Comment on Y.-H. Hsu et al., "electrical and mechanical fully coupled theory and experimental verification of Rosen-type piezoelectric transformers" [see reference [1]]

This letter discusses the difference between piezoelectric constitutive relations for the case of one-dimensional stress and the case of one-dimensional strain, and its implications in the modeling of Rosen piezoelectric transformers.     

用裂纹单元分析双压电材料界面力电耦合奇异场

为了求解双压电材料在机械荷载和(或)外加电场的作用下,界面裂纹尖端的力电耦合奇异场,提出了一种全数值方法。该全数值方法的实施可以分为两个部分:首先,用一维有限元方法求解不同压电材料界面裂纹尖端力电耦合奇异场特征解;然后,采用杂交有限元列式构造一种所谓的裂纹单元,在该杂交有限元的列式中,假设应力场和电位移场是利用上述一维有限元方法计算得到的特征解推导出来的;利用该单元可以得到全部的力电耦合奇异场的解。通过对单一压电材料中心裂纹尖端力电耦合奇异场的计算,该方法的准确性和高效性得到了验证;进而用该方法研究了双压电材料界面力电耦合场奇异场。     

One-dimensional equations for planar piezoelectric curved bars

A set of one-dimensional equations for coupled extension, flexure, and shear of a planar piezoelectric curved bar is obtained from the three-dimensional equations of piezoelectricity by expanding the mechanical displacement vector and the electric potential into power series in the cross-sectional coordinates and retaining lower-order terms. The equations are useful in the analysis and design of one-dimensional piezoelectric devices.     

Piezoelectric ceramic rectangular transducers in flexural vibration

Based on the equivalent elastic method and coupled vibration theory, an analytic method is presented to study the flexural vibration of rectangular transducers consisting of piezoelectric ceramic thin plates. By introducing a mechanical coupling coefficient, the flexural vibration of the piezoelectric ceramic rectangular thin plate is reduced to two simple, one-dimensional flexural vibrations of narrow piezoelectric ceramic strips. The resonance frequency equations for the piezoelectric ceramic rectangular thin-plate transducers in flexural vibration are derived under the free and simply supported boundary conditions analytically. The relationship between the resonance frequency and the flexural vibrational order, the geometrical shape, and the dimensions of the piezoelectric ceramic rectangular thin-plate transducer is analyzed. It is demonstrated that the one-dimensional vibrational theory for the flexural vibration of a narrow piezoelectric ceramic strip and the stripe-mode flexural vibrational theory for the piezoelectric ceramic rectangular thin plate can be derived directly from the theory obtained in this paper. Experimental results show that the measured resonance frequencies of the piezoelectric ceramic rectangular thin-plate transducers in flexural vibration under free-boundary conditions are in good agreement with the calculated results. The method presented in this paper can be used in the resonance frequency analysis of vibrating systems in coupled vibration.     

基于含金属芯压电纤维与Lamb波的一维结构损伤定位研究

含金属芯压电纤维(Metal-core Piezoelectric Ceramic Fiber,MPF)是一种新型压电功能器件.介绍了MPF的结构及其对圆形压电片激励Lamb波的传感响应模型.利用Gabor小波变换计算损伤反射信号到达时间延迟的原理,把MPF传感单一模式Lamb波在一维结构中进行了损伤定位研究.研究结果表明:MPF可以进行Lamb波的单一模式传感,采用Gabor小波变换计算损伤反射信号到达时间延迟效果较好,损伤定位精度较高.     

Exact one-dimensional computation of ultrasonic transducers withseveral piezoelectric elements and passive layers using the transmissionline analogy

We present a computation technique for one-dimensional piezoelectric transducers, resonators, or interferometers having an arbitrary number of layers and piezoelectric elements electrically in parallel. Explicit and exact expressions are derived for the electric impedance and acoustic velocities. This method is based upon a systematic use of the electrical transmission line analogy, each passive or active medium being represented by a line. It has successfully been applied to various structures, particularly a symmetrical resonator with an intermediate liquid medium and a total of 29 media     

Partially debonded circular inclusion in one-dimensional quasicrystal material with piezoelectric effect

International Journal of Mechanics and Materials in Design - In this first effort, a partially-debonded circular inclusion in a one-dimensional quasicrystal material with piezoelectric effect is...     

Elasticity solution of functionally graded circular and annular plates integrated with sensor and actuator layers using differential quadrature

Based on three-dimensional theory of elasticity axisymmetric static analysis of functionally graded circular and annular plates imbedded in piezoelectric layers is investigated using differential quadrature method (DQM). The plate has various edges boundary conditions and its material properties are assumed to vary in an exponential law with the Poisson ratio to be constant. This method can give an analytical solution along the graded direction using the state space method (SSM) and an effective approximate solution along the radial direction using the one-dimensional DQM. The method is validated by comparing numerical results with the results obtained in the literature. Both the direct and the inverse piezoelectric effects are investigated and the influence of piezoelectric layers on the mechanical behavior of plate is studied. The effects of the gradient index, thickness to radius ratio, and edges boundary conditions on the static behavior of FG circular and annular plates are investigated.     

