Effects of coupled vibrations on the parameters of tangentially polarized stripe-electroded piezoelectric cylinders (L)

The effects of coupled vibrations on the piezoelectric properties and electroacoustic transducer performance of radially polarized hollow cylindrical elements as a function of the choice of height-to-diameter ratio have been well documented [J. Acoust. Soc. Am. 120(3), 1374-1380 (2006); J. Acoust. Soc. Am. 122(6), 3419-3427 (2007)]. This letter presents experimental work on the effects of coupled (circumferential, axial, and flexural) vibrations on the resonance frequencies, effective electromechanical coupling coefficient, and acoustical performance of tangentially polarized piezoceramic cylindrical elements. Comparisons are made with analytical predictions of the properties of uniformly circumferentially polarized cylinders.     

Elastic properties of spherically anisotropic piezoelectric composites

Effective elastic properties of spherically anisotropic piezoelectric composites, whose spherically anisotropic piezo-electric inclusions are embedded in an infinite non-piezoelectric matrix, are theoretically investigated. Analytical solutions for the elastic displacements and the electric potentials under a uniform external strain are derived exactly. Taking into account of the coupling effects of elasticity, permittivity and piezoelectricity, the formula is derived for estimating the effective elastic properties based on the average field theory in the dilute limit. An elastic response mechanism is revealed, in which the effective elastic properties increase as inclusion piezoelectric properties increase and inclusion dielectric properties decrease. Moreover, a piezoelectric response mechanism, of which the effective piezoelectric response vanishes due to the symmetry of spherically anisotropic composite, is also disclosed.     

Analysis of Functionally Graded Piezoelectric Cylinders in a Hygrothermal Environment

This paper presents an analytical solution for the interaction of electric potentials, electric displacement, elastic deformations, and describes hygrothermal effect responses in hollow and solid cylinders, subjected to mechanical load and electric potential. Exact solutions for displacement, stresses and electric potentials in functionally graded piezoelectric material are determined using the infinitesimal theory. The material properties coefficients of the present cylinder are assumed to be graded in the radial direction by a power law distribution. Numerical examples display the significant of influence of material inhomogeneity. It is interesting to note that selecting a specific value of inhomogeneity parameter can optimize the piezoelectric hollow and solid cylinders responses, which will be of particular importance in modern engineering designs.     

Effects of coupled vibrations on the acoustical performance of underwater cylindrical shell transducers

An experimental investigation of the effects of coupled vibrations on the acoustical performance of underwater transducers made from radially polarized, thin walled, air-backed, piezoelectric cylinders as a function of their height-to-diameter aspect ratio is presented. Characteristics of the frequency response, directivity patterns, and effectiveness of the transducers are considered in comparison with analogous characteristics for the transducers comprised of mechanically separated rings, otherwise having the same geometry. Recommendations are made on the application of cylindrical piezoelectric elements with different aspect ratios for underwater transducer applications.     

Prediction of the properties of two-phase composites with a piezoactive component

The effective dielectric, piezoelectric, and elastic constants of two-phase macroscopically piezoactive 3-0 and 3-3 composites are calculated. It is assumed that one of the components is a polarized ferroelectric ceramic material and the other is an inactive material with variable elastic properties. The limiting case when the elastic compliances of the inactive material tend to infinity (porous ferroelectric ceramics) is considered. The adequacy of this model to production technologies of piezoelectric composites is discussed. Computational results are compared with experimental data.     

