Phase Velocity Of Love-type Wave Research Articles

Transverse surface wave in non-planar layered nearly incompressible elastic structure having imperfect contact

The prime motive of the present work is to bring out the emphatic impacts of planar boundary and non-planar boundary as well as imperfectness of the interface on the displacement components and phase velocity of Love-type wave (LTW) propagating in the layered structure. The layered structure essentially incorporates two dissimilar nearly incompressible elastic materials bonded imperfectly to each other having non-planar boundaries at the free surface and at the common interface. A linear spring model has been adopted to describe the imperfect bonding at the interface. The solution methodology features the applicability of variable separable technique along with Taylor’s series expansion that leads to establish dispersion relation and displacement components of LTW. The displacement components and phase velocity of LTW have been numerically computed, and their dependence on wave number have been graphically manifested. As a special case of the study, the dispersion relations for incompressible and isotropic elastic layered structures have been deduced. A comparative analysis between compressible, nearly incompressible and incompressible layered structures comprised of Neo–Hookean material, and isotropic layered structure has been performed to trace out the impact of imperfect bonding parameter on the phase velocity of LTW. The established result of dispersion relation for the considered geometrical structure, as a particular deduction, concur well with the result present in the literature.

Estimating the effects of imperfect bonding and size-dependency on Love-type wave propagation in functionally graded orthotropic material under the influence of initial stress

The present study deals with the investigation of Love-type wave propagation in functionally graded orthotropic material layer (FGOM) bonded imperfectly over micropolar (MP) elastic substrate. The dispersion relations are obtained analytically in compact form by employing appropriate boundary conditions for the layer and substrate. Dispersion curves are plotted to illustrate the influence of imperfectness of interface, microstructure of the substrate, thickness as well as heterogeneity involved in FGOM layer on the phase velocity of Love-type wave. Moreover, the FGOM layer is considered under an initially stressed state to extend the applicability of the obtained results in geophysical engineering. Relevant particular cases are also obtained to validate the present study.

Caliberating length scale parameter and micropolarity on transference of Love-type waves in composite of <em>CoFe</em><sub>2</sub><em>O</em><sub>4</sub> and Aluminium-Epoxy laden with Newtonian liquid

The aim of the present study is to unravel the concealed attributes of the Love-type wave propagating in a composite of $ CoFe_2O_4 $ laden with Newtonian viscous liquid (VL), resting over Aluminium-Epoxy as a semi-infinite micropolar (MP) substrate bearing size dependent properties. The admissible boundary conditions are used to obtain the dispersion relations for both magnetically open and short cases. To support the findings and reverberations of affecting parameters, graphical representations are provided. Probable particular cases are deduced and matched with the existing result. It can be perceived from graphical representations that phase velocity of Love-type wave is remarkably affected by these parameters. Findings may have meaningful practical applications towards the optimization of magnetic sensors and transducers working in liquid environment.

Microstructural and viscous liquid loading effects on the propagation of love waves in a piezomagnetic layered structure

The gist of the present study is to unfold the veiled characteristics of the Love-type wave propagation through a piezomagnetic (PM) material overlying a semi-infinite couple stress substrate, under the viscous liquid (Newtonian) loading. Dispersion equations are obtained for magnetically open and short conditions. Possible particular cases are discussed. Dispersion equation is reduced to the classical Love wave equation for validation. Graphical representations reveal that the phase velocity of Love-type wave is remarkably affected by viscous liquid loading, microstructural parameter and PM parameters. This study has meaningful practical applications toward the fabrication and enhancement of PM sensors and transducers.

