Search

The present study provides the analytical solution for magnetoelastic plane-wave diffraction by a rigid strip in an infinite orthotropic medium. The mathematical formulation of the considered model involves a mixed boundary value problem, which is solved by using the integral equation method. The contour integration technique has been used to establish the closed-form expressions of vertical diffracted displacement and normal stress. The deduced expressions of the vertical diffracted displacement and normal stress are matched with preestablished result through the special cases and serves the validation of the present study. The pattern of the diffracted displacement component in the considered medium, and its varying behavior with various affecting parameters, i.e., magnetoelastic coupling parameter, wave number, phase velocity of the propagating magnetoelastic wave, and distance, are computed numerically and delineated by means of graphical representation for orthotropic and isotropic materials. Moreover, the impact of anisotropy of the infinite medium has been unrevealed through comparative study, which is one of the achievements of the present work. Practical Applications: The diffraction of longitudinal magnetoelastic plane waves through a rigid strip in an orthotropic material holds significant applications across diverse engineering fields. In nondestructive testing (NDT), the understanding of wave diffraction patterns aids in the detection and characterization of defects or structural changes in orthotropic materials without causing damage. This knowledge is vital for structural health monitoring (SHM), allowing for the timely identification of damage, cracks, or alterations in material properties. Moreover, the insights gained from wave diffraction contribute to the design and optimization of magnetoelastic devices, including sensors, actuators, and transducers, enhancing their performance and sensitivity. In the realm of communication, the propagation of magnetoelastic waves through rigid strips in orthotropic materials is instrumental in designing efficient waveguides and communication devices. Additionally, the study of wave diffraction facilitates the development of magnetostrictive components for applications in robotics, medical devices, and automotive systems. Furthermore, the unique acoustic properties of orthotropic materials, influenced by magnetoelastic wave diffraction, contribute to the design and optimization of acoustic devices such as speakers and ultrasonic transducers. [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]

The present investigation is concerned with the study of reflection and transmission characteristics of plane waves in two distinct rotating piezo-thermo-elastic substrates under the purview of dual-phase-lag (DPL) model and Lord–Shulman (LS) theory of thermo-elasticity. Mathematical expressions for electric displacements, stresses, amplitudes and energy ratios are derived. The influence of rotation on the amplitude ratios is extensively studied and comparative analyses are performed graphically among DPL and LS theories. Energy conservation law holds in the entire process of reflection and transmission phenomena. This study may be useful in the construction and design of temperature sensors and other piezoelectric surface-acoustic-wave devices. [ABSTRACT FROM AUTHOR]

A three-dimensional (3D) plane wave incident at a functionally graded triclinic medium (FGTM) under two different types of boundary (viz. stress free (Case I) and rigid (Case II)) has been modelled. The constitutive equations of the functionally graded triclinic medium are used to deduce the Christoffel matrix of order 3. By using Cardano's method, we derive the expressions for the phase velocities of the reflected waves (qP, qSV and qSH waves). The expressions of the reflection coefficients (amplitude ratios) are obtained for the present geometry with the help of the generalized Snell's law and Cramer's rule. The obtained mathematical expressions are perfectly matched with pre-established results. Further, the slowness surface and energy ratios have been also completed to prove the correctness of the presented problem. The effect of anisotropy and functionally graded parameter on the reflection coefficients has been traced out remarkably through a comparative study by numerical modelling. The comparative analysis reveals that the functionally graded parameter and anisotropy have significant impact on the amplitude ratios and both these attributes contribute simultaneously to simulate a realistic elastodynamic model and predict the response of the medium (geo-medium) with better accuracy. [ABSTRACT FROM AUTHOR]

This study delves with the reflection phenomenon of plane-waves due to incidence of quasi-longitudinal (QL) wave at a semi-infinite structure comprising of pre-stressed piezoelectric-orthotropic substrate (POS) with stress-free (Case I) and rigid (Case II) bounding surfaces. The compact-form expressions of reflection-coefficients (RCs) of reflected QL wave, quasi-transverse (QT) wave and evanescent-electroacoustic (EA) wave for different cases of pre-stressed POS are deduced. To unravel effects of higher anisotropy in substrate, comparative analysis in pre-stressed transversely isotopic piezoelectric substrate (TIPS) medium with stress-free (Case III) and rigid (Case IV) boundaries is carried out. PVDF and ALN materials are considered for numerical computations. For validation, energy-partition and conditions of grazing incidence for all the undertaken cases are analyzed. [ABSTRACT FROM AUTHOR]

