A study of a 1-3-2 type piezoelectric composite

A novel 1-3-2 type piezoelectric composite is developed. There are piezoelectric ceramic framework supports at transverse and longitudinal directions in its structure, so it is free from the influence of any outside mechanic impact and environmental temperature change. The sample characteristic is good coherence. It has many advantages, such as a high piezoelectricity, lower density and acoustic impedance matching with water and tissue easily. Based on Newnham's series and parallel theory of composites, the calculation formulae of dielectric and piezoelectric constants of a 1-3-2 type piezoelectric composite are deduced. The sample's characteristics indicate that a 1-3-2 type piezoelectric composite's theoretic calculation values are in good agreement with the measurement results. Element samples have been designed, manufactured and measured. The results indicate that the resonant frequency, resonant impedance, piezoelectricity and static capacity of these samples are stable. It is easy to design sensor array elements using this material.     

Comparison of several methods to characterise the high frequency behaviour of piezoelectric ceramics for transducer applications

Thickness mode resonances in commercial piezoelectric ceramics have been characterised as a function of frequency by two methods. The first is based on a fit on the electrical impedance for the fundamental and the overtones. This method has been applied to a large number of PZT ceramic samples and frequency dependence for all the parameters is investigated, in particular for the piezoelectric coefficient e33. The second is based on the measurement of the mechanical displacement at the centre of the surface of a PZT ceramic disk. With a modified KLM scheme, this displacement is modelled. The dielectric, elastic and piezoelectric parameters are extracted and compared for the fundamental and the third overtone. The results are found to be in good agreement.     

Piezoacoustic wave spectra using improved surface impedance matrix: application to high impedance-contrast layered plates

Starting from the general modal solutions for a homogeneous layer of arbitrary material and crystalline symmetry, a matrix formalism is developed to establish the semianalytical expressions of the surface impedance matrices (SIM) for a single piezoelectric layer. By applying the electrical boundary conditions, the layer impedance matrix is reduced to a unified elastic form whether the material is piezoelectric or not. The characteristic equation for the dispersion curves is derived in both forms of a three-dimensional acoustic SIM and of an electrical scalar function. The same approach is extended to multilayered structures such as a piezoelectric layer sandwiched in between two metallic electrodes, a Bragg coupler, and a semi-infinite substrate as well. The effectiveness of the approach is numerically demonstrated by its ability to determine the full spectra of guided modes, even at extremely high frequencies, in layered plates comprising up to four layers and three materials. Negative slope in f-k curve for some modes, asymptotic behavior at short wavelength regime, as well as wave confinement phenomena made evident by the numerical results are analyzed and interpreted in terms of the surface acoustic waves and of the interfacial waves in connection with the bulk waves in massive materials.     

Spectral and perturbation analysis for ultrasonic guided waves

The influence of damage on waves propagating in complex geometry waveguides is investigated through a numerical model formulated by combining the Spectral Finite Element Method and Perturbation Techniques. The resulting numerical tool allows efficient computation of the wave propagation response and the analysis of the effects of damages of various extent and location. The dynamic behavior of the damaged waveguides is described through a general higher order model which couples different waves thus allowing the prediction of mode conversion phenomena. Arbitrary cross-section can be considered through Finite Element (FE) discretization according to well-established Semi-Analytical Finite Element (SAFE) procedures. Two types of damages which allow the application of perturbation theory are considered: a small localized reduction of the thickness and a reduction of material stiffness and density. A validation by comparison with a Finite Element Model as well as numerical examples are presented to illustrate the model capabilities.     

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.     

钹型换能器的优化设计*

本文研究的钹型换能器,是由一个压电陶瓷圆环和一个金属浅球壳组成。为了得到这种钹型换能器的解析解和它在不同介质中的机电性能。首先,根据前人得出的压电陶瓷圆环和金属浅球壳的理论模型,用等效电路法从理论上计算出了该换能器的共振频率并与仿真结果做了对比,发现二者近似吻合,验证了理论计算的可靠性,为这种钹型换能器的优化设计提供了理论指导。然后利用COMSOL Multiphysics分别模拟了压电陶瓷为圆盘和圆环的钹型换能器的共振频率,仿真结果表明：同等条件下,当圆环的外径和圆盘的半径相等时,压电陶瓷为圆环的钹型换能器共振频率更低,使其具有频率低、体积小的特点更加明显。利用数值方法,分析了钹型换能器的几何尺寸对其共振频率、反共振频率及有效机电耦合系数的影响。最后模拟了钹型换能器在水中的机电特性及声压分布。     

