Shear Horizontal Surface Waves Research Articles

Rotation effects on propagation of shear horizontal surface waves in piezomagnetic-piezoelectric semiconductor layered structures

In this work, the propagation characteristics of shear horizontal waves in a piezomagnetic and piezoelectric semiconductor layered structure with rotation are studied. The dispersion equation of shear horizontal waves in the rotating multiferroic composite semiconductor is obtained in the framework of coupled field theory including Coriolis and centrifugal forces. By solving the dispersion equation in complex domain, the influence of rotation on the shear horizontal waves is deeply analyzed, and the effects of steady-state carrier concentration and biasing electric field in the presence and absence of rotation are obtained, respectively. Similar to the semiconductor properties, the results show that the rotation will also cause dispersion and attenuation of shear horizontal waves. Besides, the wave speed decreases with the increase of the angular rate and the frequency shift occurs. The rotation sensitivity at long wavelengths near the surface is greater than those at short wavelengths deep into the half-space. Importantly, the increase in wave speed and amplitude gain can be achieved by applying an appropriate biasing electric field regardless of rotation or non-rotation. Specially, several critical points such as attenuation from large to small with rotation, wave speed from decrease to increase and wave amplitude from attenuation to gain in the biasing electric field are obtained. The results could be helpful for the design of surface acoustic wave gyroscopes and piezoelectric semiconductor devices related to magnetic fields.

Surface effects on wave propagation in piezoelectric–piezomagnetic loosely bonded bilayer system using nonlocal theory of elasticity

This study investigates nonlocal and surface effects on the dispersion behaviors of Shear horizontal (SH) waves in piezoelectric(PE)-piezomagnetic(PM) bilayer systems. The interface between these two layers is imperfectly bonded. The general governing equations are derived from the nonlocal magnetoelectroelastic (MEE) theory by adding an inherent length. The G-M model and generalized Young-Laplace equations have been used to incorporate surface effects into the boundary conditions of the bilayer systems. The closed-form dispersion equation is obtained analytically for electrically open and magnetically short conditions. Numerical solutions are utilized to investigate the effects of nonlocal scale parameters and surface parameters on SH surface wave propagation. Contrary to the results of classical theory, the coupling effects of nonlocal small-scale and surface piezoelectricity are more significant than individual effects. Also, it has been observed that the imperfectness parameter across the interface and the thickness ratio of the bilayer significantly affect the phase velocity. Moreover, 2D and 3D plots of the mode shapes of field variables for the propagation of SH waves are presented graphically. These results are validated by conducting analyses excluding nonlocal effects. This allows us to isolate the specific impact of surface effects in the piezoelectric–piezomagnetic bilayer system, drawing connections to existing results and enhancing the robustness of our findings. This study provides valuable insights into complex wave dynamics, helping to optimize the performance and functionality of such smart composites in various engineering applications.

New Shear Horizontal (SH) Surface-Plasmon-Polariton-like Elastic Surface Waves for Sensing Applications.

The advent of elastic metamaterials at the beginning of the 21st century opened new venues and possibilities for the existence of new types of elastic (ultrasonic) surface waves, which were deemed previously impossible. In fact, it is not difficult to prove that shear horizontal (SH) elastic surface waves cannot exist on the elastic half-space or at the interface between two conventional elastic half-spaces. However, in this paper we will show that SH elastic surface waves can propagate at the interface between two elastic half-spaces, providing that one of them is a metamaterial with a negative elastic compliance s44(ω). If in addition, s44(ω) changes with frequency ω as the dielectric function ε(ω) in Drude's model of metals, then the proposed SH elastic surface waves can be considered as an elastic analogue of surface plasmon polariton (SPP) electromagnetic waves, propagating at a metal-dielectric interface. Due to inherent similarities between the proposed SH elastic surface waves and SPP electromagnetic waves, the new results developed in this paper can be readily transferred into the SPP domain and vice versa. The proposed new SH elastic surface waves are characterized by a strong subwavelength confinement of energy in the vicinity of the guiding interface; therefore, they can potentially be used in subwavelength ultrasonic imaging, superlensing, and/or acoustic (ultrasonic) sensors with extremely high mass sensitivity.

