ANALYSIS OF A PIEZOELECTRIC MULTIMORPH IN EXTENSIONAL AND FLEXURAL MOTIONS

Impedance and admittance matrices are presented for the analysis of the beam-type piezoelectric multimorph (PM). Each piezoelectric layer is polarized in the thickness direction. The stacking sequence can be arbitrary, and both the extensional and flexural motions are considered. The variational principle is used for deriving the lumped conjugate parameters: two mechanical ports for the extensional motion, four mechanical ports for the flexural motion, and m electrical ports for the m piezoelectric layers. The resonance and antiresonance frequencies are then easily calculated from the admittance matrices. For the case of all the piezoelectric layers either in series or parallel connection, them +6 ports reduce to the seven ports, and its impedance and admittance matrices are presented. The present methods are applied to the cantilevered PM and their electromechanical behavior is studied. The tip trajectory of the cantilevered piezomotor is also investigated using the presented matrices. It is found that the present methods are very effective in analyzing the multilayer piezoelectric transducers.     

An alternative derivation of dynamic admittance matrix of piezoelectric cantilever bimorph

In this paper, the derivation method used in (J. Microelectromech. Systems 3 (1994) 105) and the solutions of dynamic admittance matrix of a piezoelectric device derived from the method are reviewed. By solving the problem of dynamic responses of a piezoelectric cantilever bimorph with mode analysis method, an alternative approach in the derivation of the dynamic admittance matrix and other related parameters of a piezoelectric system, which can be expressed explicitly in terms of series resonance characteristics of the structure, is presented. It is shown that this form of solutions may offer some conveniences in studying mechanical and electrical properties of the system in the vicinity of resonance frequencies.     

Resonances in the system “piezoelectric emitter-multilayer ultrasonic chamber with losses”

An approach to calculating resonance frequencies and acoustic characteristics of ultrasonic multilayer liquid chambers bordering an air or liquid half-space and loaded to a piezoelectric emitter is proposed. The assumption on the validity of plane motion is accepted. The approach allows for obtaining comprehensive data on physical processes in the chamber. The equation relating electrical admittance of a piezoplate with input impedance of the acoustic load is derived. An unloaded emitter and an emitter loaded to acoustic resistance with constant and frequency-dependent impedances are considered as examples.     

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.     

Dynamic modeling of thickness-mode piezoelectric transducer using the block diagram approach

This paper aims to provide an alternative method to determine the characteristics of a piezoelectric transducer from measurement. A block diagram approach is proposed to analyze the dynamic characteristics of a thickness-mode piezoelectric transducer at its resonance frequency. Based on the feedback loop framework, the input-output relations of the electromechanical interaction of the transducer are described in terms of linear block diagram models. Furthermore, the closed-loop relations from external force to vibration velocity and electric current from generated voltage are easily found by Mason’s rule to characterize the equivalent mechanical admittance and electrical impedance, respectively. An example of a Langevin transducer with 28.15 kHz resonance frequency is illustrated for dynamics analysis. The frequency responses of the piezoelectric transducer, resulting from a force and current input, are respectively measured to identify the system parameters of the feedback model. The experimental results demonstrate the effectiveness of the proposed method.     

Effects of mode coupling on the admittance of an AT-cut quartz thickness-shear resonator

We study the effects of couplings to flexure and face-shear modes on the admittance of an AT-cut quartz plate thickness-shear mode resonator. Mindlin’s two-dimensional equations for piezoelectric plates are employed. Electrically forced vibration solutions are obtained for three cases: pure thickness-shear mode alone; two coupled modes of thickness shear and flexure; and three coupled modes of thickness shear, flexure, and face shear. Admittance is calculated and its dependence on the driving frequency and the length/thickness ratio of the resonator is examined. Results show that near the thickness-shear resonance, admittance assumes maxima, and that for certain values of the length/thickness ratio, the coupling to flexure causes severe admittance drops, while the coupling to the face-shear mode causes additional admittance changes that were previously unknown and hence are not considered in current resonator design practice.     

