Parameter optimization of surface acoustic waves via multilayer structures

A method and algorithm for numerical analysis and optimization of the basic parameters of electroacoustic surface waves propagating in multilayer piezoelectric structures are described. Combinations of layer materials and piezoelectric substrates for which an electroacoustic surface wave has optimal parameters of propagation (low dispersion, high electromechanical coupling coefficient, high thermal stability, low diffraction losses, etc.) are found.     

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.     

Tunable bulk acoustic wave resonators with the induced piezoelectric effect in a ferroelectric

An electromechanical model of the piezoelectric effect induced in an acoustic resonator based on a ferroelectric film under the action of a dc or weak ac voltage is developed. The basic equation is obtained by expansion of the free energy in a series with respect to the electric induction and the mechanical deformation. The system of electromechanical equations for variable components of the induction and the mechanical deformation involves all linear terms along with the component of the electrostriction nonlinear with respect to the mechanical deformation. These electromechanical equations made it possible to obtain a one-dimensional approximation for the effective parameters of the material: the piezoelectric modulus and the elastic modulus as a function of the strength of the electric field applied to the acoustic layer. Expressions for the controlled electromechanical coupling coefficient and resonance frequencies of the tunable acoustic resonator are found. It is shown that the most significant parameter responsible for the tuning is the nonlinear electros-triction coefficient M, whose magnitude and sign were evaluated from the available experimental data.     

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.     

Electroacoustic lamb waves in piezoelectric crystal plates

The main characteristics of various types of plate electroacoustic waves propagating in piezoelectric single-crystal plates of various thickness are numerically studied. A number of piezoelectric plates and orientations in them with record high values of the electromechanical coupling coefficient for transverse plate waves are proposed.     

Nanoelectromechanics of piezoelectric indentation and applications to scanning probe microscopies of ferroelectric materials

Nanoelectromechanics of piezoelectric indentation, including the structure of coupled electroelastic fields and stiffness relations, is analysed for flat, spherical, and conical indenter geometries. Exact solutions in elementary functions for electroelastic fields inside the material are obtained using the recently established correspondence principle between the elastic and the piezoelectric problems. The stiffness relations fully describe the indentation process and relate indentation depth, indentation force and bias to the relevant material properties and indenter parameters. This extends the results of Hertzian mechanics to piezoelectric materials. The stiffness relations are utilized for quantitative understanding of the electromechanical scanning probe microscopies (SPM) of ferroelectric and piezoelectric materials, including piezoresponse force microscopy, atomic force acoustic microscopy, scanning near-field acoustic microscopy, and heterodyne ultrasonic-electrostatic force microscopy. The structure of the electroelastic field yields a quantitative measure of signal generation volume in electromechanical SPMs and also provides a quantitative basis for the analysis of tip-induced polarisation switching and local hysteresis loop measurements.     

Transverse surface waves in a layered structure with a functionally graded piezoelectric substrate and a hard dielectric layer

As to an ideally layered structure with a functionally graded piezoelectric substrate (material parameters change continuously along the thickness direction) and a hard dielectric layer, the existence and propagation behavior of transverse surface waves is studied by analytical technique. The dispersion equations for the existence of the transverse surface waves with respect to phase velocity are obtained for electrically open and short circuit conditions, respectively. A detailed investigation of the effect of gradient coefficient on dispersion relation, electromechanical coupling factor and penetration depth is carried out. It is found by numerical examples that adjusting gradient coefficient makes the electromechanical coupling factor of the transverse surface waves achieve quite high values at some appropriate ratio values of the layer thickness to the wavelength, and at the same time, the penetration depth can be reduced to the same order as the wavelength.     

Love wave propagation in functionally graded piezoelectric material layer

An exact approach is used to investigate Love waves in functionally graded piezoelectric material (FGPM) layer bonded to a semi-infinite homogeneous solid. The piezoelectric material is polarized in z-axis direction and the material properties change gradually with the thickness of the layer. We here assume that all material properties of the piezoelectric layer have the same exponential function distribution along the x-axis direction. The analytical solutions of dispersion relations are obtained for electrically open or short circuit conditions. The effects of the gradient variation of material constants on the phase velocity, the group velocity, and the coupled electromechanical factor are discussed in detail. The displacement, electric potential, and stress distributions along thickness of the graded layer are calculated and plotted. Numerical examples indicate that appropriate gradient distributing of the material properties make Love waves to propagate along the surface of the piezoelectric layer, or a bigger electromechanical coupling factor can be obtained, which is in favor of acquiring a better performance in surface acoustic wave (SAW) devices.     

