The quaternion Fourier Transform (QFT) finds extensive applications across various domains, such as signal processing and optics. This paper strengthens two important uncertainty principles for QFT. First, we proposed two different sharper versions of generalized Heisenberg’s uncertainty principle associated with quaternion Fourier transform in Lp(R2, H) space for p ∈ [1, 2]. Also a new version of Donoho–Stark’s uncertainty principle associated with QFT is discussed. Furthermore, in some particular case this new Donoho–Stark’s uncertainty principle is the sharper version than the existing one in quaternion sense.

This research paper investigates the complex dynamics of Love wave propagation on a piezoelectric plate situated atop a micropolar elastic half-space having imperfect interface. The study delves into the multifaceted effects of flexoelectricity, micro-inertia, guiding layer thickness, and interfacial imperfection on the characteristics of Love waves. The electromechanical coupling factor which is significant in analyzing SAW device performances is also studied. Variable separable method is used to solve the governing equations and desired solution is obtained analytically. The findings contribute to a deeper understanding of Love wave propagation in complex elastic structures and development of advanced sensors and communication technologies.

In this paper, we have investigated the stress distribution induced by a normal load moving across an irregular micropolar layer imperfectly bonded to an orthotropic half-space under initial stress. The analysis considers a parabolic surface irregularity on the layer and an imperfect interface between the layer and half-space. Using appropriate boundary conditions and a perturbation technique closed-form mathematical expressions are derived for normal, tangential, and couple stresses. Numerical computations and graphical analyses have been conducted to illustrate the significant effects of dimensionless parameters such as frictional coefficient, irregularity depth, irregularity factor, coupling factor, bonding parameters, and initial stresses on the normal, tangential, and couple stresses. The results reveal that these characteristics significantly influence the stress distribution within both the irregular upper layer and the underlying half-space. These findings have practical implications across various fields, including highway and airport runway construction, heavy haulage, civil engineering, and earthquake engineering, where accurate stress modeling is essential for infrastructure stability and safety.

Impulsive point sources are one of the external forces which can create a wave motion in the body. This article investigates the propagation characteristics of Love waves in a visco-porous piezoelectric (VPPE) material layered over a functionally graded piezoelectric (FGPE) substrate, with a point source applied at the interface. Green’s function approach and the Fourier transform are used to derive an analytical solution, of which the real part yields the frequency curve and the imaginary part yields the attenuation curve. Some particular cases are derived and compared with the existing studies for validation. Numerical illustrations are provided, showing the variation of phase velocity and attenuation with respect to different parameters, using lithium niobate as the substrate and PZT-5A as the visco-porous piezoelectric material. The findings of the study will be useful in the development and enhancement of surface acoustic wave devices.

This study investigates the propagation of Love waves through a composite structure comprising a piezoelectric fiber-reinforced composite (PFRC) layer resting on a heterogeneous elastic substrate, influenced by a point source. The structure is considered fluid-loaded, and the study's primary aim is to explore how fluid loading affects Love wave propagation. The fluid is modeled as a complex medium exhibiting Maxwell and Kelvin–Voigt viscoelastic behavior. Using Fourier transform techniques, Green's function, and suitable boundary conditions, the dispersion relation is derived and validated against existing results. The dispersion relation is complex, with the real part representing the frequency curve and the imaginary part representing the attenuation curve of the Love wave. The study further explores the effects of fluid viscosity, PFRC volume fraction, and initial stress on phase velocity and attenuation with the help of graphical illustrations.

Abstract : In this paper, a theoretical study is carried out to investigate the dynamic response of a structure comprising an initially stressed fiber-reinforced layer lying over an initially stressed transversely isotropic half-space subject to a moving load. There is a parabolic irregularity at the surface of the fiber-reinforced layer. Further, the interface between the two media is considered to be imperfect. The closed-form expressions of normal and shear stresses are calculated for both media by applying suitable boundary conditions and perturbation techniques. With the help of numerical examples, graphs have been plotted to show the effects of irregularity parameters, imperfect interface, initial stresses, friction coefficients, and the width of the layer on the shear and normal stresses of both media.

The present paper uses mathematical analysis to investigate Rayleigh wave transference in an orthotropic layer. The considered model comprises an orthotropic layer covering a homogeneous isotropic micropolar half-space. The surface of the layer and the interface of the two media are taken to be corrugated. The dispersion relation is obtained in the determinant form, which describes the reliance of Rayleigh wave velocity on wave number. Some particular cases have also been deduced and are found to match existing results. The primary outcome of the present study is that the corrugation present in the structure has an influential impact on the velocity of the propagating wave. This impact has been presented through graphs. Moreover, the dynamic response of the layer's height, elastic constant, material density of the orthotropic material, and micropolarity associated with the half-space on the phase velocity of Rayleigh waves have also been shown with the aid of graphs. The present paper finds its applications in the theoretical study of surface wave transference in anisotropic elastic structures.

