Piezoelectric Slab Research Articles

Theoretical Analysis and Experimental Verification of Top Orthogonal to Bottom Arrays of Conducting Strips on Piezoelectric Slab

The purpose of this work is to present a theoretical analysis of top orthogonal to bottom arrays of conducting electrodes of infinitesimal thickness (conducting strips) residing on the opposite surfaces of piezoelectric slab. The components of electric field are expanded into double periodic Bloch series with corresponding amplitudes represented by Legendre polynomials, in the proposed semi-analytical model of the considered two-dimensional (2D) array of strips. The boundary and edge conditions are satisfied directly by field representation, as a result. The method results in a small system of linear equations for unknown expansion coefficients to be solved numerically. A simple numerical example is given to illustrate the method. Also a test transducer was designed and a pilot experiment was carried out to illustrate the acoustic-wave generating capabilities of the proposed arrangement of top orthogonal to bottom arrays of conducting strips.

Electromagnetoelastic transport through a piezoelectric slab: Selective parity interplay of electromagnetic and acoustic resonances

We present the complete solution concerning to transport properties of coupled transverse electromagnetic and shear acoustic waves propagating via a piezoelectric slab embedded into a homogeneous dielectric medium. Since the electroacoustics of our setup is governed by four electromagnetoelastic eigenmodes, we had to succeed in developing a 4 × 4 transfer matrix method to analytically resolve the problem. As a result, the exact frequency spectra of the transmission, reflection, and transformation transport coefficients were obtained and analyzed in detail for two basic cases where the piezoelectric slab subjected by electromagnetic/acoustic perturbation generates acoustic/electromagnetic response. We establish that wave transformation is effectively realized in vicinities of electromagnetic and acoustic Fabry–Pérot resonances. Surprisingly, as a consequence of the problem geometry and accepted 4 mm symmetry of the piezoelectric medium, the phenomenon of the resonant parity selection arises: in the vicinity of an electromagnetic Fabry–Pérot resonance of the given (odd/even) parity, only acoustic Fabry–Pérot resonances with opposite (even/odd) parity are excited in the coefficient of generation. The piezoelectric coupling vanishes when the parities of both resonances coincide. The changes in transmission and reflection spectra turn out to be more sophisticated. The phenomenon is observed due to quite great distinction between electromagnetic and acoustic wave numbers provided by the fundamental difference between light and sound velocities. In our analysis, particular attention is also paid to the ability of increasing the mutual transformation of electromagnetic and acoustic fluxes.

Digital speckle shearography setup to measure the field-induced strain map in piezoelectric materials

Residual or induced strains are important factors in the performance of electronic devices, actuators, and sensors. In this paper, we report the application of digital speckle shearography to obtain the two-dimensional field-induced out-of-plane strain maps in a piezoelectric slab under a varying electric field. Both the free-standing and loaded (pinned) states are investigated. The results show field-dependent strain maps with parabolic profiles on the order of 10-4 and 10-3 in the free-standing and pinned states, respectively, in agreement with typical values for piezoelectric ceramics. This study provides a simple, non-destructive, and full-field method to characterize these materials.

A self-positioning linear actuator based on a piezoelectric slab with multiple pads

A component-less, long-driving-region and self-positioning piezoelectric actuator was developed to transmit several gram-weight components. The linear piezoelectric actuator was composed of a piezoelectric slab and comb-shaped capacitive position sensor. The length-to-width ratio of the driving pad was designed to ensure successive in-phase connection when the driving pad was subjected to an electric field. The proposed 44 × 8 × 1.5 mm3 piezoelectric slab had a driving region of 37.5 mm, that is, 85% of the length of the actuator larger than previous studies to save space. Two pairs of capacitive comb-shaped electrodes were screen-printed on a slider clip (mover) and piezoelectric slab (stator) to sense the position of the slider clip. Sensing electrodes abreast of guard electrodes are proposed to collimate the electric field lines and reduce noise. The kinetic model of the driven clip was based on a frictional driving equation revised using the Hammerstein–Wiener model to capture the nonlinearities and dynamic behavior variations with the duty ratios of driving signals. According to the kinetic model, the control strategies were decided and the velocity of the slider clip at any position could be estimated. Based on the velocity estimated using the Hammerstein–Wiener model, a velocity-adaptive Kalman filter was proposed. The prototype generated a maximum velocity of 18.9 mm/s, a mean steady-state error of 25 μm, and a settling time of 2.29 s for a 2.2 g weight driven vertically upwards to a distance of 25 mm.

