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Assuming different types of imperfect interfaces composed of a magnetoelectroelastic (MEE) structure, the current work investigates the transmission of a Love-type wave in a MEE solid cylindrical structure. The spatially variable quasi-classical technique is applied to derive the analytical solution of the layers. The substantial impact of factors related to the imperfect interface on the wave phase velocities is illustrated numerically. The Love-type wave's dispersion relation has been established as the determinant for electrically and magnetically open and short cases. Moreover, the article investigates the consequences of six different imperfect parameters namely mechanical imperfection, electrical imperfection, magnetic imperfection, magneto-mechanical imperfection, electro-mechanical imperfection, and magneto-electrical imperfection parameters in magnetically and electrically open and short scenarios are covered. The findings demonstrate that, in comparison to the short case, the electric and magnetic open case has a higher phase velocity. Here are some key findings: imperfection parameters strongly affect the phase velocity and attenuation coefficient curves and the bonding parameter's prominent influence is inversely proportional to the attenuation coefficient and well-proportional to the phase velocity. Identifying the piezoelectric and piezomagnetic connection and its possible use in the construction of sensors, actuators, energy harvesters, and nano-electronics is the result of this theoretical investigation. This is the first time that a polar coordinate system was used in the quasi-classical method of solving differential equations. The results argue that the outcomes of this specific model have an immense ability to deal with various commercial and industrial applications in acoustical engineering, geotechnical design, ultrasonic technology, and SAW devices.

Purpose This research aims to explore the transmission of seismic surface waves through a two magneto-strictive materials i.e. cobalt ferrite and Terfenol-D when embedded in a plate-substrate configuration with non-ideal interface. The study focuses on understanding the impact of width of the plates, imperfect parameter, heterogeneity parameter on both the materials cobalt ferrite and Terfenol-D under magnetically open and short conditions. Methodology To achieve this, the study employs a variable-separable technique following Direct Sturm-Liouville method and appropriate boundary conditions to derive frequency relations for both magnetically open and short circuit scenarios. Numerical simulations are conducted to investigate the effects of width of the plates, imperfect parameter, heterogeneity parameter on both the materials cobalt ferrite and Terfenol-D under magnetically open and short conditions. Findings The research findings indicate that the phase velocity is increasing more in Terfenol-D as compared to Cobalt ferrite, either the case magnetically open or closed. Graphical comparisons highlight the impact of width plates, imperfect parameter, heterogeneity parameter on the characteristics on wave propagation clearly. Research limitations The study is confined to linear wave propagation and does not consider nonlinear effects. Additionally, the analysis is based on idealized material properties and interface conditions. Practical implications The results of this research can contribute to the design and optimization of sensors, energy harvesters, and wave manipulation devices utilizing piezomagnetic materials. Understanding the behaviour of surface waves in these structures is crucial for their effective application. Originality This study offers a comprehensive analysis of surface wave propagation in two different types of piezomagnetic composite structure by considering heterogeneity and interface conditions. The comparative study of different piezomagnetic models and the incorporation of heterogeneity and interface conditions contribute to the originality of the research.

Generalized Love-type wave propagation in a nonlinear, heterogeneous, isotropic, low-velocity intermediate layer of uniform thickness lying between two nonlinear, homogeneous, elastic, different half-spaces is examined. The heterogeneity of the layer is considered to result from the exponential change of rigidity and density in the thickness direction. Nonlinear self-modulation of waves is characterized by a nonlinear Schrödinger equation with the aid of multiple scales asymptotic method. The influence of both nonlinear and heterogeneous characteristics of the slow intermediate layer on the existence of bright and dark soliton Love-type waves is investigated numerically. Furthermore, the considerable effect of the layer’s linear and nonlinear heterogeneity properties on the nonlinear evolution of bright and dark solitary waves is graphically shown.

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.

Purpose This mathematical analysis has been accomplished for the purpose of understanding the propagation behaviour like phase velocity and attenuation of Love-type waves through visco-micropolar composite Earth’s structure. Design/methodology/approach The considered geometry of this problem involves a micropolar Voigt-type viscoelastic stratum imperfectly bonded to a heterogeneous Voigt-type viscoelastic substratum. With the aid of governing equations of motion of each individual medium and method of separation of variable, the components of micro-rotation and displacement have been obtained. Findings The boundary conditions of the presumed geometry at the free surface and at the interface, together with the obtained components of micro-rotation, displacement and mechanical stresses give rise to the determinant form of the dispersion relation. Moreover, some noteworthy cases have also been extrapolated in detail. Graphical interpretation irradiating the impact of viscoelasticity, micropolarity, heterogeneity and imperfectness on the phase velocity and attenuation of Love-type waves is the principal highlight of the present study. Practical implications In this study, the influence of the considered parameters such as micropolarity, viscoelasticity, heterogeneity, and imperfectness has been elucidated graphically on the phase velocity and attenuation of Love-type waves. It has been noticed from the graphs that with the rising magnitude of micropolarity and heterogeneity, the attenuation curves shift upwards, that is the loss of energy of these waves takes place in a rapid way. Hence, from the outcomes of the present analysis, it can be concluded that heterogeneous micropolar stratified media can serve as a helpful tool in increasing the attenuation or in other words, loss of energy of Love-type waves, thus reducing the devastating behaviour of these waves. Originality/value Till date, the mathematical modelling as well as vibrational analysis of Love-type waves in a viscoelastic substrate overloaded by visco-micropolar composite Earth’s structure with mechanical interfacial imperfection remain unattempted by researchers round the globe. The current analysis is an approach for studying the traversal traits of surface waves (here, Love-type waves) in a realistic stratified model of the Earth’s crust and may thus, serves as a dynamic paraphernalia in various domains like earthquake and geotechnical engineering; exploration geology and soil mechanics and many more, both in a conceptual as well as pragmatic manner.