• Scattering of SH wave on an irregular surface of the piezomagnetic stratum-substrate structure is studied. • The expressions of frequency relation and group velocity of SH wave is derived in closed form for both MO and MS cases. • The expressions of mechanical displacement and magnetic potential are derived for three different shaped irregularities. • Validation of the derived results of both cases is found in well agreement with the classical Love wave equation. • The impact of material properties is depicted on the phase velocity and group velocity of SH wave for both MO and MS cases. The present paper investigates the scattering phenomenon of horizontally polarized Shear wave on an irregular surface of the piezomagnetic stratum lying over a piezomagnetic substrate. The expressions of frequency relation and group velocity of scattered Shear wave on the considered piezomagnetic stratum-substrate structure are deduced for magnetically open and magnetically short cases by inducing appropriate boundary conditions. A closed form expressions of reflected mechanical displacement and reflected magnetic potential function related to stratum and substrate are also determined for three different shaped irregularities (rectangular shaped, parabolic shaped and triangular shaped) by employing perturbation technique and residue theorem for both magnetically open and short cases. The efficacy of piezomagnetic coupling parameter, vertical irregular parameter due to presence of surface irregularities is portrayed on the phase velocity, group velocity, reflected mechanical displacement and reflected magnetic potential function related to the stratum for both magnetically open and short conditions graphically. A comparative study is also made to examine the impact of different shaped irregularities on the reflected mechanical displacement and reflected magnetic potential function of the stratum. [ABSTRACT FROM AUTHOR]

This work focuses on the study of plane wave reflection at the surface of a piezothermoelastic fiber-reinforced composite (PTFRC) half-space. The classical dynamical coupled theory, Lord-Shulman theory and Green-Lindsay theory have been employed to examine the problem. The existence of four types of waves, viz. quasi-P(qP), quasi-SV (qSV), thermal(T-mode) and electroacoustic(EA) waves has been detected in the two-dimensional model of the PTFRC medium. The closed-form expressions of the amplitude ratios of reflected waves have been obtained by using suitable boundary conditions. The impact of thermal parameters has been extensively studied and total normal energy flux at the surface has been derived. [ABSTRACT FROM AUTHOR]

This article is intended to observe the reflection and transmission phenomena of three-dimensional plane waves at the interfaces of two distinct anisotropic triclinic media under the context of the three-phase-lag model and Green-Naghdi theory. Distinct interfaces, viz. normal stiffness, transverse stiffness, thermal contact conductance, welded contact and slip boundaries have been considered to examine the impact of boundaries on the reflection and transmission phenomena of the thermoelastic waves. Mathematical expressions for the reflection and transmission coefficients of the waves have been acquired in the context of generalized thermoelasticity. Energy ratios for each of the reflected and transmitted waves have been derived to establish the energy conservation law at each of the incident angles. The findings of this study are elaborated in the form of graphical means. [ABSTRACT FROM AUTHOR]

Mathematical analysis is performed to examine the reflection and transmission phenomena of plane waves at the corrugated interface of crystalline structure separating two distinct monoclinic thermoelastic media. Analysis of this phenomena is achieved adopting classical dynamic coupled, Lord–Shulman, and Green–Lindsay theories. Using Rayleigh's methods, the expressions of reflection and transmission coefficients of reflected and transmitted waves are deduced for the case of corrugated as well as plane interfaces. The influence of corrugation and frequency parameters on reflection and transmission coefficients for all three theories has been extensively analyzed with a comparative approach. Findings of the study are demonstrated through numerical and graphical results. Furthermore, the obtained result is validated with the preexisting result. [ABSTRACT FROM AUTHOR]

The present study analysed the characteristics of a moving Griffith crack in a self-reinforced strip of finite thickness and infinite extent with the moving parallel punches of constant load acting on the boundaries of the strip at both sides due to the propagation of magnetoelastic plane waves under mechanical point loading. With the aid of integral transform technique, problem has been reduced to the pair of simultaneous singular integral equations with Cauchy-type singularities. The point load at the edge of the moving crack is considered in terms of Dirac delta function, and the expression of stress intensity factor (SIF) at the crack tip with constant point loading has been established in closed form by using the well-known properties of Hilbert transformation. Moreover, some of the special cases have been deduced from the obtained expression of SIF for the force of constant intensity, without punch pressure and anisotropy in the considered strip. Numerical computations and graphical demonstrations have been carried out to observe the profound effect of magnetoelastic coupling parameter, punch pressure, crack length, distinct positions of point load and the velocity of crack associated with magnetoelastic plane wave on SIF for self-reinforced materials and isotropic material strip. A comparative study of SIF at the tip of moving crack has been made for the self-reinforced and isotropic materials to highlight some of the important peculiarities of the problem. [ABSTRACT FROM AUTHOR]