Electromechanical response of 2-2 layered piezoelectric composites: A micromechanical model based on the asymptotic homogenization method

A micromechanical model based on the asymptotic homogenization technique has been developed to predict the complete elastic, dielectric and piezoelectric properties of a general 2-2 layered piezoelectric composite where the constituent phases are elastically anisotropic and piezoelectrically active. Two classes of layered piezoelectric composites (i.e. longitudinally and transversely layered) are considered in two widely different ceramic- and polymer-based systems and their effective properties are obtained in the limits of both large-volume (i.e. bulk) and small-volume (i.e. thin-film) systems. It is demonstrated that: (i) in the bulk, ceramic–ceramic layered composite system, the elastic, piezoelectric, and dielectric properties of the composites vary linearly with volume fraction of the second phase, while in the bulk ceramic–polymer layered composite system, the corresponding properties vary non-linearly with volume fraction of the second phase; (ii) in the prismatic (thin-film) layered piezoelectric composite system, the non-vanishing, effective elastic, piezoelectric and dielectric properties vary linearly with the volume fraction of the second phase for both the longitudinally and transversely layered composite structures in the ceramic–ceramic and the ceramic–polymer composite systems; (iii) the ceramic–polymer piezoelectric layered composites that incorporate a low density polymeric phase with lower acoustic impedance generally exhibit enhanced piezoelectric coupling constants and lowered acoustic impedance; (iv) the longitudinally layered composites exhibit higher piezoelectric coupling constants and lower acoustic impedance compared to that of the transversely layered composites; and (v) the best combination of properties for applications such as hydrophones (i.e. the highest piezoelectric coupling constants and the lowest acoustic impedance) is obtained in the ceramic–polymer, longitudinally layered, thin-film, piezoelectric composites.     

径向复合圆柱压电超声换能器

提出一种三元径向复合圆柱压电超声换能器,并对其径向振动特性进行了研究。基于弹性力学理论及机电类比原理,导出了柱坐标系中分割处理径向极化压电陶瓷管准厚度模振动及薄壁短圆管径向振动的机电等效电路;利用径向力和振速连续的边界条件,得出了径向复合圆柱压电换能器系统的径向振动机电等效电路及其共振频率方程。探讨了换能器径向共振频率及有效机电耦合系数随其几何尺寸的变化关系。研究表明,换能器的径向共振频率及有效机电耦合系数随其内芯半径和预应力管壁厚度增大而降低。研制了一些径向复合圆柱压电换能器,并对其径向共振频率进行了测试。结果表明,理论与实验结果基本一致。      

Wave propagation in layered piezoelectric rectangular bar: An extended orthogonal polynomial approach

Wave propagation in multilayered piezoelectric structures has received much attention in past forty years. But the research objects of previous research works are only for semi-infinite structures and one-dimensional structures, i.e., structures with a finite dimension in only one direction, such as horizontally infinite flat plates and axially infinite hollow cylinders. This paper proposes an extension of the orthogonal polynomial series approach to solve the wave propagation problem in a two-dimensional (2-D) piezoelectric structure, namely, a multilayered piezoelectric bar with a rectangular cross-section. Through numerical comparison with the available reference results for a purely elastic multilayered rectangular bar, the validity of the extended polynomial series approach is illustrated. The dispersion curves and electric potential distributions of various multilayered piezoelectric rectangular bars are calculated to reveal their wave propagation characteristics.     

Singular variation property of elastic constants of piezoelectric ceramics shunted to negative capacitance

Piezoelectric shunt damping has been widely used in vibration suppression, sound absorption, noise elimination, etc.In such applications, the variant elastic constants of piezoelectric materials are the essential parameters that determine the performances of the systems, when piezoelectric materials are shunted to normal electrical elements, i.e., resistance,inductance and capacitance, as well as their combinations. In recent years, many researches have demonstrated that the wideband sound absorption or vibration suppression can be realized with piezoelectric materials shunted to negative capacitance. However, most systems using the negative-capacitance shunt circuits show their instabilities in the optimal condition, which are essentially caused by the singular variation properties of elastic constants of piezoelectric materials when shunted to negative capacitance. This paper aims at investigating the effects of negative-capacitance shunt circuits on elastic constants of a piezoelectric ceramic plate through theoretical analyses and experiments, which gives an rational explanation for why negative capacitance shunt circuit is prone to make structure instable. First, the relationships between the elastic constants c_(11), c_(33), c_(55) of the piezoelectric ceramic and the shunt negative capacitance are derived with the piezoelectric constitutive law theoretically. Then, an experimental setup is established to verify the theoretical results through observing the change of elastic constant c_(55) of the shunted piezoelectric plate with the variation of negative capacitance.The experimental results are in good agreement with the theoretical analyses, which reveals that the instability of the shunt damping system is essentially caused by the singular variation property of the elastic constants of piezoelectric material shunted to negative capacitance.     