Wave propagation through a piezoelectric semiconductor slab sandwiched by two piezoelectric half-spaces

The paper analyses the wave propagation through a piezoelectric semiconductor slab sandwiched by two piezoelectric half-spaces. The two piezoelectric half-spaces (left and right) are both AlN materials, the middle piezoelectric semiconductor slab is ZnO material and is assumed to be transversely isotropic. The semiconductor effect is emphasized by considering the coupling mechanical displacement, electric potential and the carrier in the slab. The state transition differential equation is derived based on the reduction of order of the governing equations and the transfer matrix of state is obtained by solving the state transition equation. The present method can deal with not only the homogeneous slab but also the heterogeneous slab. Two cases (incident QP wave and incident QSV wave) are considered, and the energy reflection and transmission coefficients varying with the incident angle are calculated. The results show that the steady carrier density and the exterior biasing electric field have obvious influences on the reflection and transmission coefficients. This investigation provides a new thought for the adjustment and controlling of elastic wave propagation in the laminated structures.

Tunable bandgaps in novel two-dimensional piezoelectric phononic crystal slab

One of the outstanding challenges in phononic crystal development is the ability to achieve bandgap tunability in a low frequency range. The introduction of piezoelectric materials into phononic crystals is an attractive technique for actively controlling the bandgaps, which is reliable, economical and light in weight. Phononic crystal possesses an artificial periodic composite structure whose elastic constant, density and sound velocity change periodically. When the elastic wave passes through a phononic crystal, special dispersion curve is formed due to the interaction among periodically arranged materials. In order to study the tunability of phononic crystal bandgap, we propose a novel two-dimensional piezoelectric phononic crystal structure possessing a wider complete bandgap, which is composed of piezoelectric materials with hard coatings periodically connected by four thin bars. The dispersion relation, transmission spectrum and displacement field are studied by using the finite element method in combination with the Bloch theorem. Numerical results show that the frequency of the first complete bandgap of the new designed phononic crystal slab is lower and the band width is enlarged by a factor of 5 compared with the band width of the traditional binary phononic crystal. Instead of changing the geometry or orientation of the phononic crystal units or inclusions, electrical boundary conditions are used to actively control the frequency bandgap. The boundary condition for electrical open circuit and short circuit are considered in this paper. With different electrical boundary conditions imposed on the surfaces of the piezoelectric inclusions, multiple complete bandgaps can be controlled actively, which means that the new designed phononic crystal structure can adapt to the vibration and noise reduction requirements under different vibration environments. The effect of piezoelectric effect on the band structure is investigated as well. The piezoelectric effect has a great influence on the band structure, with the increase of the piezoelectric constant, a part of bands move to high-frequency and the other part of the bands are kept at the original position, which means that the piezoelectric effect is of benefit to the opening of the complete bandgap. Furthermore, according to the tunability of the bandgap, the switchable piezoelectric phononic crystal slab waveguide is analyzed. Calculation shows that the electrical boundary defects can result in defect bands existing in the complete band gap, and the elastic wave energy flows can be limited by changing the applied electrical boundary conditions. This investigation is conducive to controlling the bandgaps and also reveals potential applications in designing the sensing system and different piezoelectric devices.

Nonlinear magnetoelectric effects in a composite ferromagnetic-piezoelectric structure under harmonic and noise magnetic pumping

Low-frequency nonlinear magnetoelectric effects in a composite structure comprised of a piezoelectric langatate slab sandwiched between two Metglas amorphous alloy magnetostrictive layers under simultaneous harmonic and noise magnetic pumping have been investigated. It is shown that the frequency fp of harmonic pumping is linearly reproduced in the piezoelectric voltage spectrum accompanied by its higher harmonics. Similarly, narrow-band magnetic noise with a central frequency fN is present in the output piezoelectric voltage along with two noise peaks in the vicinity of a double 2fN and zero frequency. Simultaneous application of harmonic and noise magnetic fields produces a noticeably more complex output voltage spectrum containing additional noise satellite lines at frequencies fp±fN, 2fp±fN etc. as well as a noise “pedestal”. Amplitudes of voltage spectral components depend on the applied constant bias magnetic field, scaling as magnetostriction derivatives with respect to this field. The effects observed are well described by the theory of magnetic field mixing in magnetoelectric composites with nonlinear dependence of magnetostriction on applied fields.