An analytical model is introduced to analyse moving Griffith crack in a monoclinic crystalline layer of finite width and infinite extent with moving parallel punch pressure acting at the bounding surface of the layer because of the propagation of plane waves under mechanical point loading. Formulation of the model includes coupled singular integral equations with Cauchy‐type singularities. The expression of stress intensity factor (SIF) at the tip of moving crack having constant point loading is established in the closed‐form by employing Hilbert transformation. Further, expression of SIF is deduced for some particular cases of the crystalline layer, that is, without punch pressure and anisotropy. For the sake of validation, the obtained results are matched with pre‐established and standard results. Numerical computations and graphical demonstrations have been carried out for crystalline materials with monoclinic symmetry like lithium niobate and lithium tantalate and for isotropic material as well to unravel the effect of punch pressure, crack length, distinct positions of acting point load and the velocity of crack on SIF. Further, influence of anisotropy has been traced out remarkably through comparative study that is one of the pinnacles of the present study. [ABSTRACT FROM AUTHOR]

This theoretical work addressed an issue of the reflection and transmission of plane wave incident in a layered triclinic solids. Generalization of Snell's law is applied and suitable boundary conditions are imposed to obtain the closed-form expressions for reflection and transmission coefficients. The reflection and transmission coefficients are computed numerically by Cramer's method. Numerical results found to be strongly influenced by the initial stress, angle of incidence on the modulus of reflection and transmission coefficients. The slowness surfaces of qP, qSV, and qSH waves are also estimated in initially stressed triclinic medium. [ABSTRACT FROM AUTHOR]

With a motivation to gain physical insight of reflection as well as transmission phenomena in frozen (river/ocean) situation for example in Antarctica and other coldest place on Earth, the present article undertakes the analysis of reflection and transmission of a plane wave at the interfaces of layered structured comprised of a water layer of finite thickness sandwiched between an upper half-space constituted of ice and a lower isotropic elastic half-space, which may be useful in geophysical exploration in such conditions. A closed form expression of reflection/transmission coefficients of reflected and transmitted waves has been derived in terms of angles of incidence, propagation vector, displacement vector and elastic constants of the media. Expressions corresponding to the energy partition of various reflected and transmitted waves have also been established analytically. It has been remarkably shown that the law of conservation of energy holds good in the entire reflection and transmission phenomena for different angles of incidence. A numerical examples were performed so to graphically portray the analytical findings. Further the deduced results are validated with the pre-established classical results. [ABSTRACT FROM AUTHOR]

The present mathematical study analyzes the reflection and transmission phenomenon of a plane wave being incident at the distinct types of separating interfaces in a rotating pre-stressed structure with two semi-infinite media comprised of functionally graded piezoelectric-orthotropic (FGPO) materials. The effects of pre-stresses, rotation, and functional gradients along with six different types of boundaries viz. Normal stiffness boundary (NSB), Transverse stiffness boundary (TSB), Electric imperfection boundary (EIB), Complete debonded boundary (CDB), Slip boundary (SB), and Welded contact boundary (WCB) on reflection coefficients (RCs) of reflected qP, qSV, and EA waves and transmission coefficients (TCs) of transmitted qP, qSV, and EA waves have been examined with a comparative approach. Comparison of the obtained result with that of the case when rotating pre-stressed structure with two semi-infinite media is constituted of lesser anisotropic functionally graded transversely isotropic piezoelectric (FGTIP) materials is also carried out. To validate the findings energy-partitions of reflected and transmitted waves for both the cases of the structures have been computed and shown to observe the Law of conservation of energy. Further, on considering a grazing incident of qP wave in both the cases of structure, RCs and TCs for reflected and transmitted qSV waves and EA waves become zero, whereas the RC for reflected and TC of transmitted qP wave gets out of phase. Some important peculiarities have also been highlighted through numerical results, which serve as a salient feature of the study. [Display omitted] [ABSTRACT FROM AUTHOR]