This article is dedicated to analyse the propagation and attenuation behaviour of Love-type waves in an imperfectly bonded viscoelastic-functionally graded piezoelectric material (FGPM) layered structure. The linear spring model is adopted to portray the interfacial imperfection. The wave solutions in the FGPM substrate are approximated using Wentzel–Kramers–Brillouin (WKB) approximation technique. Dispersion relation is obtained and found to be complex in nature, when traction-free and electrically short conditions are taken into account. Numerical example and computations have been presented to analyse the dispersion equation. The pronounced effects of different parameters such as gradient coefficients, layer’s width, interfacial imperfection, and dissipation factor on the phase velocity, as well as attenuation coefficient of the Love-type wave have been illustrated graphically. Obtained results may be used to achieve better performance of surface acoustic wave (SAW) devices and Love-wave sensors.

The present article deals with the reflection and transmission of waves at an interface of piezoelectric (ALN & PZT-5T) half-spaces with microstructures. Unlike the classical piezoelectric material, in the considered media, five coupled waves (2 bulk and 3 surface) [namely the Quasi-longitudinal wave (QP), Quasi-transverse wave (QSV), Electric-acoustic wave (EA), P-type surface wave (SP) and S-type surface wave (SS)] are generated in response to an oblique incident Quasi plane wave. The main objective of this study is to investigate the influence of the characteristic length of microstructure, the inertial characteristic length and flexoelectric coefficients on the reflection and transmission coefficients. For this purpose, the linear algebraic equation, continuity conditions at the common interface are contracted. The linear system of equations comprising the reflection and transmission coefficients is derived, which is solved by using the Cramer's rule. The consequence of this electromechanical phenomenon may be advantageous in certain engineering applications that involve smart nano-composites.

In this paper, a mathematical study is carried out to investigate the reflection phenomenon of plane QP waves at mechanically traction-free and dielectrically charge-free boundary surface of a pre-stressed rotating piezoelectric half-space. The microstructure effect (flexoelectric effect) is considered in the piezoelectric half-space along with micro-inertial effect as well as strain gradient effect. Due to the reflection phenomenon at the free surface, five kinds of coupled elastic waves are generated. The reflection coefficients are evaluated numerically. Graphs are plotted, and detailed discussion is presented to elaborate the effects of initial stresses, rotation, and flexoelectric coefficient on the reflection coefficients. It is observed that aforementioned parameters have remarkable influence upon the reflection coefficients of the reflected waves.

The present paper aims to study the reflection/transmission of two-dimensional plane elastic waves (quasi-longitudinal displacement waves) at the interface between a self-reinforced half-space and an orthotropic micropolar elastic solid half-space. Three kinds of coupled elastic waves are reflected in the orthotropic micropolar half-space, and two types of waves are transmitted in the self-reinforced medium. The phase velocities obtained in closed form depend upon the angle of propagation and material parameters. The boundary conditions at the interface of the two media are solved, and reflection/transmission coefficients are obtained using Cramer’s rule. Numerical examples are given, and dependence of the reflection/transmission coefficients on the incident angle has been shown graphically. Also, the comparisons between anisotropic and isotropic cases have been marked distinctly. The obtained results may be utilised for the interpretation and analysis of geophysical data.

We examine the reflection and transmission phenomena of quasi-longitudinal plane (QP) waves in an AlN-ZnO laminated composite structure. The structure is designed under the influence of the initial stresses in which one carrier piezoelectric semiconductor (PSC) half-space is in welded contact with another PSC half-space. The secular equations in the transversely isotropic PSC material are derived from the general dynamic equation, taking the initial stresses into consideration. It is shown that the incident quasi-longitudinal wave (QP-mode) at the interface generates four types of reflected and transmitted waves, namely, QP wave, quasi-transverse (QSV) wave, electric-acoustic (EA) wave, and carrier plane (CP) wave. The algebraic equations are obtained by imposing the boundary conditions on the common interface of the laminated structure. Reflection and transmission coefficients of waves are obtained by implementing Cramer’s rule. Profound impacts of the initial stresses and exterior electric biasing field on the reflection and transmission coefficients of waves are investigated and presented graphically.

In the present article, a theoretical investigation has been carried out to analyze the propagation of shear horizontal surface waves (SH-waves) in a structure consisting of a functionally graded piezoelectric material (FGPM) layer lying over an FGPM half-space. The material properties of FGPM layer are assumed to have exponential function distribution along the thickness direction whereas those of FGPM half-space are presumed to have quadratic variation. The interface between the FGPM layer and the FGPM half-space has been considered to be imperfect. At the surface, two cases are considered, electrically open case and electrically short case. Moreover two types of imperfections at the interface are taken into account (one as mechanically compliant and dielectrically weakly conducting and other as mechanically compliant and dielectrically highly conducting). Variable separable method is used for the wave solution. In particular, the solutions for mechanical displacement and electric potential function for FGPM half-space has been obtained in the form of modified Bessel function. The dispersion relation for each case is obtained in determinant form using suitable boundary conditions. Numerical example is given and graphs are plotted. The numerical results show that the surface wave velocity is affected by the layer width, gradient coefficient of the two FGPM media, and the degree of mechanical and dielectrical imperfections at the interface between the covering layer and the substrate. This study finds its application in optimization of SAW devices.