The propagation behavior of SH surface wave in a semi-infinite magneto-electro-elastic solid with the periodically gold strips

This article theoretically investigates the propagation of shear horizontal (SH) surface wave in the periodically deposited gold strips separated by vacuum on the magneto-electro-elastic (MEE) substrate. Using field analysis theory based on Bloch-Floquet theorem and electromagnetic open boundary conditions, dispersion equations are derived. The MEE composite is comprised of 80% PZT4 and 20% CoFe2O4. The dispersion, wave mode shape, electric and magnetic potentials are being modelled and computed for the SH wave on the MEE substrate. It is observed that the bandgap occurs at resonance when the wavelength of the SH wave matches with periodicity of the grating. The width of the bandgap can be increased or decreased by increasing the strip height to periodicity ratio. It is found that the gold grating on the surface of MEE substrate can traps the SH wave by slowing down the wave when the wave number is less or equal to wave number at the resonance condition. It is observed that above the resonance condition, SH wave shows supersonic behavior where the phase velocity of SH wave is greater than the surface wave velocity. The trapping and supersonic behavior of SH wave are more pronounced as the strip height to grating periodicity ratio increases. As the strip height to periodicity ratio increases, the wave trapping is enhanced and the leakage of wave energy in the substrate is reduced. The results are relevant to design the surface acoustic wave devices.

Second gradient continuum model for anisotropic elastic and piezoelectric structures calibrated based on phonon dispersion relations

In this paper, we present a variant of the second gradient continuum model that allows description of the spatial dispersion effects of high-frequency waves in anisotropic crystals. The considered model takes into account the strain and inertia gradient effects and the classical electro-mechanical coupling. The simplified constitutive equations of the model contain seven and four length scale parameters for piezoelectric hexagonal crystals and elastic cubic crystals, respectively. It is shown that all except one length scale parameter can be identified based on the fitting of the continuum model to the lattice dynamics calculations for the dispersion relations of the bulk acoustic phonons. Examples of the identification are presented for hexagonal piezoelectric ZnO and AlN and for cubic diamond and Si crystals. Using a calibrated model, we then obtain the dispersion relations for the high-frequency Bleustein–Gulyaev wave in piezoelectric crystals and for the shear horizontal surface wave in elastic crystals. The last one is predicted by the gradient models only for the high frequencies, while at low frequencies this wave degenerates to the bulk shear wave. Examples of calculations are also provided for the Rayleigh wave propagating through the homogeneous piezoelectric half-space and layered ZnO(AlN)/diamond/Si structures. It is shown that this kind of surface wave can be used to identify the last unknown length scale parameter of the model.

Effects of Schottky junction on surface waves in a piezoelectric semiconducting film over a metal substrate

Shear horizontal (SH) waves propagating in a metal substrate covered with a transversely isotropic piezoelectric semiconductor thin film is analyzed in the present paper. The Schottky junction, which is created by the metal and the n-type piezoelectric semiconductor with a higher Fermi level, can be seen as an electrically gradient layer between the substrate and the thin film. The transfer matrix of the Schottky junction is derived by using Magnus series expansion and approximate laminated medium methods, respectively. The influences of the Schottky junction, semiconductor coupling, doping density, and electric boundary conditions on the dispersion and attenuation and the first three wave modes are discussed via numerical example. It reveals that numerical results obtained by these two methods are well matched and the existence of Schottky junction has less influence on the dispersion of SH surface wave although, but evidently influences on the attenuation. In particular, the mode shapes of electric potential, electric displacement, carrier perturbation density, and the electric current density are affected evidently by the existence of Schottky junction.

Shear Horizontal Surface Waves in a Layered Piezoelectric Nanostructure with Surface Effects.

This work aims to provide a fundamental understanding on the dispersive behaviors of shear horizontal (SH) surface waves propagating in a layered piezoelectric nanostructure consisting of an elastic substrate and a piezoelectric nanofilm by considering the surface effects. Theoretical derivation based on the surface piezoelectricity model was conducted for this purpose, and analytic expressions of the dispersion equation under the nonclassical mechanical and electrical boundary conditions were obtained. Numerical solutions were given to investigate the influencing mechanism of surface elasticity, surface piezoelectricity, surface dielectricity, as well as the surface density upon the propagation characteristics of SH surface waves, respectively. The results also reveal the size-dependence of dispersive behaviors, which indicates that the surface effects make a difference only when the thickness of the piezoelectric nanofilm stays in a certain range.

Shear-Horizontal Surface Waves in Half-Space of Piezoelectric Semiconductor with Initial Stresses

Shear-Horizontal Surface Waves in Half-Space of Piezoelectric Semiconductor with Initial Stresses

Electric field, strain and inertia gradient effects on anti-plane wave propagation in piezoelectric materials

In this study, we derive the dispersion relations for anti-plane waves in the second gradient electroelasticity theory considering the electric field, strain, and inertia gradient effects. Solutions are developed for bulk and surface shear horizontal (SH) waves including Bleustein–Gulyaev and Love waves. It is demonstrated that the presented model describes a normal dispersion of short waves in piezoelectric materials. The influence of additional model parameters (material characteristic length scales) on the phase velocity, coupled electromechanical factor, and attenuation of the SH waves is investigated. The non-classical upper bound for the Love wave velocity in the elastic layer/piezoelectric substrate system is given accounting for spatial dispersion. In the numerical examples, we use typical values of the length scale parameters of the order of the crystal lattice parameters such that all non-classical gradient effects are predicted for the electroelastic waves of the terahertz frequencies.