Green’s function technique to model Love-type wave propagation due to an impulsive point source in a piezomagnetic layered structure

The crux of the present study is to unravel the concealed characteristics on the propagation behavior of Love-type wave through a piezomagnetic material (PMM) stratum overlying a functionally graded piezomagnetic material (FGPMM) substrate under the influence of an impulsive point source at its interfacial surface. Functional gradients in the substrate is due to the spatial variation in the elastic constants and density. The elasto-magneto-dynamical equations are laid down for the piezomagnetic medium. Green’s functions are derived for the layered structure taking a point force/point charge density at the interfacial surface into account. Dispersion equation of Love-type wave is obtained with aid of admissible boundary conditions and the well known properties of Green’s function. For sake of validation, the dispersion equation is reduced to fairly match with the classical Love wave equation. To demonstrate the analytical findings numerically and set forth the parametric effects, numerical data of two PMMs are undertaken for PMM stratum and FGPMM substrate. The graphical representations reveal that phase velocity of Love-type wave is significantly affected by the material constants and the functional gradients parameters allied with the piezomagnetic layered structure. The profound effects of piezomagnetic constants, magnetic permeabilities, magnifying gradient parameters and functional gradient parameter are portrayed by graphical means. A comparative analysis to trace out the piezomagnetic effect of the PMM stratum and FGPMM substrate is accomplished owing to their transverse isotropic orientational symmetry. This study may find noteworthy dynamic and practical applications towards manufacturing and optimization of piezomagnetic sensors and transducers. In addition, the obtained result may be useful for acquiring a better performance in surface acoustic wave devices and functionally graded material waveguides.

Influence of loose bonding, initial stress and reinforcement on Love-type wave propagating in a functionally graded piezoelectric composite structure

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.

On point source influencing Love-type wave propagation in a functionally graded piezoelectric composite structure: A Green’s function approach

Green’s function plays an important role in solving the problems concerning point action or impulse responsible for wave motions in materials. Prime objective of the this article is to investigate the propagation behaviour of Love-type wave influenced by a point source in a composite structure comprising a functionally graded piezoelectric material layer lying over a functionally graded fibre-reinforced material half-space. Green’s function technique is adopted in order to obtain the dispersion equation, which is further reduced to the classical Love wave equation as a particular case of the problem. The effect of increasing thickness of functionally graded piezoelectric material layer on the circular frequency and wave number is unravelled and depicted graphically. Moreover, influence of heterogeneity, piezoelectricity and dielectric constant associated with functionally graded piezoelectric material layer and effect of heterogeneity parameter and corresponding magnification factor concerned with functional gradedness of functionally graded fibre-reinforced material half-space have been reported through numerical computation and graphical delineation. For sake of computation, numerical data of PZT-5H ceramics for the functionally graded piezoelectric material layer and carbon-fibre epoxy-resin for functionally graded fibre-reinforced material half-space have been considered. Comparative study is performed to elucidate the effect of presence and absence of reinforcement in functionally graded half-space on the phase velocity of Love-type wave propagating in composite structure.

Study of Love-type wave propagation in an isotropic tri layers elastic medium overlying a semi-infinite elastic medium structure

This paper deals with the propagation of Love-type wave in a composite isotropic structure embraced of tri layers elastic medium overlying a semi-infinite elastic medium. The heterogeneity is caused due to the variation of linear, exponential, and quadratic with respect to the depth. Modified Bessel function with Debye Asymptotic Expansion approach is used to achieve closed form of dispersion equation analytically and found to be in well agreement to the classical Love wave equation. Numerical computation has been carried out to accomplish the graphical demonstration to unravel some important peculiarities of wave number associated in presence or absence of layers medium and effect of heterogeneities on phase velocity of Love-type wave.

Influence of rectangular and parabolic irregularities on the propagation behavior of transverse wave in a piezoelectric layer