This paper studies the reflection and transmission of two dimensional quasi P wave incident at an imperfect interface between two dissimilar Functionally Graded Piezoelectric Materials (FGPM) half-spaces. The imperfect bonding behavior between the two considered half-spaces is described by the interfacial imperfections. The imperfection is characterized by the normal stiffness and tangential stiffness using the linear spring model. These interface parameters (i.e normal stiffness and tangential stiffness) are dependent on the elastic properties of interphase. Secular equations have been derived analytically for both the half-spaces. Different cases of imperfect interfaces namely perfect interface, slip interface, weak bonding interface and unbounded interface have been assumed and discussed. Influence of material gradients on the reflection and transmission coefficients (RTC's) have been inflicted graphically for all the four considered interface conditions. Further, a comparative study of the RTC's with respect to the incident angle has been carried out for the different cases of imperfections. The obtained results may be useful for measuring imperfection at the interface and designing of SAW devices.

The frequency of the Love-type surface waves in a bedded structure consisting of a porous piezoelectric (PP) medium and a functionally graded material (FGM) substrate is approximated. The FGM layer is assumed to have a constant initial stress. The Wentzel-Kramers-Brillouin (WKB) approximation technique is used for the wave solution in the FGM layer, and the method of separation of variables is applied for the solution in the porous piezoelectric medium. The dependence of the wave frequency on the wave number is obtained for both electrically open and short cases. The effects of the gradient coefficient of the FGM layer, the initial stresses (tensile stress and compressive stress), and the width of the FGM layer are marked distinctly and shown graphically. The findings may contribute towards the design and optimization of acoustic wave devices.

Present article aims to study the propagation of horizontally polarized shear waves (SH waves) in Functionally Graded Piezoelectric Material (FGPM) layer. The considered FGPM layer is lying over a piezomagnetic half-space with corrugated interface. The material properties of FGPM layer are assumed to have exponential function distribution along the x-axis. Two cases are considered - electrically and magnetically open case and electrically and magnetically short case. Dispersion relations are obtained in determinant form. Numerical example has been provided for graphical representation of findings. This study provides a theoretical foundation for optimization of Surface Acoustic Wave (SAW) devices.

We propose an analytical solution for the propagation of Love-type surface seismic waves in a piezo-composite smart structure. A model describing the Love-type wave propagation in the piezomagnetic waveguide is considered. The model is comprised of piezomagnetic layer lying on a lossy viscoelastic substrate. In this regard a direct Sturm-Liouville problem has been formulated and solved. Complex dispersion equations have been derived for both magnetically open and short cases. For each case we have obtained two nonlinear equations containing two unknowns and various parameters. These nonlinear equations are solved using suitable numerical method implemented in Mathematica 9.0 software. Further, the obtained frequency relations are matched with the classical case of Love wave to validate the problem. The influence of different parameters (thickness of the layer, frequency, piezomagnetic coefficient and elastic parameter) on the phase velocity and attenuation of Love-type waves are discussed and delineated through graphs. The results have immense applications in non-destructive evaluation, designing of viscosity sensors, SAW devices, biosensors and chemosensors.

This article investigates the propagation behaviour of horizontally polarized shear waves in a layered composite structure. In the considered model, a functionally graded piezoelectric material layer is sandwiched between corrugated piezomagnetic layer and elastic substrate. Method of separation of variables is used to obtain the displacement components in all three mediums. Dispersion relation has been established in the determinant form for the two cases, magneto-electrically open case and magneto-electrically short case. Effects of material gradient (of functionally graded piezoelectric material layer), corrugation parameters and layer width are distinctly marked and represented graphically. This study finds its application towards manufacturing and optimization of piezoelectric sensors and transducers. Also, the obtained result may be utilized for acquiring a better performance in surface acoustic wave devices.

The present problem aims to study the propagation behaviour of Shear Horizontal (SH) surface waves in a composite structure comprising of functionally graded piezoelectric plate fused with a porous piezoelectric plate. The material properties of the functionally graded piezoelectric material (FGPM) are assumed to be vary in quadratic manner. Method of separation of variables is used to obtain the solutions for the displacement and stress components in both the media. Solutions are obtained in terms of modified Bessel functions of first and second kinds. Dispersion relations are obtained for both the electrically open and short cases. Effects of thickness of the plates, gradient parameter, dielectric coefficient and piezoelectric coefficient on dispersion curve have been marked distinctly and portrayed through graphs. The electromechanical coupling factor is also plotted against wave number. Findings of the present investigation may set guidelines for the designing of more efficient Surface acoustic wave (SAW) devices.