Wave propagation through a flexoelectric piezoelectric slab sandwiched by two piezoelectric half-spaces

Reflection and transmission of plane waves through a flexoelectric piezoelectric slab sandwiched by two piezoelectric half-spaces are studied in this paper. The secular equations in the flexoelectric piezoelectric material are first derived from the general governing equation. Different from the classical piezoelectric medium, there are five kinds of coupled elastic waves in the piezoelectric material with the microstructure effects taken into consideration. The state vectors are obtained by the summation of contributions from all possible partial waves. The state transfer equation of flexoelectric piezoelectric slab is derived from the motion equation by the reduction of order, and the transfer matrix of flexoelectric piezoelectric slab is obtained by solving the state transfer equation. By using the continuous conditions at the interface and the approach of partition matrix, we get the resultant algebraic equations in term of the transfer matrix from which the reflection and transmission coefficients can be calculated. The amplitude ratios and further the energy flux ratios of various waves are evaluated numerically. The numerical results are shown graphically and are validated by the energy conservation law. Based on these numerical results, the influences of two characteristic lengths of microstructure and the flexoelectric coefficients on the wave propagation are discussed.

Acoustic-electromagnetic slow waves in a periodical defective piezoelectric slab**Project supported by the National Basic Research Program of China (Grant No. 2012CB921504), the National Natural Science Foundation of China (Grant Nos. 11374154, 10904067, and 11174142), the Natural Science Foundation of Jiangsu Province of China (Grant No. BK20151375), and the Special Fund for Research in Quality Inspection of Public Welfare Industry, China

Coupled slow waves, slow acoustic waves, and electromagnetic waves are simultaneously achieved based on a piezoelectric material, in which a line defect is created within a honeycomb lattice array of cylindrical holes etched in a LiNbO slab. Finite element simulations in frequency domain and time domain demonstrate that a highly localized slow mode is obtained in the defect. Owing to the piezoelectricity of LiNbO, acoustic and electromagnetic waves are coupled with each other and transmit along the line defect. Therefore, in addition to a slow acoustic wave, an electromagnetic wave with a group velocity even lower than conventional acoustic waves is achieved.

Acousto-optical phonon excitation in piezoelectric wurtzite slabs and crystal growth orientation effects

This paper presents a theoretical investigation of phonon dispersion in piezoelectric slabs of hexagonal crystal symmetry (wurtzite). Specifically we solve the fully coupled dispersion relations in a GaN free standing quantum well by varying the crystal growth direction from the [001] axis to the [010] axis. Accounting for the Drude model in solving the fully-coupled dispersion relations, phonon modes will generate an additional phonon band, with a high local density of phonon states, close to the plasma frequency. As opposed to cubic crystals with isotropic permittivity, the location of this band varies with crystal orientation. We also find that the phonon mode dependence on the crystal orientation is more pronounced for small in-plane wavenumbers.

Design and dynamic analysis of a piezoelectric linear stage for pipetting liquid samples

Piezoelectric actuators have been widely used in positioning stages because of their compact size, stepping controllability, and holding force. This study proposes a piezoelectric-driven stage composed of a bi-electrode piezoelectric slab, capacitive position sensor, and capillary filling detector for filling liquid samples into nanopipettes using capillary flow. This automatic sample-filling device is suitable for transmission electron microscopy image-based quantitative analysis of aqueous products with added nanoparticles. The step length of the actuator is adjusted by a pulse width modulation signal that depends on the stage position; the actuator stops moving once the capillary filling has been detected. A novel dynamic model of the piezoelectric-driven stage based on collision interactions between the piezoelectric actuator and the sliding clipper is presented. Unknown model parameters are derived from the steady state solution of the equivalent steady phase angle. The output force of the piezoelectric actuator is formulated using the impulse and momentum principle. Considering the applied forces and related velocity between the sliding clipper and the piezoelectric slab, the stage dynamic response is confirmed with the experimental results. Moreover, the model can be used to explain the in-phase slanted trajectories of piezoelectric slab to drive sliders, but not elliptical trajectories. The maximum velocity and minimum step length of the piezoelectric-driven stage are 130 mm s−1 and 1 μm respectively.

Noninvasive blood pressure monitor using strain gauges, a fastening band, and a wrist elasticity model

This paper proposes a novel continuous noninvasive blood pressure estimation method that is based on the variation of wrist skin strain occurring with changes in diastolic and systolic blood pressure. The wrist elasticity model used to estimate blood pressure was constructed according to an ultrasonic probe indentation method used for measuring and calculating the thicknesses and material properties of skin layers. The strain value of the wrist skin was measured using a dual strain sensor to avoid temperature drift. The dual strain sensor was fabricated using a screen-printing process on a polyimide film. To cause the dual strain sensor to indent the skin for ascertaining the depth to measure skin strain, the wristband is driven by a compact ultrasonic linear motor consisting of a piezoelectric slab and a flap clip. The compact ultrasonic linear motor provides an adequate driving distance, which was estimated using the energy method, and a constant holding force used for strain measurement without input power. In blood pressure measurement experiments performed with 30 subjects, the estimation mean error against a validated cuff-type blood pressure monitor was 1.6mmHg at rest for diastolic pressure. The error increased when the subjects exercised, but returned to near the rest value when the subjects rested after exercise. These results showed that the noninvasive blood pressure monitor can estimate blood pressure with a small fastening force. This device can be used for bedridden patients who require continuous blood pressure monitoring.

