves in multilayered viscoelastic orthotropic medium in the presence of initial stress by using finite difference scheme. The closed form of dispersion relation is established and has found in the complex form for the case of (n − 1) layers lying over a half-space. Real part and imaginary part of the dispersion relation is derived for one layer lie over a half space correspond to dispersion curve and attenuation curve respectively. It has been shown that the acquired dispersion equation is in affirmation with the classical Love wave equation for both the cases when single and double layers lie over a half space. The stability criterion for the utilized finite difference technique and the expression for the phase and group velocity have been formed. The effect of viscoelastic parameter, initial stress on phase velocity and attenuation coefficient of Love wave has been studied. Moreover, phase and group velocity alteration for different values of Courant number has been illustrated by means of graphs. [ABSTRACT FROM AUTHOR]

This paper contains the dispersion equation of Love waves propagating in an initially-stressed orthotropic layer coated over an initially-stressed or-thotropic semi-infinite space. Rectangular irregularity of height H and width b at the interface is considered in this paper. The surface of the layer is supposed to be traction-free. To find the numerical results, semi-infinite space is assumed to be of topaz material and the layer is assumed to be of olivine material. Based on the dispersion equation, numerical values of dimensionless velocity against dimen-sionless layer thickness are calculated. The comparison of the velocity curves for different values of initial stress has been examined graphically. Graphs for one and two modes of velocity are drawn. The effect of irregularity on the velocity of Love waves has been shown graphically. It is shown that the second mode of velocity shows more variation than the first mode of velocity. MATLAB is used to plot graphs. It is demonstrated that initial-stress and irregular interfaces significantly affect the velocity of Love waves. [ABSTRACT FROM AUTHOR]

The dispersion relation of torsional wave in a dissipative, incompressible cylindrical shell of infinite length incorporating initial stresses effects is investigated. The governing equation and closed form solutions are derived with the aid of Biot's principle. Phase velocity and damping of torsional wave are obtained analytically and the influences of dissipation and initial stresses are studied in details. We proposed a new method for obtaining the phase and damping velocities of torsional wave in a complex form. Numerical results analyzing the torsional wave propagation incorporating initial stress effects are analyzed and presented in graphs. The analytical and numerical solutions reveal that, the dissipation as well as the initial stresses have notable impacts on the phase velocity of torsional wave in a pre-stressed dissipative cylindrical shell. The numerical results reveal that, the initial stresses and dissipation, considerably, effect the phase velocity of the torsional wave. It has been observed that, any change in dissipation parameter (d) produces a substantial change in damping velocity of torsional wave. In addition, it can be seen that, the phase velocity increases as the initial stress parameter increases. Finally, the result of numerical simulation illustrated the influence of dissipation and initial stresses on damping and phase velocities of torsional wave propagation. The conclusion made shown the consistency with the Biot's incremental deformation theory, and the effective on model such as engineering mechanics and displacement of particles. [ABSTRACT FROM AUTHOR]

The primary purpose of this paper is to examine the role of initial stress, magnetic field, coefficient of heat transfer, rotation, and inhomogeneity parameter on the Rayleigh wave propagation. The present investigation studies the propagation behaviour of Rayleigh surface waves in a liquid medium lying over an orthotropic rotating magneto-thermo-elastic medium under gravity and initial stress. The displacement in the two mediums has been found in the form of Mathieu-even and Mathieu-odd functions. The frequency equation has been achieved analytically with the help of these displacements and intrinsic boundary conditions. Numerical calculations and discussions have been performed with the use of a graphical presentation. It has been observed that the inhomogeneity parameter, initial stress, and the coefficient of heat transfer affect the wave velocity to a great extent, while the magnetic field and rotation produce a slight change in the velocity. The study may help in forecasting geophysical parameters at greater depth through signal processing and seismic data modelling. Resarch highlights: Study of the dynamics of Rayleigh wave dispersion in a liquid medium. Influence of initial stress, magnetic field, and rotation on Rayleigh surface waves. Impact of heat-transfer, gravity, and inhomogeneity on velocity. Initial stress and inhomogeneity affect mostly as compared to the rest. [ABSTRACT FROM AUTHOR]