Numerical difficulties with boundary element solutions of interior acoustic problems

Although boundary element methods have been applied to interior problems for many years, the numerical difficulties that can occur have not been thoroughly explored. Various authors have reported low-frequency breakdowns and artificial damping due to discretization errors. In this paper, it is shown through a simple example problem that the numerical difficulties depend on the solution formulation. When the boundary conditions are imposed directly, the solution suffers from artificial damping, which may potentially lead to erroneous predictions when boundary element methods are used to evaluate the performance of damping materials. This difficulty can be alleviated by first computing an impedance or admittance matrix, and then using its reactive component to derive the solution for the acoustic field. Numerical computations are used to demonstrate that this technique eliminates artificial damping, but does not correct errors in the reactive components of the impedance or admittance matrices, which then causes nonexistence and nonuniqueness difficulties at the interior resonance frequencies for hard-wall and pressure release boundary conditions, respectively. It is shown that the admittance formulation is better suited to boundary element computations for interior problems because the resonance frequencies for pressure release boundary conditions do not begin until the smallest dimension of the boundary surface is at least one half the acoustic wavelength. Aside from producing much more accurate predictions, the admittance matrix is also much easier to interpolate at low frequencies due to the absence of interior resonances. For the example problem considered, only the formulation using the reactive component of the admittance matrix produces accurate solutions as long as the surface element discretization satisfies the standard six-element-per-wavelength rule.     

A FEM-based method to determine the complex material properties of piezoelectric disks

Numerical simulations allow modeling piezoelectric devices and ultrasonic transducers. However, the accuracy in the results is limited by the precise knowledge of the elastic, dielectric and piezoelectric properties of the piezoelectric material. To introduce the energy losses, these properties can be represented by complex numbers, where the real part of the model essentially determines the resonance frequencies and the imaginary part determines the amplitude of each resonant mode. In this work, a method based on the Finite Element Method (FEM) is modified to obtain the imaginary material properties of piezoelectric disks. The material properties are determined from the electrical impedance curve of the disk, which is measured by an impedance analyzer. The method consists in obtaining the material properties that minimize the error between experimental and numerical impedance curves over a wide range of frequencies. The proposed methodology starts with a sensitivity analysis of each parameter, determining the influence of each parameter over a set of resonant modes. Sensitivity results are used to implement a preliminary algorithm approaching the solution in order to avoid the search to be trapped into a local minimum. The method is applied to determine the material properties of a Pz27 disk sample from Ferroperm. The obtained properties are used to calculate the electrical impedance curve of the disk with a Finite Element algorithm, which is compared with the experimental electrical impedance curve. Additionally, the results were validated by comparing the numerical displacement profile with the displacements measured by a laser Doppler vibrometer. The comparison between the numerical and experimental results shows excellent agreement for both electrical impedance curve and for the displacement profile over the disk surface. The agreement between numerical and experimental displacement profiles shows that, although only the electrical impedance curve is considered in the adjustment procedure, the obtained material properties allow simulating the displacement amplitude accurately.     

Excitation of a waveguide transformer

Integral immitance equations for steady-state excitation of a shielded waveguide transformer with any number of arbitrarily arranged adjoint semi-infinite waveguides are derived in the general formulation. Excitation can be carried by arbitrary inner sources (extraneous electric and magnetic currents), as well as by normal modes incident from infinity. The results are extended to the case of nonideal walls for magnetodielectric and metallic inclusions. The results give a generalization of the familiar integral impedance and admittance equations for inhomogeneous waveguides.     

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.     

