The effect of initial stress on the propagation behavior of SH waves in piezoelectric coupled plates

This study analytically investigates the propagation of shear waves (SH waves) in a coupled plate consisting of a piezoelectric layer and an elastic layer with initial stress. The piezoelectric material is polarized in z-axis direction and perfectly bonded to an elastic layer. The mechanical displacement and electrical potential function are derived for the piezoelectric coupled plates by solving the electromechanical field equations. The effects of the thickness ratio and the initial stress on the dispersion relations and the phase and group velocities are obtained for electrically open and mechanically free situations. The numerical examples are provided to illustrate graphically the variations of the phase and group velocities versus the wave number for the different layers comparatively. It is seen that the phase velocity of SH waves decreases with the increase of the magnitude of the initial compression stress, while it increases with the increase of the magnitude of the initial tensile stress. The initial stress has a great effect on the propagation of SH waves with the decrease of the thickness ratio. This research is theoretically useful for the design of surface acoustic wave (SAW) devices with high performance.     

Effect of external electrical field on characteristics of a Lamb wave in a piezoelectric plate

The influence of a homogeneous electrical field E on the characteristics and propagation conditions of the Lamb wave in a piezoelectric crystalline plate is considered on the basis of the theory of acoustic wave propagation in piezocrystals under the effect of an external electrical field.     

A slow wave with the structure of an electromagnetic wave in piezoelectric and magnetostrictive media

The propagation of elastic waves in piezoelectric and magnetostrictive materials is considered theoretically. It is shown that an elastic wave in a piezoelectric can create not only a longitudinal electric field parallel to the wave normal (longitudinal piezoactivity) but also a transverse field of electric induction (transverse piezoactivity). The presence of a transverse induction field leads to the appearance of a magnetic field perpendicular to the direction of the wave normal and to the induction vector; therefore, the transverse-piezoactive wave is accompanied by a transverse wave having the structure of an electromagnetic wave and propagating with the speed of sound. Transverse-magnetostrictive elastic waves in magnetostrictive dielectrics are accompanied by a similar wave.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 32–36, October, 1976.     

Love waves in a layered functionally graded piezoelectric structure under initial stress

Abstract

To study the effect of initial stress on the propagation behavior of Love waves in a layered functionally graded piezoelectric structure, a mathematical model is established. The piezoelectric layer is taken as exponentially graded material where as half-space is taken as simply elastic substratum. The coupled electromechanical field equations are solved analytically to obtain the mechanical displacements and electrical potential functions for the piezoelectric layer and elastic substrate. The dispersion relations are obtained for electrically open and short cases. The higher mode Love wave propagation has been considered. For numerical interpretation of the results, four sets of piezoelectric layer and elastic substrate have been taken into consideration. Graphical representation reveals about the effect of initial stress and the effect of inhomogeneity parameter on the phase velocity against wave number for electrically open and electrically short cases, respectively.     

Trifurcation of band-gap structure and coexistence of lattice-like states and critical states in piezoelectric period-doubling superlattices

We study the propagation of electromagnetic wave in piezoelectric period-doubling superlattices with using the generalized 4 × 4 transfer matrix method, and the dynamics of electromagnetic wave and acoustic wave is treated on equal footing. The band-gap structure trifurcates, which is understood within the framework of perturbation theory under periodic boundary condition. The uncoupled phononic branch of field distributions is Bloch-wave-like. For the coupled polaritonic branch, the lattice-like field distributions, for which Thue-Morse sequence is famous, also manifest in this piezoelectric period-doubling system and coexist with critical states. They can be characterized as extended if the superlattice size considered is large enough. In fact, our study suggests that such lattice-like field distributions are common phenomena in piezoelectric superlattices irrespective of lattice types and depend only on the frequency and domain widths, they reflect the intrinsic symmetry of the transfer matrices for the particular domain setting and frequency.     