The effects of different types of imperfect interfaces, normal and shear initial stresses and rotation on the reflection and transmission characteristics of plane waves in two dissimilar piezothermoelastic fiber-reinforced composite (PTFRC) half-spaces are analytically studied in this article. The PTFRC structure is modeled employing the Strength of Materials (SM) technique with the Rule of Mixtures (RM) approach. Numerical studies are performed on two distinct PTFRCs comprised of CdSe–epoxy combination and PZT-5A-epoxy combination. Several reasons, like the inevitable presence of interfacial defects because of accumulative damages, have detrimental effects on the life expectancy and efficiency of structures manufactured using smart materials. For the same reasons, the bond between half-spaces is generally not perfect. Thus, the mechanical–electrical-thermally imperfect boundary is classified into seven types, viz. Normal Stiffness Boundary (NSB), Transverse Stiffness Boundary (TSB), Thermal Contact Conductance (TCC), Electrically Imperfect Boundary (EIB), Slip Boundary (SB), Completely Debonded Boundary (CDB) and Welded Contact (WC), which are analyzed individually. Initial stresses and rotation are also considered for making the present model more realistic. The closed-form expressions of amplitude ratios of reflected and transmitted quasi-longitudinal (qP), quasi-transverse (qSV), thermal (T-mode) and electro-acoustic (EA) waves are derived by means of appropriate mechanical–electrical-thermally imperfect boundary conditions. Using these, the energy ratios of all waves along with the interaction energy among various waves are obtained and the Law of Conservation of Energy is validated. Comparative analysis among the Classical dynamical coupled, Lord–Shulman and Green–Lindsay thermoelasticity theories is performed. The influences of the incident angle, imperfect interfaces, rotation, varying magnitudes of normal and shear initial stresses and thermal relaxation parameters on the energy ratios are illustrated graphically. Some special cases exclusive to this study are shown which validate the obtained results with extant literature and possible scientific and engineering applications of the present model are discussed. [Display omitted] • PTFRC micro-mechanics model is analyzed by Strength of Materials & Rule of Mixtures. • qP, qSV, T-mode & EA waves get reflected & transmitted. • 7 imperfect interfaces, normal/shear initial stresses & rotation are analyzed. • Energy ratios of all reflected/transmitted waves & interaction energy are studied. • Classical, Lord–Shulman & Green–Lindsay thermoelasticity theories are examined. [ABSTRACT FROM AUTHOR]

• A mathematical model is presented to discuss the reflection and refraction phenomena of plane wave. • Reflection and refraction coefficients for all reflected and refracted waves are obtained. • Energy ratios are found to be in well agreement with the energy conservation law. • The deduced results are compared and validated with the pre-established classical results. A physically realistic mathematical problem has been modelled to discuss the reflection and refraction phenomena of three-dimensional (3-D) plane waves. The considered composite structure comprises of water layer of finite width lying between isotropic and ice substrate has been considered. The mathematical analysis pertaining to this problem has been addressed analytically. The closed form expressions for reflection and refraction coefficients of different reflected and refracted waves are derived. Mathematical expressions for the energy share associated with the various waves are also enlisted in a very concise form in connection with the reflection and refraction coefficients. The effects of various polar and azimuthal angles have been exhibited on the reflection and refraction coefficients. The energy conservation law is established to validate this model. Numerical examples and computations have been performed to illustrate the results of this model graphically. Further, as a particular case of the present problem, the deduced results are compared and validated with the pre-established classical results. [ABSTRACT FROM AUTHOR]

• The proposed three dimensional model comprised with a fluid layer sandwich between two dissimilar viscoelastic semi-infinite media. • The phase velocities are computed for the triclinic viscoelastic and fibre viscoelastic materials as well as for the fluid layer. • A generalized method has been adopted to compute the amplitude ratios. • From graphical representation, amplitude ratios are found to be strongly influenced by viscoelasticity and anisotropy. A unified approach is presented to study the nature of reflection and transmission of seismic waves in a concerned layered structure. The geometrical configuration of the layered structure comprised with a fluid layer of finite thickness embedded between two dissimilar viscoelastic anisotropic semi-infinite media. Analytical formulae are implemented to obtain the phase velocities of the corresponding medium. The generalized Snell's law is used to compute the expression of amplitude ratios for the undertaken geometry. In order to solve the system of linear equations for amplitude ratio, Cramer's rule has been applied. The analytical findings are demonstrated graphically and observed that the amplitude ratios are significantly influenced by viscoelasticity and anisotropy as well. Equations governing slowness section of the material medium is derived using constitutive equations. The outcomes provided novel information about the reflected and transmitted amplitude ratios which may further helpful in the field of geophysical exploration. [ABSTRACT FROM AUTHOR]