Mathematical analysis of surface wave transference through imperfect interface in FGPM bedded structure

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.

Giant Magnetoelastic Coupling in a Love Acoustic Waveguide Based on TbCo2 / Fe Co Nanostructured Film on ST-Cut Quartz

Coupling between dynamic strain and magnetization in ferromagnetic thin films has attracted special consideration as it presents both intriguing fundamental physics problems and technological importance for potential multi-functional devices and information handling. The dynamic strain can be generated by acoustic waves including bulk, surface or guided waves. In this work, we propose the theoretical and experimental investigation of the interaction of pure shear horizontal (SH) wave with a uniaxial multilayered TbCo2/FeCo thin film in a delay line configuration fabricated on Quartz ST-90X cut. We evaluate theoretically the evolution of phase velocity as a function of magnetic field and experimentally the variation of the transmission coefficient. A piezomagnetic model was developed allowing us to calculate the elastic stiffness constants of the multilayer as a function of the applied magnetic field. The model was also implemented for acoustic waves dispersion curves calculation. We show that the evolution of phase velocity is dominated by the C66 elastic stiffness constant variation as expected for the case of shear horizontal surface wave. The fabricated device let us exciting both fundamental and third harmonic shear mode at 410 MHz and 1.2 GHz, respectively. For both modes, the theoretical results corroborate very well the experimental ones. At 1.2 GHz the mode exhibits a maximum phase velocity shift close to 2.5% and an attenuation reaching 500 dB/cm, for a sensitivity as high as 250 ppm/Oe. The reported theoretical model and experimental results are of tremendous interest for the development of advanced devices for magnetic field sensing applications as well as investigating magnon-phonon interaction at a fundamental level.

A new Rayleigh-like wave in guided propagation of antiplane waves in couple stress materials.

Motivated by the unexpected appearance of shear horizontal Rayleigh surface waves, we investigate the mechanics of antiplane wave reflection and propagation in couple stress (CS) elastic materials. Surface waves arise by mode conversion at a free surface, whereby bulk travelling waves trigger inhomogeneous modes. Indeed, Rayleigh waves are perturbations of the travelling mode and stem from its reflection at grazing incidence. As is well known, they correspond to the real zeros of the Rayleigh function. Interestingly, we show that the same generating mechanism sustains a new inhomogeneous wave, corresponding to a purely imaginary zero of the Rayleigh function. This wave emerges from 'reflection' of a bulk standing mode: This produces a new type of Rayleigh-like wave that travels away from, as opposed to along, the free surface, with a speed lower than that of bulk shear waves. Besides, a third complex zero of the Rayleigh function may exist, which represents waves attenuating/exploding both along and away from the surface. Since none of these zeros correspond to leaky waves, a new classification of the Rayleigh zeros is proposed. Furthermore, we extend to CS elasticity Mindlin's boundary conditions, by which partial waves are identified, whose interference lends Rayleigh-Lamb guided waves. Finally, asymptotic analysis in the thin-plate limit provides equivalent one-dimensional models.

Analysis of mechanical vibration (SH wave) in Piezo-composite plates

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.

The impact of reinforcement and piezoelectricity on SH wave propagation in irregular imperfectly-bonded layered FGPM structures: An analytical approach

The present paper deals with the propagation behavior of Shear Horizontal surface wave propagating in two distinct models, i.e. functionally graded piezoelectric stratum imperfectly-bonded to a functionally graded piezoelectric substrate with rectangular shaped irregularity at the common interface (Model I) and functionally graded piezoelectric stratum imperfectly-bonded to a functionally graded fiber-reinforced substrate with rectangular shaped irregularity at the common interface (Model II). The dispersion equations of two types of SH waves, i.e. Love wave and Bleustein-Gulyaev wave propagation in Model I and II have been deduced analytically for both electrically open and short condition in distinct cases. The results are found to be in well-agreement with the classical cases of dispersion equation of Love wave and non-dispersive equation of Bleustein-Gulyaev wave. Substantial influence of various affecting parameters, viz. wave number, irregularity, imperfect bonding, piezoelectric coupling, reinforcement and functional gradients on phase velocities of SH waves and on electromechanical coupling has been analysed through numerical and graphical illustrations in distinct vibrational modes. The comparative study of Model I and Model II on the propagation behaviour of SH wave and electromechanical coupling serves as a major highlight of present work.