A disk-pivot structure micro piezoelectric actuator using vibration mode B11

Micro piezoelectric actuator using vibration mode B(11) (B(mn), where m is the number of nodal circles, n is the nodal diameters) is designed. Different from conventional wobble-type ultrasonic motor using piezoelectric rod or cylinder, piezoelectric disc is used to excite wobble modes and metal cylinder stator is used to amplify the transverse displacement, metal rod rotor is actuated to rotate. The outer diameter of the actuator is 14mm. There are features such as low drive voltage, micromation, and convenient control of wobble state by modifying the structure of stator, etc. Finite element analysis (FEA) of the stator has been made. It is found that the resonant frequency of vibration mode B(11) is 49.03kHz, which is measured at 45.7kHz by the laser vibrometer and impedance analyzer. The rotation speed has been measured, which could be as high as 10,071rpm under an alternating current 100V. Such piezoelectric actuator can be optimized and adjusted to fit practical conditions. It can be applied in the fields of precise instrument, bioengineering and other micro actuator system.     

High speed imaging for material parameters calibration at high strain rate

To describe the material behaviour at high strain rates dynamic experimental tests are necessary, and appropriate constitutive models are to be calibrated accordingly. A way to achieve this is through an inverse procedure, based on the minimization of an error function calculated as the difference between experimental and numerical data coming from Finite Element analysis. This approach, widely used in the literature, has a heavy computational cost associated with the minimization process that requires, for each variation of the material model parameters, the execution of FE calculations. In this work, a faster but yet effective calibration procedure is studied Experimental tests were performed on an aluminium alloy AA6061-T6, by means of a direct tension-compression Split Hopkinson bar. A fast camera with a resolution of 192 × 128 pixels and capable of a sample rate of 100,000?fps captured images of the deformation process undergone by the samples during the tests. The profile of the sample obtained after the image binarization and processing, was postprocessed to derive the deformation history; afterwards it was possible to calculate the true stress and strain, and carry out the inverse calibration by analytical computations. The results of this method were compared with the ones coming from the Finite Element approach.     

A 2D equivalent circuit of piezoelectric ceramic ring for transducer design

In this paper a 2D equivalent circuit of longitudinally polarized piezoelectric ceramic rings is established, which is obtained as an approximated analytical solution of 3D constitutive equations in the hypothesis of axial symmetry when the shearing stress and torsion are ignored. The mechanical part of the equivalent circuit can be divided into two branches; one branch characterizes the longitudinal extensional vibration, the other represents the radial vibration. The two branches, which are coupled to an electrical port by two transformers separately, mechanically couple to each other by some mechanical impedance at the same time. Similar circuit is also presented when piezoelectric disk is concerned. Based on this model it is able to compute all the relations between the input applied voltage and the output forces and velocities on every external surface analytically. Compared with the 1D equivalent circuits, the 2D equivalent circuit gives a more comprehensive predicts of the thickness and radial modes with sufficient accuracy when the ring or disk is thin. When the ring or disk is so thick that the 1D theory is not validated, an effective predict of the coupled vibration can also be presented. Comparisons with the experimental results show this model is rather accuracy in frequency calculation.     

A multiple degree of freedom electromechanical Helmholtz resonator

The development of a tunable, multiple degree of freedom (MDOF) electromechanical Helmholtz resonator (EMHR) is presented. An EMHR consists of an orifice, backing cavity, and a compliant piezoelectric composite diaphragm. Electromechanical tuning of the acoustic impedance is achieved via passive electrical networks shunted across the piezoceramic. For resistive and capacitive loads, the EMHR is a 2DOF system possessing one acoustic and one mechanical DOF. When inductive ladder networks are employed, multiple electrical DOF are added. The dynamics of the multi-energy domain system are modeled using lumped elements and are represented in an equivalent electrical circuit, which is used to analyze the tunable acoustic input impedance of the EMHR. The two-microphone method is used to measure the acoustic impedance of two EMHR designs with a variety of resistive, capacitive, and inductive shunts. For the first design, the data demonstrate that the tuning range of the second resonant frequency for an EMHR with non-inductive shunts is limited by short- and open-circuit conditions, while an inductive shunt results in a 3DOF system possessing an enhanced tuning range. The second design achieves stronger coupling between the Helmholtz resonator and the piezoelectric backplate, and both resonant frequencies can be tuned with different non-inductive loads.     