Dispersion relations of elastic waves in one-dimensional piezoelectric/piezomagnetic phononic crystal with functionally graded interlayers

The effects of functionally graded interlayers on dispersion relations of elastic waves in a one-dimensional piezoelectric/piezomagnetic phononic crystal are studied in this paper. First, the state transfer equation of the functionally graded interlayer is derived from the motion equation by the reduction of order (from second order to first order). The transfer matrix of the functionally graded interlayer is obtained by solving the state transfer equation with the spatial-varying coefficient. Based on the transfer matrixes of the piezoelectric slab, the piezomagnetic slab and the functionally graded interlayers, the total transfer matrix of a single cell is obtained. Further, the Bloch theorem is used to obtain the resultant dispersion equations of in-plane and anti-plane Bloch waves. The dispersion equations are solved numerically and the numerical results are shown graphically. Five kinds of profiles of functionally graded interlayers between a piezoelectric slab and a piezomagnetic slab are considered. It is shown that the functionally graded interlayers have evident influences on the dispersion curves and the band gaps.

An Investigation of Lateral Modes in FBAR Resonators.

Using first principles and the constitutive equations for a piezoelectric, we solve the 2D acoustic wave inside a single, infinite, piezoelectric membrane in order to study the dispersion of Thin Film Bulk Acoustic Resonator (FBAR) lateral modes, with and without infinitely-thin electrodes. The acoustic eigenfunction is a dual wave, composed of longitudinal and shear components, able to satisfy the 2D acoustic boundary conditions at the vacuum interfaces. For the single piezoelectric slab we obtain analytical expressions of the dispersion for frequencies near the longitudinal resonant frequency (Fs) of the resonator. These expressions are more useful for the understanding of dispersion in FBARs and more elegant than numerical methods like Finite Element Modeling (FEM) and various matrix methods. We additionally find that the interaction between the resonator's electrodes and the acoustic wave modifies the lateral mode dispersion when compared to the case with no electrodes. When correctly accounting for these interactions the dispersion zero is placed clearly at Fs, unlike what is calculated from a 2D model without electrodes where the dispersion zero is placed at Fp. This is important since all experimental evidence of measures FBAR resonators shows that the dispersion zero is at Fs. Furthermore, we introduce an electrical current flow model for the propagating acoustic wave inside the electroded piezoelectric and based on this model we can discuss an electrode-loss mechanism for FBAR lateral modes which depends on dispersion. From our model it results that lateral modes with real kx have higher electrode dissipation if they are closer to the resonant frequency. This is consistent with the typical behavior of measured FBAR filters where the maximum lateral mode damage on the insertion loss takes place for frequencies immediately below Fs.

Dispersion relations of elastic waves in one-dimensional piezoelectric phononic crystal with initial stresses

The effects of initial stresses on dispersion relations of elastic waves in a one-dimensional piezoelectric phononic crystal are studied in this paper. It is taken into account that initial normal and shear stresses acted on piezoelectric slabs and their influences on constitutive equations, governing equations and boundary conditions under in-plane and anti-plane strain cases. Based on the transfer matrices of ingredient piezoelectric slabs, the total transfer matrix of a single cell is derived. Furthermore, the Bloch theorem is used to obtain the dispersive equation of in-plane and anti-plane Bloch waves. The dispersive equations are solved numerically and the numerical results are shown graphically. In the case of normal propagation of elastic waves within piezoelectric slabs, the analytical expressions of the dispersion equation are derived and compared with other literatures. The influences of initial stresses on the dispersive relations are discussed based on the numerical results. It is found that the initial normal stresses have more evident influences than that of initial shear stresses, no matter that in-plane Bloch waves or anti-plane Bloch wave are concerned. Moreover, the influences of initial stress are more evident on the dispersion curves at high frequency than that at the low frequency.