A theoretical model is established to analyze the propagation behavior of Love-type wave in a composite structure which is comprised of two different functionally graded pre-stressed magneto-visco-elastic fiber-reinforced media as layer and substrate. Traction free surface along with the common interface of layer and substrate are of sinusoidal type. The closed form expressions of displacement components have been deduced for both the layer and substrate adopting the perturbation technique. The derived expression for displacement component consists of two-part in which the first part corresponds to the case of plane boundaries whereas the remaining part appears due to non-zero curvature of the boundaries. The influence of the sinusoidal type of curved boundaries on the displacement of a particle in a functionally graded pre-stressed magneto-visco-elastic fiber-reinforced media due to the propagation of Love-type wave has been unraveled explicitly. The substantial influence of dimensionless undulation frequency parameter, undulation amplitude parameter, functionally gradient parameter, initial stress, viscoelasticity and magneto-elasticity on displacement components are distinctly traced out through numerical simulations and graphical illustrations. Furthermore, the deduced results are validated with the classical and pre-established results. [ABSTRACT FROM AUTHOR]

The present paper articulates a mathematical model for the propagation of Shear wave in a layered structure comprised of slightly compressible finitely deformed layer over a foundation with pre-stressed fibre-reinforced stratum and pre-stressed dry sandy viscoelastic substrate. Method of separation of variables has been adopted as the solution technique for the problem. Closed form of dispersion equation for the propagation of shear wave in the layered structure has been deduced analytically and the obtained result has been found in agreement with the classical case. The effect of various parameters, viz. wave number, width ratio, bonding parameter, initial stress, sandiness parameter and shear viscosity on the phase velocity of shear wave has been studied through numerical computations and graphical illustrations. Some remarkable results regarding the propagation behavior of shear wave in the considered layered structure due to various affecting parameters serve as the major highlights of the present work which has significant relevance to field of geophysics, earthquake engineering and civil engineering. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to study the attenuation and dispersion phenomena of shear waves in anelastic and elastic porous strips. Numerical investigations are performed for the phase and damped velocity profiles of the wave. For numerical computation purposes, water-saturated limestone and kerosene oil saturated sandstone for the first and second porous strips, respectively. Some other peculiarities have been observed and discussed. Design/methodology/approach: Dispersion and attenuation characteristic of the shear wave propagations have been studied in an inhomogeneous poro-anelastic strip of finite thickness, which is clamped between an inhomogeneous poroelastic strip of finite thickness and an elastic half-space. Both the strips are initially stressed and the half-space is self-weighted. Analytical methods are used to calculate the interior deformations of the model with the involvement of special functions. The determination of the frequency equation, which includes the Bessel's and Whittaker functions, has been obtained using the prescribed boundary conditions. Findings: Impacts of attenuation coefficient, dissipation factor, inhomogeneities, initial stresses, Biot's gravity, porosity and thickness ratio parameters on the velocity profile of the wave have been demonstrated through the graphical visuals. These parameters are playing an important role and working as a catalyst in affecting the propagation behaviour of the wave. Originality/value: Inclusion of the concept of doubly layered initially stressed inhomogeneous porous structure of elastic and anelastic medium bedded over a self-weighted half-space medium brings a novelty to the existing literature related to the study of shear wave. It may be helpful to geologists, seismologists and structural engineers in the development of theoretical and practical studies. [ABSTRACT FROM AUTHOR]

Introduction: In this paper, a mathematical model of Love-type wave propagation in a heterogeneous transversely isotropic elastic layer subjected to initial stress and rotation of the resting on a rigid foundation. Frequency equation of Love-type wave is obtained in closed form. The material constants and initial stress have been taken as space dependent and arbitrary functions of depth in the respective media. Objectives: The dispersion equation is determined to study the effect of different types of parameters such as inhomogeneity, initial stress, rotation, wave number, the phase velocity on the Love-type wave propagation. Methods: The analytical solution has been obtained, we have used the separation of variables, method and the numerical solution using the bisection method implemented in MATLAB. Results: We present a general dispersion relation to describe the impacts as the propagation of Love-type waves in the structures. Numerical results analyzing the dispersion equation are discussed and presented graphically. Moreover, the obtained dispersion relation is found in well agreement with the classical case in isotropic and transversely isotropic layer resting on a rigid foundation. Finally, some graphical presentations have been made to assess the effects of various parameters in the plane wave propagation in elastic media of different nature. [ABSTRACT FROM AUTHOR]