Potential of a piezoelectric energy harvester from sea waves

A sea wave energy harvester from the longitudinal wave motion of water particles is developed. The harvester consisting of a cantilever substrate attached by piezoelectric patches and a proof mass is used to collect electrical energy owing to the electromechanical coupling effect of the piezoelectric patches from the longitudinal wave motion. To describe the energy harvesting process, a mathematical model is developed to calculate the output charge and voltage from the piezoelectric patches according to the Airy linear wave theory and classical elastic beam model. Results show that the mean value of the generated power increases with the increase in the ratio of the width to the thickness of the cantilever, the wave height, the sea depth (which equals to the cantilever height in this study), the ratio of the proof mass to the cantilever mass, and the ratio of the sea depth to the wave length. A value of the power up to 55 W can be realized for a practical sea wave with the values of the sea depth, wave height and wave length to be 3 m, 2 m, and 15 m, respectively. The collected power harvesting with respect to different categories of the sea waves are provided. Our simulations also show the generated electric power can be further increased by an increase in dimensions of the harvester considering the scale effect. This research develops a new technique for energy harvesting from sea waves by piezoelectric energy harvesters.     

Love waves in functionally graded piezoelectric materials by stiffness matrix method

A numerical matrix method relative to the propagation of ultrasonic guided waves in functionally graded piezoelectric heterostructure is given in order to make a comparative study with the respective performances of analytical methods proposed in literature. The preliminary obtained results show a good agreement, however numerical approach has the advantage of conceptual simplicity and flexibility brought about by the stiffness matrix method. The propagation behaviour of Love waves in a functionally graded piezoelectric material (FGPM) is investigated in this article. It involves a thin FGPM layer bonded perfectly to an elastic substrate. The inhomogeneous FGPM heterostructure has been stratified along the depth direction, hence each state can be considered as homogeneous and the ordinary differential equation method is applied. The obtained solutions are used to study the effect of an exponential gradient applied to physical properties. Such numerical approach allows applying different gradient variation for mechanical and electrical properties. For this case, the obtained results reveal opposite effects. The dispersive curves and phase velocities of the Love wave propagation in the layered piezoelectric film are obtained for electrical open and short cases on the free surface, respectively. The effect of gradient coefficients on coupled electromechanical factor, on the stress fields, the electrical potential and the mechanical displacement are discussed, respectively. Illustration is achieved on the well known heterostructure PZT-5H/SiO₂, the obtained results are especially useful in the design of high-performance acoustic surface devices and accurately prediction of the Love wave propagation behaviour.     

New polymer-containing piezoelectric materials

A review is presented of the data on the design of polymer-containing piezoelectric materials: electrets exhibiting a piezoelectric effect, ferroelectric polymers, piezoelectric composites (piezoelectric ceramic + polymer), and new piezoelectric polymer materials, such as piezoelectrics based on porous polymers and elastic active dielectrics, whose piezoelectric properties considerably surpass the characteristics of conventional piezoelectric materials, as well as the characteristics of electromechanical and mechanoelectrical transducers operating in receiving, generating, and deformation-inducing modes.     

Calculation of thermostable directions and the effect of external electric field on the propagation of Lamb and SH waves in a langasite-crystal plate

The effect of dc electric field E on the characteristics, propagation conditions, and temperature delay coefficients of Lamb and SH waves in a piezoelectric langasite plate is considered based on the theory of acoustic-wave propagation in piezoelectric crystals exposed to such a field. The cuts characterized by a thermal stability and large electromechanical coupling coefficient are determined.     

