Messung elastischer Wellen in Stahl- und Gesteinsstäben mit Hilfe des magnetoelastischen Effektes

Measurements effect of elastic waves in steel- and rock rods using the magneto-elastic Stress waves in steel and iron ore rods produced by a mechanical impact can be measured by a sensor using the magneto-elastic effect. A detection of the changing magnetic flux is made. The function describing the propagation of longitudinal waves in rods is known as the stress wave equation. The agreement with theory is verified by examinations of steel rods using strain gauges. Afterwards the signals of three iron ores (magnetite, hematite, siderite) are recorded. Induced voltage is measured by the magneto-elastic sensor in the case of magnetite and hematite, however it is not possible to detect any signal for siderite. This means that the change of magnetic flux depends on the kind of bulk magnetic appearance, not on content of iron. Using the magneto-elastic sensor the magneto-elastic effect offers the possibility to detect tree of contact mechanical waves produced by a mechanical impact in ferro- or ferrimagnetic solids.     

High-Precision Displacement Sensing of Monolithic Piezoelectric Disk Resonators Using a Single-Electron Transistor

A single-electron transistor (SET) can be used as an extremely sensitive charge detector. Mechanical displacements can be converted into charge, and hence, SETs can become sensitive detectors of mechanical oscillations. For studying small-energy oscillations, an important approach to realize the mechanical resonators is to use piezoelectric materials. Besides coupling to traditional electric circuitry, the strain-generated piezoelectric charge allows for measuring ultrasmall oscillations via SET detection. Here, we explore the usage of SETs to detect the shear-mode oscillations of a 6-mm-diameter quartz disk resonator with a resonance frequency around 9 MHz. We measure the mechanical oscillations using either a conventional DC SET, or use the SET as a homodyne or heterodyne mixer, or finally, as a radio-frequency single-electron transistor (RF-SET). The RF-SET readout is shown to be the most sensitive method, allowing us to measure mechanical displacement amplitudes below \(10^{-13}\) m. We conclude that a detection based on a SET offers a potential to reach the sensitivity at the quantum limit of the mechanical vibrations.     

Novel modeling technique for the stator of traveling wave ultrasonic motors

Traveling wave ultrasonic motors (TWUM) are a promising type of piezoelectric transducers, which are based on the friction transmission of mechanical propagating waves. These waves are excited on the stator by using high Q piezoelectric ceramics. This article presents a modeling strategy, which allows for a quick and precise modal and forced analysis of the stator of TWUM. First-order shear deformation laminated plate theory is applied to annular subdomains (super-elements) of the stator. In addition to shear deformations, the model takes into account the effect of rotary inertia, the stiffness contribution of the teeth, and the linear varying thickness of the stator. Moreover, the formulation considers a more realistic function for the electric field inside the piezoelectric ceramic, i.e., a linear function, instead of the generally assumed constant electric field. The Ritz method is used to find an approximated solution for the dynamic equations. Finally, the modal response is obtained and compared against the results from classical simplified models and the finite element method. Thus, the high accuracy and short computation times of the novel strategy were demonstrated.     

Acoustoelectric charge injection in semiconductors

A considerable change of trapped and free electric charge is observed in piezoelectric semiconductors in the presence of a traveling acoustic wave. The electric field, induced by the ultrasound, alters the electric equilibrium of the semiconductor sample, resulting in an accumulation of majority carriers at the surface with a consequent decrease in surface resistance. In specific cases, charge injection occurs at the semiconductor-metal contact area due to the large electric field induced by the acoustic wave. This effect, here referred to as the Acoustoelectric Charge Injection, was also investigated for the case in which a Surface Acoustic Wave (SAW) is propagating along the metalized surface of a semiconductor. The injected charge is experimentally measured having a exponential time decay typical of a deep trap level, thus suggesting that Acoustic Charge Injection can modify the transient behavior of high-speed analog signal processing devices based on SAW, acoustooptic, and acoustic charge transport (ACT) phenomena. Experimental results and theoretical calculations are presented for CdS samples and for a metalized GaAs-epilayer grown on semi-insulating GaAs substrate     