The initial stresses have a strong effect on the mechanical behavior of underground rock masses, and the initial stressed rock masses are usually under strong dynamic disturbances such as blasting and earthquakes. The influence mechanism of a blasting excavation on underground rock masses can be revealed by studying the propagation of stress waves in them. In this paper, the improved Mohr-Coulomb elasto-plastic constitutive model of the intact rock considering the initial damage was first established and numerically implemented in Universal Distinct Element Code (UDEC) based on the variation of the experimental stress wave velocity in the initial stressed intact rock, and the feasibility of combining the established rock constitutive model and the BB (Bandis-Barton) model which characterizes the nonlinear deformation of the joints to simulate stress waves across jointed rock masses under initial stress was validated by comparing the numerical and model test results subsequently. Finally, further parameter studies were carried out through the UDEC to investigate the effect of the initial stress, angle, and number of joints on the transmission of the blasting stress wave in the jointed rock mass. The results showed that the initial stress significantly changed the propagation of the stress waves in the jointed rock mass. When the initial stress was small, the transmission coefficients of the stress waves in the jointed rock were vulnerable to be influenced by the variation of the angle and the number of joints, while the effect of the angle and the number of joints on the stress wave propagation gradually weakened as the initial stress increased. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to investigate the effect of reinforcement, inhomogeneity and initial stress on the propagation of shear waves. The problem consists of magneto poroelastic medium sandwiched between self-reinforced medium and poroelastic half space. Using Biot's theory of wave propagation, the frequency equation is obtained. Design/methodology/approach: Shear wave propagation in magneto poroelastic medium embedded between a self-reinforced medium and poroelastic half space is investigated. This particular setup is quite possible in the Earth crust. All the three media are assumed to be inhomogeneous under initial stress. The significant effects of initial stress and inhomogeneity parameters of individual media have been studied. Findings: Phase velocity is computed against wavenumber for various values of self-reinforcement, heterogeneity parameter and initial stress. Classical elasticity results are deduced as a particular case of the present study. Also in the absence of inhomogeneity and initial stress, frequency equation is discussed. Graphical representation is made to exhibit the results. Originality/value: Shear wave propagation in magneto poroelastic medium embedded between a self-reinforced medium, and poroelastic half space are investigated in presence of initial stress, and inhomogeneity parameter. For heterogeneous poroelastic half space, the Whittaker's solution is obtained. From the numerical results, it is observed that heterogeneity parameter, inhomogeneity parameter and reinforcement parameter have significant influences on the wave characteristics. In addition, frequency equation is discussed in absence of inhomogeneity and initial stress. For the validation purpose, numerical results are also computed for a particular case. [ABSTRACT FROM AUTHOR]

Propagation of harmonic plane waves is considered in an orthotropic elastic medium in the presence of initial stress and gravity. Roots of a quadratic equation define the propagation of one quasi-longitudinal wave and one quasi-transverse wave in a symmetry plane in this medium. These two waves are coupled in the identical phase to define the propagation of Rayleigh waves at the boundary of the medium. Two conditions at the stress-free boundary translate into a complex frequency equation, which explains the dispersive behavior of this Rayleigh wave. For the presence of radical terms, this complex equation is rationalized into a real algebraic equation. Only one root of this algebraic equation satisfies the mother frequency equation and hence represents the propagation of dispersive Rayleigh waves at the boundary of the orthotropic solid. The influence of initial stress and gravity on velocity and polarization of Rayleigh waves is observed through a numerical example. [ABSTRACT FROM AUTHOR]

A study is presented to observe the effect of residual stress on waves in an incompressible, hyper-elastic, thick and hollow cylinder of infinite length. The problem is based on the non-linear theory of infinitesimal deformations occurring after a finite deformation. A prototype model of strain energy function is used which adequately includes the effects of residual stress and deformation. The expressions for internal pressure and the axial load are calculated and graphical illustrations are presented. Analysis of infinitesimal wave propagation is carried for the axisymmetric case in the considered cylinder. Numerical solution is obtained in the undeformed configuration and analyzed for the two-point boundary-value problem. Dispersion curves are plotted for varying choice of parameters. [ABSTRACT FROM AUTHOR]