Resonance frequencies of piezoelectric plates surrounded by solid and fluid half-spaces

The design of ultrasound transducers, resonators and other piezoelectric devices usually requires the calculation of the resonance frequencies of piezoelectric plates. Recent studies have shown that the resonance frequencies for plates in vacuum correspond to frequencies where the waveguide group velocity vanishes (zero-group-velocity points). However, those studies are limited to vacuum boundary conditions. The objective of the present study is to analyze the resonance frequencies of layered piezoelectric plates in contact with solid and fluid half-spaces and their relation to the dispersion behavior of the elastic guided wave propagation. Theoretical analysis using partial-wave approach of leaky Lamb waves is performed to study wave propagation in, and resonance behavior of, multilayered plates in contact with solid and fluid half-spaces. A novel observation resulted from this analysis is that, for plates in contact with solid and fluid half-spaces, the resonance frequencies occur at points where the magnitude of the wavenumber reaches a minimum. This frequency is named as a ‘transition frequency’. Such observations are important because they allow an easy identification of resonance frequencies with high amplitude response directly from the dispersion curves. This study will be helpful for the design of piezoelectric components used for resonators and sensors.     

The theoretical simulation of magnetized electron beam effects on radially polarized of an annular cylindrical piezoelectric crystal

By using the equilibrium equations for a hollow cylindrical piezoelectric layer in absence of body forces and taking into the account a magnetized electron beam in hollow region of this system the effects of thermal pressure, electrostatic self field and the strength of external magnetic field of a non-relativistic magnetized electron beam column on radially polarized of an annular cylindrical piezoelectric crystal in the steady state are simulated. The electrostatic potential profile in piezoelectric layer due to the mechanical pressure and electrostatic self field of electron beam are studied. Furthermore the graphs of the difference of potential Δϕ between inner and outer surfaces of piezoelectric versus to electron temperature, density of beam and the strength of external magnetic field are presented.     

Modeling of piezoelectric transducers with combined pseudospectral and finite-difference methods

A new hybrid finite-difference (FD) and pseudospectral (PS) method adapted to the modeling of piezoelectric transducers (PZTs) is presented. The time-dependent equations of propagation are solved using the PS method while the electric field induced in the piezoelectric material is determined through a FD representation. The purpose of this combination is to keep the advantages of both methods in one model: the adaptability of FD representation to model piezoelectric elements with various geometries and materials, and the low number of nodes per wavelength required by the PS method. This approach is implemented to obtain an accurate algorithm to simulate the propagation of acoustic waves over large distances, directly coupled to the calculation of the electric field created inside the piezoelectric material, which is difficult with classical algorithms. These operations are computed using variables located on spatially and temporally staggered grids, which attenuate Gibbs phenomenon and increase the algorithm's accuracy. The two-dimensional modeling of a PZT plate excited by a 50 MHz sinusoidal electrical signal is performed. The results are successfully compared to those obtained using the finite-element (FE) algorithm of ATILA software with configurations spatially and temporally adapted to the FE requirements. The cost efficiency of the FD-PS time-domain method is quantified and verified.     

Modeling electro-mechanical properties of layered electrets: application of the finite-element method

We present calculations on the deformation of two- and three-layer electret systems. The electrical field is coupled with the stress–strain equations by means of the Maxwell stress tensor. In the simulations, two-phase systems are considered, and intrinsic relative dielectric permittivity and Young's modulus of the phases are altered. The numerically calculated electro-mechanical activity is compared to an analytical expression. Simulations are performed on two- and three-layer systems. Various parameters in the model are systematically varied and their influence on the resulting piezoelectricity is estimated. In three-layer systems with bipolar charge, the piezoelectric coefficients exhibit a strong dependence on the elastic moduli of the phases. However, with mono-polar charge, there is no significant piezoelectric effect. A two-dimensional simulation illustrated that higher piezoelectric coefficients can be obtained for non-uniform surface charges and low Poisson's ratio of phases. Irregular structures considered exhibit low piezoelectric activity compared to two-layer structures.     

Anisotropy of Lamb and SH waves propagation in langasite single crystal plates under the influence of dc electric field

Paper is presented the results of computer simulation. Effect of the homogeneous dc electric field influence on the propagation of zero and first order Lamb and SH waves in piezoelectric langasite single crystal plates for a lot of cuts and directions have been calculated. Crystalline directions and cuts with maximal and minimal influence of dc electric field have indicated. Effect of hybridization of plate modes has been discussed.     