Wave propagation in non-homogeneous magneto-electro-elastic hollow cylinders

A dynamic solution is presented for the propagation of harmonic waves in imhomogeneous (functionally graded) magneto-electro-elastic hollow cylinders composed of piezoelectric BaTiO₃ and magnetostrictive CoFe₂O₄. The materials properties are assumed to vary in the direction of the thickness according to a known variation law. The Legendre orthogonal polynomial series expansion approach is employed to determine the wave propagating characteristics in the hollow cylinders. The dispersion curves of the imhomogeneous piezoelectric-piezomagnetic hollow cylinder and the corresponding non-piezoelectric and non-piezomagnetic hollow cylinders are calculated to show the influence of the piezoelectricity and piezomagnetism. Electric potential and magnetic potential distributions are obtained to illustrate the different influences of the piezoelectricity and piezomagnetism and the different influences of the piezoelectric effect and piezomagnetic effect on longitudinal modes and torsional modes. For the radial polarizing piezoelectric-piezomagnetic hollow cylinder, the piezoelectric effect and piezomagnetic effect take mostly on the longitudinal mode. Finally, a hollow cylinder at different ratio of radius to thickness is calculated to show the influence of the ratio on the piezoelectric effect and piezomagnetic effect.     

径向极化压电陶瓷长圆管复合超声换能器的径向振动

提出了一种圆管式径向复合压电陶瓷换能器,并对其径向振动特性进行了分析。该换能器由径向极化的压电陶瓷圆管以及金属外圆管组成。利用解析法得出了金属圆管以及具有任意壁厚的径向极化压电陶瓷圆管径向振动的机电等效电路。基于金属圆管与压电圆管的机械边界条件,得出了换能器的六端机电等效电路。在此基础上得出了换能器共振及反共振频率方程的解析表达式,给出了换能器的共振及反共振频率与其几何尺寸之间的依赖关系。利用数值方法对换能器的径向振动特性进行了模拟及仿真,并与解析结果进行了比较。最后,设计并加工了一些径向复合管式压电陶瓷换能器,利用精密阻抗分析仪对其共振及反共振频率进行了实验测试。研究结果表明,利用解析理论得出的换能器共振及反共振频率与数值模拟结果以及实验测试结果符合很好。      

A modular scanning tunneling microscope with an interchangeable elastic closed cell and external actuators

We introduce a novel modular cell based scanning tunneling microscope with external piezoelectric actuators. A tip and a sample are contained in a closed interchangeable cell, consisting of a stiff top plate and a bottom part, fastened together by an elastic material. The bottom part, containing a scanning tip, is fastened to a base unit while the top plate, containing a sample, is capable of scanning motion by external piezoelectric actuators mounted in the same base unit. The actuators are pre-loaded by the deformation of the elastic material of the cell, giving an increased stability. This design is expected to simplify the scanning tunneling microscope (STM) operation in difficult environments greatly by enclosing only the tip and sample in a small cell-module, which is pluggable to a scanning mechanism and other supportive functionalities. A frequency characterization and an image scan showing atomic resolution of highly oriented graphite in air, at room temperature, is presented.     

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.     

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.     

Complete ultrasonic transducer characterization and its use for models and measurements

Transmitting and receiving properties of ultrasonic piezoelectric crystal transducers that directly affect the measured output voltage in an ultrasonic measurement system are described. These transducer properties are the transducer's electrical impedance and sensitivity, the transducer's radiation impedance, and the transducer's effective parameters (effective radius and focal length). It is shown that all these properties can be obtained with a series of calibration measurements, most of them purely electrical in nature. This series of measurements is described, including a newly developed method that makes the determination of the transducer sensitivity simpler than with previous methods. It is demonstrated that by combining these transducer properties with knowledge of the electrical properties of the pulser/receiver and cabling and the acoustic/elastic processes present in an ultrasonic measurement system, it is possible to accurately simulate the output voltage of the system.     