On saturation-strip model of a permeable crack in a piezoelectric ceramic

Summary. The saturation-strip model for piezoelectric crack is re-examined in a permeable environment to analyze fracture toughness of a piezoelectric ceramic. In this study, a permeable crack is modeled as a vanishing thin but finite rectangular slit with surface charge deposited along crack surfaces. This permeable saturation crack model reveals that there exists a possible leaky mode for electrical field, which allows applied electric field passing through the dielectric medium inside a crack. By taking into account the leaky mode effect, a first-order approximated solution is obtained with respect to slit height, h ₀, in the analysis of electrical and mechanical fields in the vicinity of a permeable crack tip. The permeable saturation crack model presented here also considers the effect of charge distribution on crack surfaces, which may be caused by any possible charge-discharge process in the dielectric medium inside the crack. A closed form solution is obtained for the permeable crack perpendicular to the poling direction under both mechanical as well electrical loads. Both local and global energy release rates are calculated. Remarkably, the global energy release rate for a permeable crack has an expression, where M is elastic modulus, a is the half crack length, is permittivity constant, and e is piezoelectric constant. This result is in a broad agreement with some experimental observations and may be served as the fracture criterion for piezoelectric materials. This contribution elucidates how an applied electric field affects crack growth in piezoelectric ceramic through its interaction with permeable environment surrounding a crack. The author would like to acknowledge the support from the Academic Senate Committee on Research at University of California (Berkeley) through the fund of BURNL-07427-11503-EGSLI.     

一次逆、二次正压电效应在自感知执行器上的应用

提出利用一次逆、二次正压电效应为同一压电体内的双向效应原理,进行传感器与执行器集成一体化——自感知执行器的研究.即利用一次逆压电效应输出一个微位移,作为执行器使用;利用二次正压电效应的输出电荷自感知执行器的输出位移,作为传感器使用.在准静态（电压0～50V）和低频（电压100V,频率10Hz）条件下,分别进行了一次逆压电效应输出位移、二次正压电效应输出电压的实验,并将得到的数据进行归一化处理.实验结果表明,通过测量二次正压电效应产生的电荷能够较好地自感知一次逆压电效应产生的位移.     

Dynamic stress from a cylindrical inclusion buried in a functionally graded piezoelectric material layer under electro-elastic waves

This paper presents a theoretical method to investigate the multiple scattering of electro-elastic waves and dynamic stress around a subsurface cylindrical inclusion in a functionally graded piezoelectric material layer bonded to homogeneous piezoelectric materials. The analytical solutions of wave fields are expressed by employing wave function expansion method, and the expanded mode coefficients are determined by satisfying the boundary conditions around the inclusion. The image method is used to satisfy the mechanical and electrically short conditions at the free surface of the structure. Through the numerical solutions of dynamic stress concentration factors around the inclusion, it is found that when the cylindrical inclusion possesses higher rigidity and greater piezoelectric constant than the two phases of functionally graded materials, the dynamic stress around the inclusion increases greatly. When the distance between the surface of the structure and the inclusion is smaller, the effect of the properties of the inclusion becomes greater. When the cylindrical inclusion possesses lower rigidity and smaller piezoelectric constant than the two phases of functionally graded materials, the maximum dynamic stress shows little difference; however, the variation of the distribution of the dynamic stress around the inclusion is greater. The effect of the properties of the inclusion on the dynamic stress around the inclusion is greater than that on the electric field. The effects of wave frequency on the dynamic stress and electric field are also examined.     

Anti‐plane mechanical and in‐plane electrical fields for a finite electrode/punch on a finite piezoelectric layer

The problems of a surface electrode and a rigid punch on a finite piezoelectric layer are considered in this paper. The resultant force and the accumulated electric charge on the electrode/punch are prescribed. Closed‐form solutions for the electromechanical fields at the electrode/punch tip are obtained and are expressed in terms of the applied strain and electric field intensity factors. For infinite layer thickness, the strain and electric field intensity factors are obtained in closed‐form. For finite layer thickness, the strain and electric field intensity factors are obtained numerically by the singular integral equation technique. The effect of layer thickness on the electrode/punch tip fields is discussed. It is found that the field intensities at the electrode/punch tip can be reduced considerably by decreasing layer thickness. In addition to the single electrode/punch problem, this paper also provides a solution technique for two collinear surface electrodes/punches on a finite piezoelectric layer. The effect of the relative distance between the two electrodes/punches on the electromechanical fields in the piezoelectric layer is also discussed.     

Subsonic slip waves along the interface between two piezoelectric solids in sliding contact with local separation

The Stroh formalism of piezoelectric crystals and singular integral equation technique are applied to study the propagation of possible slip waves in presence of local separation at the interface between two frictionless contact piezoelectric solids, which are pressed together by uniaxial pressure and laid in the electric field. The problem is cast into a set of singular integral equations of which the closed solutions are obtained. Discussion on the existence of such slip waves is presented. The results show that such slip waves, which have square-root singularities at both ends of the local separation zones, can propagate in some special material combinations. And the existence of such slip waves is related with the applied mechanical and electric fields.     