The atomistic origin of the inverse piezoelectric effect in α-quartz

Ab initio calculations have been carried out using the FP-APW+lo method in order to understand the atomic origin of the inverse piezoelectric effect in α-quartz. The external electric field was modelled by a saw-like potential V_ext in order to achieve translational symmetry within a supercell (SC) containing 72 atoms. The original trigonal quartz structure was repeated along the [110] direction, which corresponds to the direction of the external field. An electric field with 550 kV/mm was applied and the atomic positions of the SC were relaxed until the forces acting on the atoms vanished. In parts of the SC, V_ext changes almost linearly and thus the relaxed atomic positions can be used to determine the structural response due to the external electric field. The calculations provide the piezoelectric modulus of the correct order of magnitude. In contrast to previous models and in agreement with recent experimental results, the atomic origin of the piezoelectric effect can be described by a rotation of slightly deformed SiO₄ tetrahedra against each other. The change of the Si-O bond lengths and the tetrahedral O-Si-O angles is one order of magnitude smaller than that of the Si-O-Si angles between neighbouring tetrahedra. The calculated changes of X-ray structure factors are in agreement with experiment when the theoretical data are extrapolated down to the much smaller field strength that is applied in the experiment (E<10 kV/mm).     

Vectorial structure of helical hollow Gaussian beams in the far field

The analytical vectorial structure of helical hollow Gaussian beam (HHGB) is investigated in the far field based on the vector plane wave spectrum and the method of stationary phase. The energy flux distributions of HHGB in the far-field, which is composed of TE term with the electric field transverse to the propagation axis, and TM term with the magnetic field transverse to the propagation axis, are demonstrated. The physics pictures of HHGB is illustrated from the vectorial structure, which is important to understand the theoretical aspects of both scalar and vector HHGB propagation.     

Two new designs of lamp-type piezoelectric metamaterials for active wave propagation control

A major limitation of current metamaterials is that they control the wave propagation depending on their structure. Active metamaterials in this paper are designed whose physical structure is fixed, yet the position where they control the wave propagation can be changed by piezoelectric conditions. Two kinds of lamp-type piezoelectric metamaterials were assembled from an aluminum base, rubber plate and steel column, the piezoelectric patches were attached on both sides of the steel column, which can change the equivalent elastic modulus of the whole structure when the pair of patches are accessed by an LC circuit. The equivalent elastic modulus becomes zero or negative when the frequency of the circuit varies between 29,000 Hz and 30,000 Hz, in this case the two kinds of lamp-type piezoelectric metamaterials behave as a wave localization and a wave guide, respectively. The advantage of the lamp-type piezoelectric metamaterials is that we can control the wave propagation actively, as long as we change the position of the piezoelectric patches or choose the kind of lamp-type piezoelectric metamaterial. This is more flexible than a traditional passive metamaterial and provides a new way for us to design some acoustic equipment, such as acoustic cloaking, an acoustic black hole, filter or wave guide.     

Theory of 2×2 switch based on electro-optic and piezoelectric effects in photorefractive LiNbO3 crystal

Based on the electro-optic and piezoelectric effects, the principle of a 2×2 bypass-exchange switch in photorefractive LiNbO₃ crystal is discussed. In photorefractive volume grating, the Bragg condition can be changed by applying a field during readout. That is, by applying a specific field E_s or zero, the diffraction efficiency will be 0 or 1, respectively and this property can be used to realize the bypass or exchange operation of the switch. In this paper, considering both the piezoelectric and electro-optic effects caused by the applied electric field, we analyzed relations of both the specific field and the incident intensity ratio with respect to the writing angles and polarizations of writing beams.     

Theoretical validation on the existence of two transverse surface waves in piezoelectric/elastic layered structures

In this paper, we analytically study the dispersion behavior of transverse surface waves in a piezoelectric coupled solid consisting of a transversely isotropic piezoelectric ceramic layer and an isotropic metal or dielectric substrate. This study is a revisit to the stiffened Love wave propagation done previously. Closed-form dispersion equations are obtained in a very simple mathematical form for both electrically open and shorted cases. From the viewpoint of physical situation, two transverse surface waves (i.e., the stiffened Love wave and the FDLW-type wave) are separately found in a PZT-4/steel system and a PZT-4/zinc system. All the observed dispersion curves are theoretically validated through the discussion on the limit values of phase velocity using the obtained dispersion equations. Those validation and discussion give rise to a deeper understanding on the existence of transverse surface waves in such piezoelectric coupled structures. The results can be used as a benchmark for the study of the wave propagation in the piezoelectric coupled structures and are significant in the design of wave propagation in the piezoelectric coupled structures as well.     