Shear horizontal wave propagation along a periodic metal grating surface of a magneto-electro-elastic substrate

This paper analyzes shear horizontal (SH) waves propagating in thin metal strips deposited periodically onto the surface of a magneto-electro-elastic (MEE) substrate. The MEE substrate is assumed to be a transversely isotropic crystal with 6 mm symmetry or a hexagonal (6 mm) crystal. A field analysis method, which is based on the Bloch–Floquet theory and the coupled equations of wave motion, is employed to derive the dispersion equations and wave mode shapes. Numerical examples are presented for an MEE composite (PZT4/CoFe2O4) and an aluminum (Al) strip. For comparison, different constituent ratios of PZT4/CoFe2O4 are considered. The effect of the ratios of strip height and width to grating periodicity on frequencies, phase velocities, as well as wave mode shapes is discussed in detail. The results show that there is a bandgap at the resonance condition when the grating periodicity matches the wavelength of the SH surface wave. This metal grating surface can trap SH surface waves by slowing the SH waves. The wave mode shapes indicate that the SH surface waves are trapped mainly on these metal strips. As the ratio of strip height to grating periodicity increases, the trapping effect is more pronounced and the gap becomes wider. The ratio of strip width to grating periodicity significantly affects the behavior of SH surface waves. The present results are relevant in the application of MEE surface acoustic wave resonators.

A novel method for shear horizontal surface waves in periodically layered semi-infinite structures with coating layers

The motivation of this paper is to draw attention to the research of shear horizontal (SH) surface wave dispersions in periodically layered semi-infinite structures with coating layers. Based on the properties of the symplectic matrix, a series of important conclusions regarding this subject are presented and confirmed. The propagation behaviour of SH surface waves in periodically layered semi-infinite structures can be analysed using only a single unit cell, which implies a significant reduction in the computational cost. Then based on the Wittrick-Williams (W-W) algorithm, the proposed method was extended to predict SH surface waves in periodically layered semi-infinite structures with coating layers. All eigenfreqencies can be computed by using the concept of the eigenvalue count. Two types of boundary conditions (free and clamped surfaces) are considered in this study. Finally, serval numerical examples are provided to illustrate the performance of the proposed method, which involves a comparison with previously published results and results obtained via the seeking root technique.

Love waves dispersion by phononic pillars for nano-particle mass sensing

We present a design of a pillared phononic crystal based structure for Love wave manipulation to achieve high mass sensitivity. The structure is made of phononic micro-pillars constructed by stacking tungsten and SiO2 layers, distributed on a substrate designed for Love wave propagation. The multilayered pillar allows the creation of bandgaps, which leads to the existence of resonant modes where the elastic energy is confined within the SiO2 free surface layer of the pillar. We study particularly a resonant mode where this layer exhibits torsional mechanical motion which can only be excited by shear horizontal surface waves. We show that Love wave interaction with the torsional mode gives rise to a sharp attenuation in the surface wave transmission spectrum with a high quality factor. We also study the variation of the mass sensitivity of the system by evaluating the resonant mode's frequency shift induced by a mass perturbation using two theoretical approaches: a perturbation theory based approximation and a numerical method. The system presents very promising mass sensitivity which provides an interesting approach to increase the detection performance of Love wave based bio-sensors.

Shear horizontal wave in a classical elastic half-space covered by a surface membrane treated by the couple stress theory

In the present study, we examine the surface shear horizontal (SH) wave in a classical linear elastic half-space covered by a surface layer modeled by the couple stress theory [Mindlin and Tiersten, Arch. Ration. Mech. Anal. 11, 415 (1962)]. The boundary conditions on the surface of the half space are translated into the “body” forces in the surface layer according to the surface elasticity proposed by Gurtin and Murdoch [Arch. Ration. Mech. Anal. 57, 291 (1975)]. Combining the surface elasticity and the couple stress theory, we find that the surface SH waves are only available for a limited range of wavelengths due to the presence of the micro-length in the couple stress theory.

Shear horizontal surface waves in piezoelectric materials with surface stress

ABSTRACTThe propagation of shear horizontal (SH) surface waves in piezoelectric semi-infinite bodies is investigated theoretically. The surface stress exerting on the boundary is taken into account through surface piezoelectricity theory, and the velocity ranges and existence conditions of such surface waves for both electrically open and shorted cases are derived in detail. Analysis results show that the SH surface waves occurring with surface stress are dispersive in contrast to the classical situation, and the propagation characteristics strongly depend on the relative value of surface elasticity, surface piezoelectricity and surface density.

Surface shear horizontal waves in a double-layered nonlinear elastic half space

Surface shear horizontal waves in a double-layered nonlinear elastic half space