Wave propagation analysis in inhomogeneous piezo‐composite layer by the thin‐layer method

The thin‐layer method (TLM) is used to study the propagation of waves in inhomogeneous piezo‐composite layered media caused by mechanical loading and electrical excitation. The element is formulated in the time‐wavenumber domain, which drastically reduces the cost of computation compared to the finite element (FE) method. Fourier series are used for the spatial representation of the unknown variables. The material properties are allowed to vary in the depthwise direction only. Both linear and exponential variations of elastic and electrical properties are considered. Several numerical examples are presented, which bring out the characteristics of wave propagation in anisotropic and inhomogeneous layered media. The element is useful for modelling ultrasonic transducers (UT) and one such example is given to show the effect of electric actuation in a composite material and the difference in the responses elicited for various ply‐angles. Further, an ultrasonic transducer composed of functionally graded piezoelectric materials (FGPM) is modelled and the effect of gradation on mechanical response is demonstrated. The effect of anisotropy and inhomogeneity is shown in the normal modes for both displacement and electric potential. The element is further utilized to estimate the piezoelectric properties from the measured response using non‐linear optimization, a strategy that is referred to as the pulse propagation technique (PPT). Copyright © 2005 John Wiley & Sons, Ltd.     

Shear-horizontal surface waves on piezoelectric ceramics with depolarized surface layer

Theoretical analysis and numerical results describing the propagation of SH (shear-horizontal) surface waves on piezoelectric ceramics with a depolarized surface layer are described. SH surface waves propagating in piezoelectric ceramics with a depolarized surface layer are shown to be a mixture of the Bleustein-Gulyaev surface wave, electrical potential, and the Love surface-wave mechanical displacement. Depolarization of the surface layer in piezoelectric ceramics produces strong dispersion and a multimode structure of the SH surface wave. The penetration depth of the SH surface waves propagating on an electrically free surface of a piezoelectric ceramic with a depolarized surface layer can be significantly smaller than that of the Bleustein-Gulyaev surface waves propagating on a free piezoelectric half-space. It is concluded that piezoelectric ceramics with a depolarized surface layer can be used in hybrid piezoelectric semiconductor convolvers of reduced size.     

Green’s functions of a half-infinite piezoelectric body: Exact solutions

Summary. Greens functions of a half-infinite piezoelectric space play an important role in electroelastic analyses of piezoelectric media. However, almost all works available on the topic are based on the assumption that the normal component of the electric displacement is zero on the surface of the piezoelectric solid, neglecting the effect of polarized surface charge. In the present work, we develop an exact solution for the Greens functions of a half-infinite piezoelectric solid by means of the Stroh formalism. The solution is based on using the exact electric boundary conditions at the interface between the solid and the air medium. First, Greens function for an arbitrary line load in the solid is derived taking into account the effect of polarized charge at the interface, and then the surface Greens function for a surface load is obtained as a special example. Finally, by using the superposition principle, a general expression for the polarized charge distribution on the surface of the piezoelectric solid is presented when an arbitrarily distributed force is exerted on the boundary. It is shown that the normal component of the electric displacement on the solid surface is not zero and it is dependent on the applied loads and the electro-elastic constants of the piezoelectric material and air.     

Dynamic fracture mechanics study of an electrically impermeable mode III crack in a transversely isotropic piezoelectric material under pure electric load

The dynamic response of an electrically impermeable Mode III crack in a transversely isotropic piezoelectric material under pure electric load is investigated by treating the electric loading process as a transient impact load, which may be more appropriate to mimic the real service environment of piezoelectric materials. The stress intensity factor, the mechanical energy release rate, and the total energy release rate are derived and expressed as a function of time for a given applied electric load. The theoretical results indicate that a purely electric load can fracture the piezoelectric material if the stress intensity factor or the mechanical energy release rate is used as a failure criterion.     

Cut‐off Frequencies Induced by the Length of Strain Gauges Measuring Impact Events

Abstract: The finite length of strain gauges may induce filtering effects when measuring impact events. In this study, we are interested in quantifying these effects. Precisely, we determined the cut‐off frequencies of strain gauges cemented on visco‐elastic bars and measuring impact‐induced strain waves. This study shows that the cut‐off frequencies increase with the bar’s wave velocity and decrease with the bar’s diameter. The asymptotic value, corresponding to an infinite bar diameter, is reached rapidly (bar diameter ≈ 15 mm). Moreover, we showed that the mode cut‐off frequencies are more severe (lower) than the gauge length cut‐off frequencies for bar diameters greater than 8 mm.     