Axisymmetric vibration of infinite piezoelectric cylinders using one-dimensional finite elements

A general finite-element analysis for infinite piezoelectric cylinders has been formulated. The classical three-dimensional elasticity equations of motion are used. The dependence on theta, z, and time are included by assuming appropriate trigonometric functions, and the three-dimensional problem is reduced to a one-dimensional finite element with four degrees of freedom per node. The tabulated results are limited to cylinders with stress-free, shorted electrode (phi=0) boundary conditions at the outside surface of the cylinder. However, solutions for a variety of boundary conditions are possible. Solutions for the piezoelectric cylinder compare favorably with the existing literature. The motion of piezoelectric cylinders with thin coatings is analyzed by modeling the cylinder and thin coating as a layered cylinder.     

Electric properties of an embedded piezoelectric layer

The one-dimensional vibration mode of a piezoelectric layer under different load conditions has been reconsidered. Derived analytical expressions for admittance and impedance at special frequencies are listed. Based on the expressions derived, two applications are proposed involving electrical measurements on a piezoelectric plate. Concerned are first the determination of such plate material parameters which are relevant for its thickness mode of vibration. Difficulties due to spurious vibration modes are avoided in this approach. The second application deals with an alternative determination of acoustic material-impedances otherwise not easily obtainable: a piezoelectric plate is coupled to the material surface by a liquid. The influence of the coupling layer thickness is discussed and a measurement procedure is given by which the detrimental layer thickness effect is minimized.     

The band gaps of plate-mode waves in one-dimensional piezoelectric composite plates: polarizations and boundary conditions

Theoretical studies are presented for the band structures of plate-mode waves in a one-dimensional (1-D) phononic crystal plate consisting of piezoelectric ceramics placed periodically in an epoxy substrate. The dependences of the widths and starting frequencies of first band gaps (FBG) on the filling fraction and the thickness to lattice pitch ratio are calculated for different polarizations of piezoelectric ceramics under different electric boundary conditions, i.e., short circuit (SC) and open circuit (OC). We found that the FBG always is broadened by polarizing piezoelectric ceramics, and the FBG widths with SC always are larger than that with OC for the same polarization. Our research shows that there are three critical parameters which determine the FBG: the polarized directions, the filling fraction, and the ratio of the plate thickness to the lattice pitch, respectively. Therefore, we can control the width and starting frequency of the FBG in the engineering according to need by choosing these parameters of the system.     

Concept and model of a piezoelectric structural fiber for multifunctional composites

The use of piezoceramic materials for structural sensing and actuation is a fairly well developed practice that has found use in a wide variety of applications. However, just as advanced composites offer numerous benefits over traditional engineering materials for structural design, actuators that utilize the active properties of piezoelectric fibers can improve upon many of the limitations encountered when using monolithic piezoceramic devices. Several new piezoelectric fiber composites have been developed, however almost all studies have implemented these devices such that they are surface-bonded patches used for sensing or actuation. This paper will introduce a novel active piezoelectric structural fiber that can be laid up in a composite material to perform sensing and actuation, in addition to providing load bearing functionality. The sensing and actuation aspects of this multifunctional material will allow composites to be designed with numerous embedded functions including, structural health monitoring, power generation, vibration sensing and control, damping, and shape control through anisotropic actuation. A one-dimensional micromechanics model of the piezoelectric fiber will be developed to characterize the feasibility of constructing structural composite lamina with high piezoelectric coupling. The theoretical model will be validated through finite element (FE) modeling in ABAQUS. The results will show that the electromechanical coupling of a fiber-reinforced polymer composite incorporating the active structural fiber (ASF) could be more than 70% of the active constituent.     

Unidimensional model of polarisation changes in piezoelectric ceramics based on the principle of maximum entropy production

This paper presents a one-dimensional model for piezoelectric ceramics developed using the principle of maximum entropy production. Changes in polarisation are assumed to occur only as a consequence of domain wall movement. Such movement, it is assumed, can occur as a consequence of applied load or applied electric field. Simulations of experiments conducted by Fang and Li (J Mater Sci, 34:4001–4010, 1999) are presented and show good agreement with the experimental results. This suggests that abrupt domain switching (known to occur in piezoelectric ceramics at very high applied stresses and fields) may have less influence on the dissipative behaviour of piezoelectric sensors and actuators than previously thought.     

Analysis of rosen piezoelectric transformers with a varying cross-section

We study the effects of a varying cross-section on the performance of Rosen piezoelectric transformers operating with length extensional modes of rods. A theoretical analysis is performed using an extended version of a one-dimensional model developed in a previous paper. Numerical results based on the theoretical analysis are presented.     