The prime objective of the present article is to analyze the effects of rotation and initial stress on the propagation of Rayleigh surface waves in a homogeneous, orthotropic magneto-thermoelastic half space subjected to gravity field. The frequency equations in closed form are derived and the amplitude ratios of surface displacements, temperature change during the Rayleigh wave propagation on the surface of half space have been computed analytically. The highlights of this study are the effects of different parameters (rotation, magnetic field, initial stress, and gravity) on the velocity of Rayleigh waves. Variation in phase velocity of Rayleigh waves against a wave number is shown graphically. Some particular cases have been deduced. Also, the classical Rayleigh wave equation is obtained as a special case of the present study. Numerical example has been carried out and represented by the means of graphs. Impacts of various involved parameters appearing in the solutions are carefully analyzed. In fact, in the absence of various parameters, these equations are in agreement with the results for isotropic medium. [ABSTRACT FROM AUTHOR]

Present analysis is concerned with the propagation of plane waves in an initially stressed magneto-thermoelastic half-space with microtemperatures and voids. It is noticed that there exist four kinds of coupled dilatational waves in addition to shear and microtemperature waves in such type of medium. Using appropriate boundary conditions, the amplitude and energy ratios for the reflected waves have been presented in closed form when (i) a set of coupled dilatational waves is made incident and (ii) a shear wave is made incident. Amplitude ratios of various reflected waves are presented graphically to explore the effects of magnetic field, initial stress and void parameter. It is verified that there is no loss of energy at the free surface during reflection phenomena. [ABSTRACT FROM AUTHOR]

This work investigates the propagation of Bleustein–Gulyaev waves in a piezoelectric layered rotating prestressed half-space. The main solution consists in the obtained expressions for the phase velocity equation of the Bleustein–Gulyaev wave. The phase velocity is numerically calculated and graphically illustrated for the electric open and short cases for different thicknesses of the layer and wave. Numerical outcomes are produced in case of LiNbO 3 . [ABSTRACT FROM AUTHOR]

In this paper, influence of the bonded imperfectness on torsional wave dispersion in the finitely pre-strained hollow compound circular cylinder made of highly-elastic material were investigated. The investigations are carried out within the scope of the piecewise homogeneous body model with the use of the Three-dimensional Linearized Theory of Elastic Waves in Initially Stresses Bodies (TLTEWISB). The mechanical relations of the materials of the cylinders are described through the harmonic potential. Numerical results on the effects of the imperfectness of the boundary condition on the influence of the initial stresses on the wave propagation velocity are presented and discussed. [ABSTRACT FROM AUTHOR]

This article explores the effect of initial-stress, heterogeneity and anisotropy on the propagation of SH-wave (Case-1) and Rayleigh-type wave (Case-2) in a semi-infinite medium while propagation of Love-type wave (Case-3) is analysed in a composite structure with distinct initial-stressed heterogeneous anisotropic layer and semi-infinite medium. Velocity equations have been deduced in the closed-form for SH-wave and Rayleigh-type wave respectively whereas dispersion equation has been accomplished analytically for Love-type wave. Deduced results have been matched with the pre-established and classical results. Numerical results have been portrayed and to unravel the influence of various affecting parameters and set forth the analytical findings. [ABSTRACT FROM AUTHOR]

The propagation of thermoelastic waves in a homogeneous, isotropic elastic semi-infinite space is subjected to rotation and initial stress, which is at temperature T0 - initially, and whose boundary surface is subjected to heat source and load moving with finite velocity. Temperature and stress distribution occurring due to heating or cooling and have been determined using certain boundary conditions. Numerical results have been given and illustrated graphically in each case considered. Comparison is made with the results predicted by the theory of thermoelasticity in the absence of rotation and initial stress. The results indicate that the effect of the rotation and initial stress is very pronounced [ABSTRACT FROM AUTHOR]