Definition and measurement of the normalized electrical impedance of lossy piezoelectric resonators for ultrasonic transducers

Relevant equivalent circuit parameters and values of material constants of a piezoelectric resonator can be determined from measurements of its electrical input impedance as a function of frequency. The complex electrical impedance curves and the associated critical frequencies are the basis of this characterization by the piezoelectric resonance method. In this paper, the previously introduced concept of normalized electrical impedance of the lossy resonator, extended to include piezoelectric losses, is applied to the analysis of the effects of different types of intrinsic losses on peak values, bandwidths and characteristic frequencies. The resulting impedance patterns depend solely on the electromechanical coupling coefficient and the loss tangents, providing a useful tool for the analysis of low-Q resonators. The normalized impedance is experimentally evaluated from the basic data provided by an HP 4194A impedance analyser by means of specifically developed ASP programs.     

Free vibration analysis of piezoelectric coupled circular plate with open circuit

A vibration analysis of a circular steel substrate surface bonded by a piezoelectric layer with open circuit is presented. A solution for the electrical potential along the thickness direction of the piezoelectric layer satisfying the open circuit electric boundary condition is developed for the first time. The mechanical model and solutions for the vibration analysis of the piezoelectric coupled circular plate are then established based on the developed electrical potential, the Kirchhoff plate model, and the Maxwell equation. The first four mode shapes and the corresponding resonant frequencies of the plate with two standard boundary conditions are presented in numerical simulations and compared with those of a piezoelectric coupled plate with the closed circuit condition. The simulations show that the resonant frequencies of the open circuit piezoelectric coupled plate are higher than those of the closed circuit piezoelectric coupled plate. Corresponding discussions are thus provided for the higher piezoelectric effect from the open circuit piezoelectric layer.     

A general model of the axle vibration in piezoelectric motors

In the present work a general model of the vibrational behavior of the axle of a piezoelectric motor is proposed. In this motor, a cylinder-shaped permanent magnet, which act as a rotor, is pressed in contact with an end of a steel axle by means of the magnetic forces. The other end of the axle is fitted at the center of a rotating traveling wave generator. A piezoelectric membrane, vibrating in a flexural anti-symmetrical mode, or a thick disk, vibrating in a radial anti-symmetrical mode, can be exploited as traveling wave generators. In the first case a bending moment, in the second case a transverse force is applied to the axle. In both cases, if the driving frequency coincides with a resonance frequency of the axle, the axle acts as a resonant displacement amplifier; a continuous slipping takes place between the axle and the rotor, and a torque is transmitted to the rotor. The proposed model is able to describe the axle vibrational behavior when it is excited by a bending moment, by a transverse force, and also when these two excitations are simultaneously applied. The axle is modeled as a four-port system and all its transfer functions, as well as the transversal displacement along the axle at each frequency can be easily computed. Computed results have been compared with experimental measurements carried out on two motor prototypes that exploit as traveling wave generators a membrane and a disk, respectively. A good agreement was obtained by properly taking into account the loading effect of the generator on the axle.     

Computation of the scattering matrix of guided acoustical propagation by the Wave Finite Element approach

This work aims to study the guided acoustical propagation. The Wave Finite Element method is applied rather than the classic Finite Element method. Finite Element libraries are used for an elementary portion modelling. The dynamic stiffness matrix is then calculated. Periodicity conditions lead to a simple eigenvalue problem and the wave basis can be extracted. The dynamic stiffness matrix of the coupling elements corresponding to the lined parts can be also calculated considering the acoustical impedance. The use of the coupling’s conditions provides the scattering matrix. Within the framework of this method, the dispersion curves, the evolution of the scattering coefficients and the forced response to pressure excitations for both single and coupled waveguides can be represented, and compared to the FE method. The WFE method, treated in literature, and its main interests are reviewed, while adding the impedance notion into the calculation of the scattering matrix.     

A numerical model of streamlines in coplanar electrodes induced by non-uniform electric field

A new model for investigating the non-uniform electric field and potential distribution of fluid flow and streamlines induced by non-uniform electric field with the induced charge in the electrical double layer on the electrode surfaces is presented. Accurate computation of the non-uniform electric field is a pre-requisite for observing fluid flow and streamlines. The electric field distribution is obtained from Laplace's and Neumann's equations. Finite Element Methods is adopted for this work. The simulation results has been compared with available experimental observations of the fluid flow profile obtained by superimposing images of particle movement in a plane normal to the electrode surface. A good agreement is found between the numerical and experimental streamlines.     