PurposeThe purpose of this paper is to theoretically analyze the propagation of Love-type wave in an irregular piezoelectric layer superimposed on an isotropic elastic substrate.Design/methodology/approachThe perturbation technique and Fourier transform have been applied for the solution procedure of the problem. The closed-form expressions of the dispersion relation have been analytically established considering different type of irregularities, namely, rectangular and parabolic for both the cases of electrically open and short conditions.FindingsThe study reveals that the phase velocity of Love-type wave is prominently influenced by wave number, size of irregularity, piezoelectric constant and dielectric constant of an irregular piezoelectric layer. Numerical simulation and graphical illustrations have been effectuated to depict the pronounced impact of aforementioned affecting parameters on the phase velocity of Love-type wave. The major highlight of the paper is the comparative study carried out for rectangular irregularity and parabolic irregularity in both electrically open and short conditions. Classical Love wave equation has been recovered for both the electrical conditions as the limiting case when both media are elastic and interface between them is regular.Practical implicationsThe consequences of the study can be utilized in the design of surface acoustic wave devices to enhance their efficiency, as the material properties and the type of irregularities present in the piezoelectric layer enable Love-type wave to propagate along the surface of the layer promoting the confinement of wave for a longer duration.Originality/valueUp to now, none of the authors have yet studied the propagation of Love waves in a piezoelectric layer overlying an isotropic substrate involving both parabolic and rectangular irregularities. Further, the comparative study of rectangular irregularity and parabolic irregularity for both the cases of electrically open and short conditions elucidating the latent characteristics is among the major highlights and reflects the novelty of the present study.

Propagation characteristics of transverse surface wave in a heterogeneous layer cladded with a piezoelectric stratum and an isotropic substrate

An analytical treatment studying the propagation behavior of Love-type wave in a piezoelectric layer bonded perfectly to an isotropic heterogeneous layer overlying an unbounded isotropic homogeneous substrate has been taken into account. Debye asymptotic expansion has been employed to attain the closed-form expressions of dispersion relation for both the cases of electrically open condition and electrically short condition. The significant impact of various affecting parameters, namely, wave number, piezoelectric constant and dielectric constant of the uppermost piezoelectric layer, width ratio of the layers, and heterogeneity parameter of the intermediate isotropic layer on the phase velocity of Love-type wave, has been remarkably traced out by means of numerical computation and graphical illustrations. In addition to this, comparative study has been carried out to unfold the concealed characteristics of the problem. As a special case of the problem, it is identified that the established dispersion relation for both the cases of electrically open condition and electrically short condition is in well agreement with the classical Love wave equation.

Influence of imperfectly bonded piezoelectric layer with irregularity on propagation of Love-type wave in a reinforced composite structure

The present paper investigates the propagation of Love-type wave in a composite structure comprised of imperfectly bonded piezoelectric layer with lower fiber-reinforced half-space with rectangular shaped irregularity at the common interface. Closed-form expression of phase velocity of Love-type wave propagating in the composite structure has been deduced analytically for electrically open and short conditions. Some special cases of the problem have also been studied. It has been found that the obtained results are in well-agreement to the Classical Love wave equation. Significant effects of various parameters viz. irregularity parameter, flexibility imperfectness parameter and viscoelastic imperfectness parameter associated with complex common interface, dielectric constant and piezoelectric coefficient on phase velocity of Love-type wave has been reported. Numerical computations and graphical illustrations have been carried out to demonstrate the deduced results for various cases. Moreover, comparative study has been performed to unravel the effects of the presence of reinforcement and piezoelectricity in the composite structure and also to analyze the existence of irregularity and imperfectness at the common interface of composite structure in context of the present problem which serves as a salient feature of the present study.

Love-type wave propagation in a corrugated piezoelectric structure

This study delves into the propagation of Love-type wave in a corrugated piezoelectric layer overlying an isotropic elastic half-space. The expression of dispersion relation has been established in a closed form for both the cases of electrically open condition and electrically short condition. The pronounced effect of various affecting parameters, namely wave number, corrugation parameter of upper boundary surface, corrugation parameter of common interface between the layer and the half-space, piezoelectric constant and dielectric constant of corrugated piezoelectric layer, undulation parameter and position parameter on the phase velocity of Love-type wave, has been remarkably traced out. In order to observe the prominent effect of these affecting parameters on the phase velocity of Love-type wave, numerical computation and graphical demonstration have been accomplished for specific type of corrugated boundary surfaces present in the layer. Moreover, comparative study has been wrapped up to reveal the latent characteristics of the problem by means of graphical illustrations for both the cases of electrically open and electrically short conditions. As a special case of the problem, it is observed that procured dispersion relation for both the cases of electrically open condition and electrically short condition is in well agreement with the classical Love wave equation.