Electromechanical properties and anisotropy of acoustic wave propagation in CuB<Subscript>2</Subscript>O<Subscript>4</Subscript> copper metaborate

The propagation of bulk acoustic waves in single-crystal CuB₂O₄ copper metaborate is studied. The elastic, piezoelectric, and dielectric constants are calculated. The anisotropy in the parameters of bulk acoustic wave propagation in this crystal are determined.     

Frequency-dependent localization length of SH-wave in randomly disordered piezoelectric phononic crystals

In this paper, the localization length that represents the distance of elastic waves propagating along the disordered periodic structures is defined as the reciprocal of the smallest positive Lyapunov exponent, i.e. the localization factor. The algorithm for determining all the Lyapunov exponents in continuous dynamic systems presented by Wolf et al. is employed to calculate those in discrete dynamic systems. Numerical results of the localization lengths of SH-wave are presented and discussed in ordered and disordered piezoelectric phononic crystals to identify the different effect degrees for the decay of electrical potential in the polymers and the randomness on the localization level. For the disordered case, disorder in the thickness of the polymers and disorder in the elastic constant of the piezoelectric ceramics are all considered. The results show that some parameters such as the incident angle of elastic wave, the randomness degree and the piezoelectricity of piezoelectric ceramics and so on have pronounced effects on the frequency-dependent localization length.     

Stoney formula for piezoelectric film/elastic substrate system

With the trends in miniaturization, and particularly the introduction of micro- and nano-electro-mechanical system,piezoelectric materials used in microelectronic devices are deposited usually in the form of thin film on elastic substrates.In this work, the bending of a bilayer comprising a piezoelectric film deposited on an elastic substrate, due to the mismatch,is investigated. An analytic formula relating the curvature of the bilayer to the mismatch, the electroelastic constants and the film thickness is obtained, and from this formula, a transverse piezoelectric constant d_31 can be estimated. Meanwhile the influence of electromechanical coupling coefficient on the curvature is discussed.     

Size-dependent dispersion characteristics in piezoelectric nanoplates with surface effects

In this paper, surface effects on the dispersion characteristics of elastic waves propagating in an infinite piezoelectric nanoplate are investigated by using the surface piezoelectricity model. Based on the surface piezoelectric constitutive theory, the presence of surface stresses and surface electric displacements exerting on the boundary conditions of the piezoelectric nanoplate is taken into account in the modified mechanical and electric equilibrium relations. The partial wave technique is employed to obtain the general solutions of governing equations, and the dispersion relations with surface effects are expressed in an explicit closed form. The impacts of surface piezoelectricity, residual surface stress and plate thickness on the propagation properties of elastic waves are analyzed in detail. Numerical results show that the dispersion behaviors in piezoelectric nanoplates are size-dependent, and there exists a critical plate thickness above which the surface effects may vanish.     

Study on the electromechanical coupling coefficient of Rayleigh-type surface acoustic waves in semi-infinite piezoelectrics/non-piezoelectrics superlattices

The electromechanical coupling coefficient of Rayleigh-type surface acoustic waves in semi-infinite piezoelectrics/non-piezoelectrics superlattices is investigated by the transfer matrix method. Research results show the high electromechanical coupling coefficient can be obtained in these systems. The optimization design of it is also discussed fully. It is significantly influenced by electrical boundary conditions on interfaces, thickness ratios of piezoelectric and non-piezoelectric layers, and material parameters (such as velocities of pure longitudinal and transversal bulk waves in non-piezoelectric layers). In order to obtain higher electromechanical coupling coefficient, shorted interfaces, non-piezoelectric materials with large velocities of longitudinal and transversal bulk waves, and proper thickness ratios should be chosen.     

Continuum theory for nanotube piezoelectricity

We develop and solve a continuum theory for the piezoelectric response of one-dimensional nanotubes and nanowires, and apply the theory to study electromechanical effects in boron-nitride nanotubes. We find that the polarization of a nanotube depends on its aspect ratio, and a dimensionless constant specifying the ratio of the strengths of the elastic and electrostatic interactions. The solutions of the model as these two parameters are varied are discussed. The theory is applied to estimate the electric potential induced along the length of a boron-nitride nanotube in response to a uniaxial stress.     

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.