PurposeThe purpose of the present study is to investigate the dispersion and damping behaviors of Love-type waves propagating in an irregular fluid-saturated fissured porous stratum coated by a sandy layer.Design/methodology/approachTwo cases are analyzed in this study. In case-I, the irregular fissured porous stratum is covered by a dry sandy layer, whereas in case-II, the sandy layer is considered to be viscous in nature. The method of separation of variables is incorporated in this study to acquire the displacement components of the considered media.FindingsWith the help of the suitable boundary conditions, the complex frequency relation is established in each case leading to two distinct equations. The real and imaginary parts of the complex frequency relation define the dispersion and attenuation properties of Love-type waves, respectively. Using the MATHEMATICA software, several graphical implementations are executed to illustrate the influence of the sandiness parameter, total porosity, volume fraction of fissures, fluctuation parameter, flatness parameters and ratio of widths of layers on the phase velocity and attenuation coefficient. Furthermore, comparison between the two cases is clearly framed through the variation of aforementioned parameters. Some particular cases in the presence and absence of irregular interfaces are also analyzed.Originality/valueTo the best of the authors' knowledge, although many articles regarding the surface wave propagation in different crustal layers have been published, the propagation of Love-type waves in a sandwiched fissured porous stratum with irregular boundaries is still undiscovered. Results accomplished in this analytical study can be employed in different practical areas, such as earthquake engineering, material science, carbon sequestration and seismology.

The prime thrust of this proposed mathematical model is to investigate on Love type wave propagation in a visco-porous piezoelectric waveguide with complex fluid loaded on its surface, with loosely bonded common interfaces. To describe the fluid viscoelasticity the Maxwell and Kelvin–Voigt equations are incorporated, with the aid of varying Deborah number. Solving the equation of motion for different media, namely, complex fluid layer, visco-porous piezoelectric waveguide layer, and porous half-space, a direct Sturm–Liouville problem has been formulated, which is a salient feature of this analysis. Employing suitable boundary conditions an accurate generalized complex dispersion equation is derived. To validate the results, comparison has been done with a pre-established study as a particular case, and a strong agreement is revealed. Effect of several parameters viz. fluid viscosity (glycerol concentration), fluid layer thickness, waveguide layer thickness, and bonding parameters, on the phase velocity and attenuation of Love type wave has been delineated by means of graphs. The effect of glycerol concentration and thickness of the complex fluid layer is among the key outcome of the study. It is established that Kelvin–Voigt fluid model is most appropriate when the glycerol concentration is high, as compared to other models, in the case of rapid simulation, while the Newtonian fluid model may be preferred for problems involving varying thickness of the medium. The findings of this study may be utilized in the optimal design and development of viscosity sensors Love wave fluid sensing devices.

PurposeThis study aims to explore the characteristics of the Love wave propagation through a heterogeneous hydrogel layer bounded to a functionally graded PFRC substrate while determining the displacement and electric potential in a di-electrically faintly conducting, mechanically compliant interface.Design/methodology/approachIn order to calculate the value of response variables, the Wave mode method has been used. The governing modeled equations are non-homogeneous. The analytical solution has been obtained by deploying the boundary conditions.FindingsThe effect of thickness on the field variables for different values of variation parameter, mechanical constant of proportionality, electrical constant of proportionality and volume fraction of the PFRC substrate is examined for both, electrically open and short cases.Originality/valueTo the best of authors' knowledge, no attempt has been made to analyze the propagation characteristics of Love wave through the heterogeneous hydrogel Layer bedded over the functionally graded piezoelectric fiber-reinforced composites substrate.

This research article aims to conduct a more thorough examination of the effects of size on piezoelectric composites when subjected to Love-type mechanical wave propagation. The objective is to take into account the structural size influences by employing Eringen’s nonlocal theory. By utilizing Maxwell’s relation and electric boundary conditions, the distribution of electric potentials along the piezoelectric composite is derived. Through exact analysis, the dispersion relations for the piezoelectric composite are obtained. Specific outcomes are acquired and validated by comparing them to existing results. Subsequently, a detailed investigation of various influential parameters such as the nonlocal parameter and material parameters on the wave dispersion characteristics of the nanoscaled structure is conducted. These findings demonstrate that the nonlocality parameter within the medium significantly affects wave propagation.

The 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.