Propagation of Love-Type Wave in a Corrugated Fibre-Reinforced Layer

AbstractThe present paper investigates the propagation of Love-type waves in an initially stressed heterogeneous fibre-reinforced layer with corrugated boundary surfaces, lying over a viscoelastic half-space under hydrostatic state of stress. The dispersion relation is obtained in closed form and found to be in well-agreement with the classical Love wave equation. The substantial effect of reinforcement, position and undulation parameters (i.e.corrugation), heterogeneity, horizontal initial stress and hydrostatic state of stress are discussed briefly. It is established through comparative study that reinforced layer supports more to phase velocity of Love-type wave as compare to reinforced free layer.

Influence of initial stress, irregularity and heterogeneity on Love-type wave propagation in double pre-stressed irregular layers lying over a pre-stressed half-space

The present paper deals with the propagation of Love-type wave in an initially stressed irregular vertically heterogeneous layer lying over an initially stressed isotropic layer and an initially stressed isotropic half-space. Two different types of irregularities, viz., rectangular and parabolic, are considered at the interface of uppermost initially stressed heterogeneous layer and intermediate initially stressed isotropic layer. Dispersion equations are obtained in closed form for both cases of irregularities, distinctly. The effect of size and shape of irregularity, horizontal compressive initial stress, horizontal tensile initial stress, heterogeneity of the uppermost layer and width ratio of the layers on phase velocity of Love-type wave are the major highlights of the study. Comparative study has been made to identify the effects of different shapes of irregularity, presence of heterogeneity and initial stresses. Numerical computations have been carried out and depicted by means of graphs for the present study.

Influence of corrugated boundary surfaces, reinforcement, hydrostatic stress, heterogeneity and anisotropy on Love-type wave propagation

It may not be enough to hold all the engineering problems by the supposition that material mediums are isotropic, homogeneous, without initial stress and have a planar boundary surface, as the concept cannot indulge many features of the continuum response which are of great significance. This motivates us to study the influence of corrugated boundary surfaces, reinforcement, hydrostatic stress, heterogeneity and anisotropy on the propagation of Love-type wave in a corrugated heterogeneous orthotropic layer lying over a fibre-reinforced half-space under hydrostatic state of stress. The heterogeneity in the upper corrugated layer is caused due to exponential variation in the elastic constants with respect to the space variable pointing positively downwards. The dispersion relation has been obtained in closed form and found in well-agreement to the classical Love wave equation. The substantial effect of corrugation parameters, reinforcement, undulatory parameter, hydrostatic state of stress, heterogeneity parameter, position parameter and wave number on the phase velocity of Love-type wave has been observed and depicted by means of graph. The comparative study to unravel the effect of presence and absence of corrugated boundary surfaces of layer, heterogeneity in upper layer, reinforcement in half-space and anisotropy existing in both layer and half-space, on the dispersion curve is among the important peculiarities of the present paper.

Love-type wave propagation in a piezoelectric structure with irregularity

The present study delves to study the propagation of Love-type wave in an irregular piezoelectric layer lying over a piezoelectric half-space. The closed form expressions of dispersion relation for both the cases of electrically open and electrically short condition have been established. Wave number, irregularity, dielectric constant and piezoelectric constant of irregular piezoelectric layer and piezoelectric half-space have their substantial effect on the phase velocity of Love-type wave. Numerical computation and graphical demonstration has been carried out to observe the profound effect of these affecting parameters on the phase velocity of Love-type wave. In order to highlight some of the important peculiarities of the problem, comparative study of the phase velocity of Love-type wave propagating in an irregular piezoelectric layer lying over a piezoelectric half-space and an irregular piezoelectric layer lying over a half-space without piezoelectricity for both the cases of electrically open and electrically short condition has been made. It is remarkable to quote that the size of irregularity disfavors the phase velocity of Love-type wave for both electrically open and electrically short condition. As a special case of the problem, it is found that the obtained dispersion relation is in well agreement to the classical Love wave equation for both the cases of electrically open condition and electrically short condition.