Influence of temperature on the properties of one-dimensional piezoelectric phononic crystals

The current study investigates the influence of temperature on a one-dimensional piezoelectric phononic crystal using tunable resonant frequencies. Analytical and numerical examples are introduced to emphasize the influence of temperature on the piezoelectric phononic crystals. It was observed that the transmission spectrum of a one-dimensional phononic crystal containing a piezoelectric material(0.7 PMN-0.3 PT) can be changed drastically by an increase in temperature.The resonant peak can be shifted toward high or low frequencies by an increase or decrease in temperature, respectively.Therefore, we deduced that temperature can exhibit a large tuning in the phononic band gaps and in the local resonant frequencies depending on the presence of a piezoelectric material. Such result can enhance the harvesting energy from piezoelectric materials, especially those that are confined in a phononic crystal.     

性能可调的纵向振动圆锥形超声变幅杆*

提出了一种基于压电效应的性能可调纵向振动圆锥形超声变幅杆,并对其振动性能进行了研究。该变幅杆由传统的圆锥形超声变幅杆和压电陶瓷材料组合而成。论文研究了圆锥变幅杆中压电陶瓷材料的厚度、位置以及电阻抗的改变对变幅杆性能参数的影响,并进行了数值模拟仿真及实验验证。结果表明,通过改变压电陶瓷材料的厚度、位置和电阻抗值,可以实现变幅杆共振频率和位移放大系数的改变。理论计算结果与数值模拟值和实验测试值符合得很好。     

Characteristics of backing impacts on the performance of the thickness mode piezoelectric transducer

The impacts of the thickness, the specific acoustic impedance and the mechanical loss factor of the backing on the performance of the thickness mode piezoelectric transducer are systemically studied, which are focused on the effective electromechanical coupling coefficient and the mechanical quality factor near the center frequency. The results show that with contin?uous increasing of the backing thickness, the effective electromechanical coupling coefficient and the mechanical quality factor are found rapidly declined by oscillation way. With the increase of the difference value of the acoustic impedance between the backing material and the piezoelec?tric material, the effective electromechanical coupling coefficient deceases and the mechanical quality factor increases. Under condition that the thickness of the piezoelectric material is fixed, the effective electromechanical coupling coefficient is found declined with the increase of the mechanical loss factor by monotonous way. The mechanical quality factor has minimum value and the electric characteristic curve tends to be smooth in a given frequency range. The equivalent circuit theory result is in good agreement with the ones by finite element method and the experimental results. The work mentioned above provides a theoretical guidance for the design and experimental fabrication of the thickness mode piezoelectric transducer.     

一种弯张换能器及其共振频率计算方法

提出一种弯张换能器即欧米伽换能器,推导出其共振频率和位移振形函数。把欧米伽换能器分成四个构成部分,利用旋转薄壳理论和压电理论分别求出各部分的能量并进行相加,得到整个欧米伽换能器能量的泛函表达式;把几何边界连续条件和包含待定系数的位移振形函数代入到欧米伽换能器能量泛函中,运用Rayleigh-Ritz法求出欧米伽换能器的共振频率,再把共振频率代入Rayleigh-Ritz偏微分方程和边界方程中求出位移振形函数的待定系数以获得确定的位移振形函数。该方法也被推广到对钹式换能器共振频率和位移振形函数的求解上。上述求解结果与实验结果和数值软件相结合论证了该方法的有效性。可获得以下结论:(1)欧米伽换能器陶瓷片的径向振动与金属端帽顶部的纵向振动同相,减少了声场中的反相分量,易作为低频换能器使用;(2)为解决欧米伽换能器和钹式换能器的优化设计提供了理论支持;(3)文中求解共振频率和位移振形函数的方法,即可以应用在由旋转薄壳组成的弯张换能器上也可以应用在由旋转薄壳组成的其它结构上,具有普遍性。      

Impedance as a characteristic of relaxation polarization

The electrical characteristics of a dielectric material that can be used to determine the parameters of relaxation polarization arising in a dielectric and the influence on these characteristics of the steady leakage electrical conductivity are discussed. For weak relaxation processes at high electrical conductivities, the imaginary part of impedance can be used as such a characteristic. Extrema in the impedance frequency dependence are observed at any conductivity. However, the frequency dependence of the imaginary part of impedance contains two maxima whose frequency positions depend not only on the relaxation time but on other characteristics of the dielectric as well. In addition, the temperature shifts of the extrema of these curves depend not only on the activation energy of the relaxation process but on the activation energy of the electrical conductivity as well.