In this article, the problem of reflection and refraction of thermoelastic wave at a solid–liquid interface in the presence of magnetic field and initial stress has been investigated. The problem has been solved in the context of three-phase-lag model of thermoelasticity. The appropriate expressions to find the amplitude ratios for all the three cases of p-wave incidence, SV-wave incidence, and thermal wave incidence have been developed. However, the ratios of amplitudes of reflected and refracted waves to that of incident wave are computed numerically for earth's crust-water interface, for incident SV wave only, considering the initial stress to be tensile as well as compressional both. The obtained results have been presented graphically to show the effect of phase lags, magnetic field, and initial stress. [ABSTRACT FROM AUTHOR]

The objective of this study is to develop a theory to study the propagation of Rayleigh-type waves in an inhomogeneous layer having yielding surface. A detailed study of a Rayleigh-type wave propagating in an exponentially graded incompressible layer resting on yielding surface is considered. The frequency equation being a function of phase velocity, wave number and heterogeneity parameter associated with the yielding parameter and density of inhomogeneous layer reveals the fact that Rayleigh-type wave propagation is greatly influenced by the above-stated parameters. In particular cases, the dispersion relation has been discussed for stress-free foundation by taking yielding parameter tending to zero. In numerical and graphical computation, the significant effects of distortional velocity have been carried out. Moreover, the obtained dispersion relation is found in well agreement to the classical case in homogeneous isotropic layer resting on a yielding foundation. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

• Damage of specimens are investigated by blasting tests with different coupling mediums. • The potential ability of STFs to adjust rock fracture is tested. • The effect of pre-stress on crack extension is studied using fractal theory. The performance of rock blasting is significantly influenced by the coupling medium between the explosive and borehole wall. In this study, two shear-thickening fluids (corn starch suspension (CSS) and silica dioxide suspension (SDS)) and water, were used as coupling mediums. The blasting tests were conducted on cement mortar specimens under coupled blasting load and uniaxial static stresses ranging from 0 to 7.5 MPa at intervals of 2.5 MPa. Fractal theory was employed to analyze the extent of damage, crack extension and fractal characteristics of the 3D reconstructed specimens after blasting. The experimental findings revealed that specimens using SDS showed a decrease in damage followed by an increase with increasing static stress, presenting an opposite trend compared to specimens using CSS. The specimens using water exhibited intermediate results. Furthermore, numerical simulations were performed to understand the stress transmission from explosive transferring coupling medium to rock under blasting loads. The variable viscous characteristics of the coupling medium led to divergence in blast load propagation and decay, directly influencing the damage to the specimen. Under blasting load, CSS with a stronger shear-thickening effect played a beneficial buffering role, reducing the strength of the blasting load and minimizing specimen damage. On the other hand, SDS with a weaker shear-thickening effect demonstrated better stress wave propagation ability compared to water. This was reflected in the higher maximum pressure exerted by SDS, as well as the more uniform distribution of pressure, maximum shear stress, and resultant velocity along the borehole wall. The study also highlighted the potential for adjusting blast stress wave distribution by changing the detonation point's location and emphasized the advantages of CSS and SDS as stemming materials in boreholes. [ABSTRACT FROM AUTHOR]

This present study investigates Love-type wave propagation in composite structure consists of a loosely bonded functionally graded piezoelectric material (FGPM) stratum lying over a functionally graded initially-stressed fibre-reinforced material (FGIFM) substrate. The closed-form expressions of the dispersion relation have been obtained analytically for both the cases of electrically open and electrically short conditions. Some special cases of the problem have also been studied and the obtained results are found in well-agreement with the classical Love wave equation. The emphatic influence of wave number, bonding parameter associated with bonding of stratum with substrate of the composite structure, piezoelectric coefficient as well as dielectric constant of the piezoelectric stratum, horizontal initial stresses, and functional gradedness of the composite structure on the phase velocity of Love-type wave has been reported and illustrated through numerical computation along with graphical demonstration in both the cases of electrically open and electrically short condition for the reinforced and reinforced-free composite structure. Comparative study has been carried out to analyze the distinct cases associated with functional gradedness of the composite structure and also various cases which reveals the influence of piezoelectricity, reinforcement and horizontal initial stress acting in the composite structure, and bonding of the stratum and substrate of the composite structure in context of the present problem which serves as one of the major highlights of the study. [ABSTRACT FROM AUTHOR]