Thin-film characterization using a scanning laser acoustic microscope with surface acoustic waves

The use of surface acoustic waves in a scanning laser acoustic microscope for the characterization of the mechanical or acoustic properties of thin films deposited on piezoelectric substrates is demonstrated. Quantitative measurements of mass loading effects of 5000-A-thick tungsten films deposited on lithium niobate substrates were obtained using 100-MHz surface acoustic waves. No information about the tungsten film could be obtained using 100-MHz compressional waves. Methods of generating surface waves on nonpiezoelectric materials so that this technique could be used on arbitrary substrates are discussed.     

Light-induced mechanical oscillations in GaAs single crystals

The phenomenon of the excitation of natural mechanical oscillations by pulsed light in high-ohmic single crystal plates of gallium arsenide has been discovered. The intensity of light-induced oscillations depends on the piezoelectric properties, electric conductivity, and internal friction parameter of the crystal. It is suggested that a bending deformation arises in the plate due to the inverse piezoelectric effect, which is caused by a gradient of the free charge carrier density in the region of optical absorption.     

Modeling of functionally graded smart plates with gradient elasticity effects

ABSTRACT

In this article, the equations of motion for functionally graded plates with surface-mounted piezoelectric layers, while accounting for the gradient elasticity through the modified couple stress model and linear piezoelectricity, are derived using Hamilton’s principle. The formulation includes the coupling between mechanical deformations and the charge equations of electrostatics. The mathematical model developed herein is an equivalent single layer theory for mechanical displacement field and the potential functions. The in-plane displacements are assumed to vary as cubic functions of the thickness coordinate while the transverse displacement is assumed to vary as a quadratic function of the thickness coordinate through plate thickness. The potential function is assumed as the combination of half cosine variation of electric potential and linear variation of applied voltage on outer surfaces. The approach described here is that standard plate models can be enhanced to include the coupling between the charge equations and the mechanical deformations as well as the size dependent effect of micro- and nano-scale structures. An analytical solution of the developed model is presented using the Navier solution technique. A parametric study is performed to study the effect of material variation through thickness of plates, length scale parameters to capture the size-dependent effects, and thickness ratio between piezoelectric layers and the whole plate.     

PVDF薄膜传感器用于测试块状岩石表面爆炸应力的研究

采用PVDF（聚偏二氟乙烯）薄膜传感器对岩石表面爆炸应力进行测量,并分析炮孔内不同填塞介质对爆炸应力波在岩石介质中传播的影响。在直径为28 mm、孔深为25 cm的炮孔内填塞不同的介质（空气、水或沙子）,采用不同的装药结构分别进行爆破试验,通过PVDF薄膜传感器得到了不同工况下岩石表面应力波时程曲线。分析炮孔内不同填塞介质对爆炸应力波透射的影响发现,水作为炮孔填塞介质时,爆炸应力波透射能力强,炸药爆炸产生的能量用于岩石破碎的比例高。水作为炮孔填塞介质时,为达到岩石开裂效果,装药结构设计为1发8^#雷管加2 g传爆药（聚黑-14）;当沙子作为炮孔填塞介质时,为达到岩石的开裂效果,装药结构设计为1发8^#雷管、2 g传爆药（聚黑-14）和20 g炸药（聚黑-2）;前者炸药用量仅为后者的15.3%。炸药使用量减少,也降低了爆破次生危害的影响程度。用PVDF薄膜传感器在岩石表面直接测量爆炸应力的方法是可行的。     

石灰岩在爆炸载荷作用下的破坏机理试验研究

为了探讨岩石在爆炸载荷下的力学特性和破坏机理,采用耦合填塞装药、耦合无填塞装药和不耦合填塞结构模拟了爆炸应力波和爆生气体的不同加载强度,在石灰岩中进行模拟爆破试验,对爆炸应变波及其参数、以及爆破后岩石内部的声波速度进行了测试.基于模拟爆破试验结果,对石灰岩的力学特性和爆破损伤程度进行了分析,得到了岩石在不同爆破条件下的爆破损伤和破坏规律.     

Computational approach of piezoelectric shells by the GDQ method

A piezoelectric laminated cylindrical shell with shear rotations effect under the electromechanical loads and four sides simply supported boundary condition was studied by using the two-dimensional generalized differential quadrature (GDQ) computational method. The typical hybrid composite shells with 3-layered cross-ply [90°/0°/90°] graphite–epoxy laminate and bounded PVDF layers are considered under the sinusoidal pressure loads and electric potentials on the shell. The governing partial differential equation with first-order shear deformation theory in terms of mid-surface displacements and shear rotations can be expressed in series equations by the GDQ formulation. Thus we obtain the GDQ numerical solutions of non-dimensional displacement and stresses at center position of laminated piezoelectric shells. Displacement is generally affected by the thickness of laminated piezoelectric shells under the action of mechanical load. Stresses are generally affected by the thickness and the length of laminated piezoelectric shells under the actions of mechanical load and electric potential.