Modeling of Coulomb coupling and acoustic wave propagation in LiNbO3

The angular spectrum propagation technique is applied to modeling of wave propagation through piezoelectric media. The calculations of the angular spectrum propagator are based on the relevant equation for the slowness surface resulting from the solution of the Christoffel equation with piezoelectrically stiffened elastic constants. A two-dimensional FFT algorithm is applied in the final field superposition. We concentrate on the case of Coulomb coupling through local electrical point contacts on both the excitation and detection side. To model that case we superpose solutions for acoustic Green's functions of different propagation modes convoluted with equivalent distributed effective sources. Calculated results are in good agreement with the measured ones.     

Electric field induced nonlinear optical properties of a confined exciton in a ZnO/Zn1−xMgxO strained quantum dot

Electric field induced exciton binding energy as a function of dot radius in a ZnO/Zn_1−xMg_xO quantum dot is investigated. The interband emission as a function of dot radius is obtained in the presence of electric field strength. The Stark effect on the exciton as a function of the dot radius is discussed. The effects of strain, including the hydrostatic and the biaxial strain and the internal electric field, induced by spontaneous and piezoelectric polarization are taken into consideration in all the calculations. Numerical calculations are performed using variational procedure within the single band effective mass approximation. Some nonlinear optical properties are investigated for various electric field strengths in a ZnO/Zn_1−xMg_xO quantum dot taking into account the strain-induced piezoelectric effects. Our results show that the nonlinear optical properties strongly depend on the effects of electric field strength and the geometrical confinement.     

Analysis of the space-time dynamics of acoustic fields on the surface of a solid

The space-time dynamics of an acoustic field produced by a piezoelectric transducer in a pulsed mode is studied. The detection of acoustic fields is achieved using a Doppler laser interferometer. It is shown that, for a pictorial representation of the dynamics of a pulsed process, it is convenient to use the patterns of instantaneous spatial field distributions within the scanning area, the observation of which at successive instants makes it possible to trace the acoustic field variations on a time scale considerably smaller than the period of the ultrasonic wave. Experimental data demonstrating the process of phase propagation along the sample boundary as a function of time are presented. They are in good agreement with theoretical results obtained by using various methods of acoustic field calculation and different scalar potential distributions over the transducer surface. It is shown that the velocity of phase propagation along the sample boundary, which is mainly determined by the wave front curvature of the elastic wave incident on the sample surface, can considerably exceed the wave velocity in the unbounded medium.     

Velocity and attenuation of ultrasonic waves in n-GaAs at low temperatures

Measurements of velocity and attenuation of ultrasonic waves in n-type GaAs have been made between 4.2 and 240 K. They are interpreted in terms of available theory dealing with sound propagation in piezoelectric semiconductors. We find the piezoelectric constant $\text{e}{}_{14}\text{=}\text{0.16 C}\text{m}{}^2$.     

Acoustical method for the determination of the elastic and piezoelectric constants of crystals of classes 6mm and 4mm

An acoustical method is proposed for the determination of the elastic and piezoelectric constants of crystals of classes 6mm and 4mm. The method is based on the technique developed for orthorhombic crystals of class mm2 and described in the previous paper [9]. Only three samples are required for the determination of all elastic and piezoelectric constants of crystals belonging to the two symmetry classes of interest; for the crystals of class 6mm, only two samples are necessary. The proposed method can be used only when the signs of the piezoelectric constants are known beforehand. Knowing the sign of electrostriction for the crystals under study, the relative signs of the piezoelectric constants can be uniquely determined in accordance with the data reported earlier [10]. This approach allows one to extend the method used in the previous paper [9] to crystals of classes 6mm and 4mm.