The present article deals with Rayleigh surface wave propagation in homogeneous magneto-thermoelastic orthotropic medium. Effect of initial stress and magnetic field on Rayleigh waves is studied in the context of three-phase-lag model of generalized thermoelasticity. The normal mode analysis is used to obtain the exact expressions for the displacement components, stresses and temperature distribution. Various frequency equations are derived and compared with the existing literature. The path of surface particles is elliptical during Rayleigh wave propagation. Effect of phase-lags on Rayleigh wave velocity, attenuation coefficient and specific loss are presented graphically. It is observed from graphical presentation that the effect of magnetic field and initial stress on different wave characteristics is pronounced. [ABSTRACT FROM AUTHOR]

An analytical approach is adopted to investigate the SH waves in a composite structure consisting of initially stressed rotating piezoelectric layer and initially stressed substrate with rotation. The interface between the layer and the substrate is assumed to be imperfect. Two distinct types of imperfect interfaces (dielectrically weakly and highly conducting) are considered. Secular equations have been obtained for both electrically open and short cases with weakly and highly performing interface. Particular cases have been derived and matched with existing result. The characteristics of SH wave through the considered framework and their state of relying on different physical and geometrical parameters have been scrutinized based on their numerical results. The parallel simulated outcomes of disparate physical quantities, namely, phase velocity, group velocity, dispersive curves, initial stress, rotation and electromechanical coupling factor, and stress distribution of SH wave in the considered structure are investigated. The considered model may be useful in theoretical foundation and practical application for the development of piezoelectric sensors, structural health monitoring, and surface acoustic wave devices. [ABSTRACT FROM AUTHOR]

Propagation of Rayleigh-type surface waves in an incompressible visco-elastic material over incompressible visco-elastic semi-infinite media under the effect of initial stresses is discussed. The dispersion equation is determined to study the effect of different types of parameters such as inhomogeneity, initial stress, wave number, phase velocity, damping factor, visco-elasticity, and incompressibility on the Rayleigh-type wave propagation. It is found that the affecting parameters have a significant effect on the wave propagation. Cardano's and Ferrari's methods are deployed to estimate the roots of differential equations associated with layer and semi-infinite media. The MATHEMATICA software is applied to explicate the effect of these parameters graphically. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Wentzel–Kramers–Brillouin approximation technique serves as a powerful tool to find the particle displacements due to surface wave propagation in bedded structure with distinct material properties. This study is carried out to investigate the transference of Love-type waves in functionally graded piezoelectric material layer bonded between viscous liquid and pre-stressed piezoelectric half-space. Following the elastic wave theory, the mathematical model is established. Wentzel–Kramers–Brillouin method is applied to obtain the theoretical derivations in functionally graded piezoelectric material stratum where variation in material gradients is taken exponentially. Separation of variables method is employed to obtain the displacement components in viscous liquid and piezoelectric medium. Dispersion equations for considered surface wave are obtained in both electrically open and short cases. Profound effect of material gradient coefficient on phase velocity has been remarkably established. Some numerical examples are carried out and represented through graphs. The considered model facilitates a theoretical foundation and practical application for the development of surface acoustic wave devices. [ABSTRACT FROM AUTHOR]

In this paper, we study the effects of magnetic field and initial stress on plane waves propagation. We have investigated the problem of reflection and refraction of thermoelastic waves at a magnetized solid-liquid interface in the presence of initial stress, in the context of CT (Classical theory) of thermoelasticity, the problem has been solved. The boundary conditions applied at the interface are: (i) continuity of the displacement, (ii) vanishing of the tangential displacement, (iii) continuity of normal force per unit initial area, (iv) vanishing of the tangential stress and (v) continuity of temperature. The amplitudes ratios for the incident p-, T-, and SV- waves have been obtained. The reflection and transmission coefficients for the incident waves are computed numerically, considering the initial stress and magnetic field effects and the results are represented graphically. [ABSTRACT FROM AUTHOR]