A sub-layer model for a thick piezoelectric patch bonded on elastic substrate

Summary. In this paper, the two-dimensional electromechanical coupling problems that a piezoelectric patch of finite size bonded to an elastic substrate are considered. A subdivision model that the single physical piezoelectric layer is mathematically divided into a number of thinner layers is proposed to analyze the electromechanical responses of the structures. Within each virtual sub-layer of the piezoelectric patch the electric displacement and normal stress in the axial direction are assumed to be linear functions of the thickness coordinate. Hellinger-Reissner variational principle for elasticity is extended to the systems of piezoelectric multi-materials. The governing equations that comprise one-dimensional differential equations and integro-differential equations are rigorously derived from the stationary conditions of the variational functional along with substitution of the assumed electromechanical fields. The subdivision model satisfies all mechanical and electric continuity conditions across the virtual interfaces and the physical interface of piezoelectrics/substrate. The numerical solutions of the governing equations are conducted, and the convergence of the subdivision model is demonstrated.     

Trajectory tracking of piezoelectric positioning stages using a dynamic sliding-mode control

Trajectory tracking performance of a piezoelectric positioning stage almost depends on whether the tracking controller can effectively compensate the inherent hysteresis phenomenon. In this paper, a dynamic sliding-mode control (DSMC) with backstepping is proposed for the trajectory tracking of the piezoelectric positioning stage, which is suitable for a component of scanning microscopes. An equivalent model developed from a linear motion dynamics with addition of the hysteresis nonlinearity and strain-dependent function first is proposed to approximately represent the dynamics of motion of a one-dimensional piezoelectric positioning stage. Then, based on the equivalent model, the DSMC with an asymptotical sliding surface is proposed for the trajectory tracking control of the piezoelectric positioning stage. Moreover, the analysis of stability can be completed by mathematics, and the convergence rate of the tracking error can be governed by the choice of the control parameter values. Using the DSMC to trajectory tracking control, the piezoelectric positioning stage becomes more suitable for practical applications, especially with the need of various trajectories tracking in microscopy. To validate the proposed control scheme, a computer-based controller and a piezoelectric positioning stage with a capacitive displacement sensor are implemented. Experimental results illustrate the feasibility of the proposed controller for trajectory tracking applications.     

Messung des piezoelektrischen Effektes an stoßbelasteten Gesteinsstäben

Measurements of the piezoelectric effect of impact loaded rock bars The piezoelectric effect, which causes electric charge at the surface of impact loaded rock bars, is shown by measurements using electrodes. Moreover, electric field of this charge leads to measuring with antenna. The one-dimensional theory of elastic waves in bars is the theoretical basis of computation. The comparison of all the experimentally and numerically determined data has proven a good agreement of typical features of mechanical waves measured by used methods. The electric charge and the antenna signal are measurable on the front surface and on the lateral surfaces of samples. For using later measuring points needs a certain relation between wave length and sensor length. With respect of material of used granite samples the essential requirements are piezoelectrically active rocks. These properties dont depend on quartz content alone. So the piezoelectric effect enables to measure mechanical stress waves by transducer(antenna)which is not physically in contact with the appropriated rock sample.     

A coupled-mode theory for periodic piezoelectric composites

A coupled oscillator model to calculate the resonance spectrum of a one-dimensional piezoelectric composite plate, used in ultrasonic transducers, is proposed. Two resonant modes, one produced by the elastic wave reflection on the plate boundaries (thickness resonance) and the other by the reflection on the periodic discontinuities (lateral resonance) are considered. A Kronig-Penney model is used to calculate the lateral resonances. The thickness resonance is obtained with an effective medium model. The coupling of these two modes is described by a biquadratic equation whose solutions are the resonant frequencies of the piezoelectric composite plate. A criterion for a distribution of phases to keep the spurious lateral resonances away from the thickness resonance vicinity is obtained.     

A one-dimensional model for non-linear behaviour of piezoelectric composite materials

In this paper, a one-dimensional analytical model is proposed to investigate the non-linear behaviour for piezoelectric and piezoelectric fibre reinforced composite (PFRC) materials in the fibre direction. The required linear and non-linear constants for purely piezoelectric materials are obtained using the curve-fitting method and the measured S₃–E₃ non-linear loops of the corresponding piezoelectric materials, whereas those for PFRC materials are determined by employing the quadratic non-linear constitutive equations for a purely piezoelectric material, the iso-field assumptions and linear and non-linear constants of the composite constituents. A numerical study is conducted. The numerical results reveal a significant effect of stress T₃ on S₃–E₃ non-linear behaviour for both soft PZT–5H ceramics and PZN–4.5%PT crystals. It is also found that the piezoelectric fibre volume fraction V_f and strain S₃ can significantly affect the T₃–E₃ non-linear behaviour for both PZT–5H/piezo-polymer polyvinylidene fluoride (PVDF) and PZN–4.5%PT/PVDF PFRC materials. A good correlation is noted between the piezoelectric constants d₃₃ and e₃₃ predicted using the present method and those recommended by manufacturer for PZT–5H ceramics and PZN–4.5%PT crystals.