复合圆环弯曲振动四极子模态分析

针对压电圆环弯曲振动机电转换性能较差的问题,提出了一种复合圆环弯曲振动换能器,它由一个径向极化的压电陶瓷内圆环和一个金属外圆环复合而成。基于能量原理推导得到了复合圆环弯曲振动的谐振频率和有效机电耦合系数,探讨了弯曲振动四极子模态特性与其结构尺寸间的关系。当压电圆环尺寸不变时,随外侧金属圆环壁厚增加,复合圆环弯曲振动四极子模态谐振频率上升,有效机电耦合系数迅速上升到极大值后缓慢下降。最后,设计制作了圆环换能器并对其谐振频率和有效机电耦合系数进行了实验测试,测试结果与解析结果和数值模拟结果吻合得较好。      

Ab initio lattice dynamics and piezoelectric properties of MgS and MgSe alkaline earth chalcogenides

We have studied structural, elastic, dielectric, vibrational, and piezoelectric properties of rock-salt and zinc-blende Mg alkaline earth chalcogenides (MgS, and MgSe) by using the plane-wave pseudopotential method within the local density approximation. The calculated lattice constant, bulk modulus, and elastic constants for these compounds are found to be in good agreement with experiment. The density functional perturbation theory has been employed to derive the Born effective charge and high-frequency dielectric constant and to calculate phonon dispersion curves and density of states. The piezoelectric constant has also been determined. The calculated results are compared with theory and experiment when available and showed reasonable agreement. In other cases, our results are predictions. The pressure dependence of the studied quantities has been examined and discussed. The pressure coefficients and mode Grüneisen parameters are determined.     

Propagation of elastic waves in hexagonal piezoelastic crystals

The propagation of elastic waves in an arbitrary direction through a hexagonal piezoelectric crystal is investigated. Orientational relations are obtained in analytic form for the effective elastic moduli and the piezoelectric and dielectric constants, and also for the basic parameters of the elastic waves: the phase velocity, electromechanical coefficient, and the divergence between the displacement vector and the energy flux. Expressions are given for the directions in which the electromechanical coefficient takes an extremal value, and the basic parameters are calculated for cadmium sulfide.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 101–105, May, 1977.     

Piezoelectric relaxations in polymers: Spherical dispersion model

For the interpretation of piezoelectric relaxation in oriented polymers, a spherical dispersion model is proposed in which piezoelectric spheres are dispersed in a nonpiezoelectric medium. The influence of the dielectric and elastic relaxations in the medium and the sphere on the piezoelectric stress constant and strain-constant is analyzed in detail. The origins of piezoelectric relaxations in oriented poly-γ-methyl-L-glutamate are assigned to the elastic relaxation (at about ?70°) and the dielectric relaxation (at about 0°C) in the piezoelectric phase, and the elastic relaxation (at about 100°C) in the non-piezoelectric phase, respectively.     

Wave propagation in axially polarized piezoelectric hollow cylinders of sector cross section

In this paper, the problem of electroelastic waves propagating in piezoelectric hollow cylinders of sector cross section is studied for the case when the boundary surfaces of sector cut are covered by non-extensible membranes. The three-dimensional linear equations of motion for the piezoelectric cylinder are analytically integrated and different boundary conditions on the cylindrical surfaces yield frequency equations, which relate the frequencies of elastic waves to their wavenumbers. Numerical results for waveguides with various boundary conditions are presented to illustrate the approach. Analysis of the dispersion spectra is carried out, and cutoff frequencies are obtained and characterized; mode asymptotic behavior and amplitude distributions of wave characteristics are analyzed. The main effects of their transformation by variation of the angular measure and the ratio of inner and outer radii are discussed. The results obtained are in good agreement with the results for the special case of a hollow semicircular cylinder.