Unified treatment of coupled optical and acoustic phonons in piezoelectric cubic materials

A unified treatment of coupled optical and acoustic phonons in piezoelectric cubic materials is presented whereby the lattice displacement vector and the internal ionic displacement vector are found simultaneously. It is shown that phonon couplings exist in pairs only; either between the electric potential and the lattice displacement coordinate perpendicular to the phonon wave vector or between the two other lattice displacement components. The former leads to coupled acousto-optical phonons by virtue of the piezoelectric effect. We then establish three new conjectures that entirely stem from piezoelectricity in a cubic structured material slab. First, it is shown that isolated optical phonon modes generally cannot exist in piezoelectric cubic slabs. Second, we prove that confined acousto-optical phonon modes only exist for a discrete set of in-plane wave numbers in piezoelectric cubic slabs. Third, it is shown that coupled acousto-optical phonons do not exist at the longitudinal-optical (LO) phonon frequency where the dielectric constant vanishes.

Dispersion relations of elastic waves in one-dimensional piezoelectric/piezomagnetic phononic crystal with initial stresses

The dispersion relations of elastic waves in a one-dimensional phononic crystal formed by periodically repeating of a pre-stressed piezoelectric slab and a pre-stressed piezomagnetic slab are studied in this paper. The influences of initial stress on the dispersive relation are considered based on the incremental stress theory. First, the incremental stress theory of elastic solid is extended to the magneto-electro-elasto solid. The governing equations, constitutive equations, and boundary conditions of the incremental stresses in a magneto-electro-elasto solid are derived with consideration of the existence of initial stresses. Then, the transfer matrices of a pre-stressed piezoelectric slab and a pre-stressed piezomagnetic slab are formulated, respectively. The total transfer matrix of a single cell in the phononic crystal is obtained by the multiplication of two transfer matrixes related with two adjacent slabs. Furthermore, the Bloch theorem is used to obtain the dispersive equations of in-plane and anti-plane Bloch waves. The dispersive equations are solved numerically and the numerical results are shown graphically. The oblique propagation and the normal propagation situations are both considered. In the case of normal propagation of elastic waves, the analytical expressions of the dispersion equation are derived and compared with other literatures. The influences of initial stresses, including the normal initial stresses and shear initial stresses, on the dispersive relations are both discussed based on the numerical results.

Dispersion relations of elastic waves in one-dimensional piezoelectric phononic crystal with mechanically and dielectrically imperfect interfaces

The effects of mechanically and dielectrically imperfect interfaces on dispersion relations of elastic waves in a one-dimensional piezoelectric phononic crystal are studied in this paper. Six kinds of imperfect interfaces between two different piezoelectric materials constituting the phononic crystal are considered. These imperfect interfaces include: the mechanically compliant dielectrically weakly conducting interface, the mechanically compliant dielectrically highly conducting interface, the grounded metallized interface, the low dielectric interface, the tangent fixed interface and the tangent slippery interface. Based on transfer matrices of piezoelectric slabs and imperfect interfaces, the total transfer matrix of a typical single cell in the periodical structure is obtained. Furthermore, the Bloch theorem is used to obtain the dispersive equations of in-plane and anti-plane Bloch waves. The dispersive equations are solved numerically and the numerical results are shown graphically. In the case of normal propagation of elastic waves within piezoelectric slabs, the analytical expressions of the dispersion equations are derived and compared with other literatures. The influences of mechanically and dielectrically imperfect interfaces on the dispersive relations are discussed based on the numerical results.

Investigation of complete bandgaps in a piezoelectric slab covered with periodically structured coatings

The propagation of elastic waves in a piezoelectric slab covered with periodically structured coatings or the so-called stubbed phononic crystal slab is investigated. Four different models are selected and the effects of distribution forms and geometrical parameters of the structured coatings on complete bandgaps are discussed. The phononic crystal slab with symmetric coatings can generate wider complete bandgaps while that with asymmetric coatings is favorable for the generation of multi-bandgaps. The complete bandgaps, which are induced by locally resonant effects, change significantly as the geometry of the coatings changes. Moreover, the piezoelectric effects benefit the opening of the complete bandgaps.

Two-dimensional transient analysis of wave propagation in functionally graded piezoelectric slabs using the transform method

In this study, the transient responses of a functionally graded piezoelectric slab were analyzed using the transform technique. The slab was subjected to a dynamic anti-plane concentrated force and an in-plane point electric displacement on the top surface, and the bottom surface was assumed to be open-circuit or grounded. The analytical solutions were obtained in the Laplace transform domain, and a numerical inversion was performed using the Durbin method. The numerical results showed that an applied point electric displacement may instantaneously induce shear stress waves due to the piezoelectricity for both open-circuit and grounded cases. When the bottom surface was grounded, a visible electric wave was induced by the grounded boundary and the influence of this wave was significant when the gradient coefficient of the functionally graded piezoelectric materials (FGPMs) was large enough.