压电换能器导纳的研究

本对压电换能器的等效电路及导纳圆测定方法进行了介绍．对于提供压电换能器与所在电路间的阻抗匹配有重要意义。     

Electric impedance and amplitude-frequency response of a one-dimensional ultrasonic liquid-filled resonator with flat piezoelectric plates

The impedance method is used to determine the electric impedance of a resonator. The amplitude-frequency response of a one-dimensional liquid-filled ultrasonic resonator is calculated by directly solving the wave equations and piezoelectric effect equations under the corresponding boundary conditions. An analysis of the amplitude-frequency response shows that the simple analytical expression obtained from the aforementioned solution is in good agreement with experimental data. An anomalous variation of the electric current in the radiating piezoelectric plate versus the excitation frequency is theoretically revealed near the high-Q resonance peaks. This effect is confirmed experimentally. It gives rise to errors in the measured absorption coefficient and multiply broadens the resonance peaks when the measurements are performed near the resonance frequencies of the piezoelectric plates.     

高次谐波体声波谐振器机械品质因数的谐振谱特性

高次谐波体声波谐振器(High-overtone Bulk Acoustic Resonator,HBAR)是由基底、压电薄膜及上下电极所组成的器件,它具有高的品质因数Q和多模谐振频谱特性.从给出HBAR的谐振谱出发,以各层的结构(厚度)和材料特性(特性阻抗和机械衰减因子)为参数,系统研究了机械品质因数Q_M的谐振谱特性。Q_M随基底或压电薄膜的厚度变化表现为一系列对应不同阶数的曲线。在给定频率下,Q_M随基底厚度的增加振荡上升,且最终趋于基底材料的机械品质因数,而其随压电薄膜厚度的增加呈波浪式下降。对于给定结构的HBAR,Q_M随频率(阶数)的增加呈波浪式下降。此外,考虑电极的厚度对Q_M的变化规律影响不大。为了获得较大的Q_M,应选择Al/AlN/Al/Sapphire或YAG结构的HBAR,且基底要较厚,压电薄膜和电极厚度要适中。      

Electromagnetic propagation at interfaces and in waveguides in uniaxial crystals

The use of surface-impedance and surface-admittance concepts for analyzing reflection and refraction at an isotropic dielectric interface (first developed about 1938) is extended to include an interface between uniaxial birefringent dielectrics. Total internal reflection and the polarizing (Brewster) angle at an anisotropic interface are shown to be naturally explainable in terms of surface impedance (for TM polarization) and surface admittance (for TE polarization). The allowable modes in an integrated optical uniaxial asymmetric dielectric slab waveguide are also shown to be directly obtainable using the surface impedance/admittance approach. Numerical examples are presented.     

Slotted piezoelectric ring deep ocean hydrophone

Based on the energy method,the underwater resonance frequency equation and electrical admittance curve of the slotted piezoelectric ring are derived.By establishing the equivalent circuit of slotted piezoelectric ring in low-frequency receiving condition,the lowfrequency open circuit voltage sensitivity of slotted piezoelectric ring is deduced.Compared the low-frequency receiving sensitivity of the slotted piezoelectric ring and the complete ring,the thought to design the deep ocean hydrophone is presented,which combines the slotted piezoelectric ring and the free flooded structure.By establishing finite element simulation model of free flooded slotted piezoelectric ring,the relationship between ring structure parameters and low-frequency open circuit voltage sensitivity are discussed.Through the simulation and optimization,the deep-sea slotted piezoelectric ring hydrophone with the resonance frequency of 600 Hz is fabricated.The acoustic and pressure tests results indicated that the low-frequency open circuit voltage sensitivity of free flooded slotted piezoelectric ring hydrophone in work bandwidth 100-300 Hz is-193.2 dB and the least value is-197.9 dB with the-4.7 dB fluctuation.Hydrostatic pressure resistance of 30 Mpa is obtained.Compared with the same structure size free flooded piezoelectric ring hydrophone,the low-frequency open circuit voltage sensitivity of slotted piezoelectric ring hydrophone raised 20 dB.The results verify the practicability of deep ocean hydrophone presented here with free flooded slotted piezoelectric ring structure.     

基于AlN声表面波滤波传感器器件的有限元仿真

声表面波器件是一种利用压电材料的压电效应与逆压电效应工作电子器件, 文章首先详细描述了声表面波器件的设计与仿真过程,运用有限元分析的方法分别计算了利用声表面波的 SAW 器件与利用体波的 BAW 器件的性能与各项参数,对相关的器件进行了计算分析,分别用上述方法研究了基于 AlN 薄膜的声表面波器件和悬臂梁结构的体波器件,推导得出了器件的电学导纳与频率之间的关系, 通过分析器件的导纳-频率曲线,推导出器件内部声波的模式以及合适的工作频率,最终得出在 IDT 周期为 8 微米的情况下,SAW 器件的理想工作频率是 0.7-1.95GHz,BAW 器件的理想工作频率在 0.6-3.2GHz 的结果。     

Scattering from loaded grooves

Electromagnetic scattering from a two-dimensional groove recessed in an arbitrarily thick conducting screen is studied. The groove may be empty or loaded with a lossy material which may or may not completely fill the cavity. For the partially loaded groove, the filling material is assumed electrically dense so that the standard impedance boundary condition is applicable at the top surface of the material. Employing a full-wave analysis, integral equations are derived for the tangential components of the electric field over the aperture. It is shown that the equations are identical for both partially loaded and completely loaded (or empty) cases provided that the aperture admittance of the groove is treated as the equivalent admittance of the internal medium looking into the aperture, thus simplifying the integral equations.When the groove is completely filled by a dense material, the formulation reduces to that corresponding to a direct application of the impedance boundary condition over the aperture.     

Reflection characteristics of chiral microwave absorbing coatings

The formulations of reflection coefficients for metal-backed one- and multi-layered chiral microwave absorbing coatings are derived in a much straight way in this paper. It is found that the propagation of normally incident plane waves in chiral coatings can be treated as in their achiral counterparts if the intrinsic impedance and wavenumber of the achiral structure are replaced by their associated chiral impedance and average chiral wavenumber, respectively. From a practical point of view, examples of one- and two-layered chiral microwave absorbing coatings are given, and the effects of the real and imaginary parts of the chiral admittance on the antireflection characteristics are examined for the first time, the results show that with a appropriate complex chiral admittance, the reduction in reflection can be enhanced and the minimum-reflection-frequency can be controlled.     

Resonance-mode effect on piezoelectric microcantilever performance in air,with a focus on the torsional modes

A high quality factor is preferred for a microresonator sensor to improve the sensitivity and resolution. In this paper we systematically investigate the performance of the microcantilever in different resonance modes, which are the first three flexural modes, the first lateral mode, and the first and the second torsional modes. An aluminum nitride-based piezoelectric cantilever is fabricated and tested under controlled pressure from an ultra-high vacuum to a normal atmosphere, using a custom-built vacuum chamber. From the experiment results, it can be seen that the torsional modes exhibit better quality factors than those of the flexural and lateral ones. Finally, an analytical model for the air damping characteristics of the torsional mode cantilever is derived and verified by comparing with experimental results.     

FREE VIBRATIONS OF SIMPLY SUPPORTED AND MULTILAYERED MAGNETO-ELECTRO-ELASTIC PLATES

Analytical solutions are derived for free vibrations of three-dimensional, linear anisotropic, magneto-electro-elastic, and multilayered rectangular plates under simply supported edge conditions. For any homogeneous layer, we construct the general solution in terms of a simple formalism that resembles the Stroh formalism, from which any physical quantities can be solved for given boundary conditions. In particular, the dispersion equation that characterizes the relationship between the natural frequency and wavenumber can be obtained in a simple form. For multilayered plates, we derive the dispersion relation in terms of the propagator matrices. The present solution includes all previous solutions, such as piezoelectric, piezomagnetic, and purely elastic solutions as special cases, and can serve as benchmarks to various thick plate theories and numerical methods used for the modelling of layered composite structures. Typical natural frequencies and mode shapes are presented for sandwich piezoelectric/piezomagnetic plates. It is shown clearly that some of the modes are purely elastic while others are fully coupled with piezoelectric/piezomagnetic quantities, with the latter depending strongly upon the material property and stacking sequence. These frequency and mode shape features could be of particular interest to the analysis and design of various “smart” sensors/actuators constructed from magneto-electro-elastic composite laminates.