功能梯度压电材料反平面裂纹问题

基于三维弹性理论和压电理论，导出了材料系数在横观各向同性平面内梯度分布的压电体的状态方程，进而对材料系数指数函数规律分布的半无限大压电体中的反平面裂纹问题进行了求解，利用Fourier变换给出了半无限大压电体中位移，应力，电势及电位移的解析表达式，并求得了裂纹尖端的应力强度因子和电位移强度因子，分析了不同的非均匀材料系数及几何尺寸对它们的影响。     

Damage analysis and fracture criteria for piezoelectric ceramics

Both the mechanical and the electrical damages are introduced to study fracture mechanics of piezoelectric ceramics in this paper. Two kinds of piezoelectric fracture criteria are proposed by using the damage theory combined with the well-known piezoelectric fracture experiments of Park and Sun [Fracture criteria of piezoelectric ceramics, J. Am. Ceram. Soc. 78 (1995) 1475-1480]. One is based on a critical state of the mechanical damage and the other on a critical value of a proper linear combination of both the mechanical and the electrical damage variables. It is found that the fracture load predicted, which takes the mechanical damage into account only (mode 1), has greater deviation than predicted result by considering a proper linear combination of the mechanical and the electrical damages (mode 2). And the fracture criterion corresponding to mode 2 presented is shown to be superior to mode 1. It is also demonstrated that the mechanical damage has greater effect on fracture than the electrical damage.     

Label-free immunosensor for monitoring vitellogenin as a biomarker for exogenous oestrogen compounds in amphibian species

A label-free, optical waveguide lightmode spectroscopy based immunosensor was developed for frog (Bombina orientalis) vitellogenin (Vtg) determination in biological samples as a biomarker for exogenous oestrogen compounds. Antibody against Vtg was produced in rabbits immunised with purified lipovitellin (Lpv), a precursor of Vtg, from the homogenised ovary of oriental fire-bellied toads (B. orientalis). The purified protein and Lpv/Vtg-specific serum were applied in both competitive and direct immunoassay formats using optical waveguide lightmode spectroscopy immunosensor. When measuring Vtg in direct manner, the Lpv antibody (1.76 µg mL^?1) was immobilised on the sensor surface, and the linear measuring range for Vtg was 0.1–10 µg mL^?1. During the competitive measurement, 100 ng mL^?1 Lpv was applied for the immobilisation. The linear measuring range for Vtg was 0.5–50 ng mL^?1. We studied the relative substrate specificity of the antibody, and it was concluded that the method is suitable for the sensitive and selective determination of Vtg levels in toads. Heart, liver and gonad samples from male animals were spiked with Vtg and were analysed using the newly developed method, and female toads and spawn samples were tested and compared to the calibration curve obtained by the spiked samples.     

Boundary-layer of torsion in a piezoelectric material with a symmetry of order six

An analytical model for the boundary-layer of torsion in a piezoelectric thin plate with a symmetry of order six is proposed on the basis of the method of asymptotic expansions. The local behaviour of the three-dimensional solution of the problem of linear piezoelectricity is formulated in the vicinity of the lateral contour of the plate, and the solution of the problem for the boundary-layer of torsion is then obtained. However, we denote that full proof of the theorems is not given in this paper. Only hints of the proof are given.     

Stabilization of Parametric Vibrations of a Nonlinear Continuous System

The purpose of the present paper is to solve an active control problem of nonlinear continuous system parametric vibrations excited by the fluctuating force. The problem is solved using the concept of distributed piezoelectric sensors and actuators with a sufficiently large value of velocity feedback. The direct Liapunov method is proposed to establish criteria for the almost sure stochastic stability of the unperturbed (trivial) solution of the shell with closed-loop control. The distributed control is realized by the piezoelectric sensor and actuator, with the changing widths, glued to the upper and lower shell surface. The relation between the stabilization of nonlinear problem and a linearized one is examined. The fluctuating axial force is modeled by the physically realizable ergodic process. The rate velocity feedback is applied to stabilize the shell parametric vibrations.     

A theoretical model for electroelastic analysis in piezoelectric fibre push-out test

A theoretical model is presented to study the elastic deformation process and frictional sliding behavior in single piezoelectric fibre push-out tests. Based on the theoretical model and some necessary simplifications, stress and electric fields are obtained for push-out tests of a circular piezoelectric fibre embedded in an elastic matrix. Numerical results of a piezoelectric fibre/expoxy matrix system are presented to verify the proposed formulation. The study shows that there is a significant effect of the piezoelectric parameter and embedded fibre length on stress transfer, electric field distribution and load-displacement curve of the frictional sliding process. This study also indicates that the piezoelectric effect has a distinct influence on the mechanical behavior and properties of the interface in a fibre/matrix system.     

Stress singularities near the apex of a cylindrically polarized piezoelectric wedge

Summary In this paper, the stress singularities for a cylindrically polarized piezoelectric wedge are investigated. The characteristic equations are derived analytically by using the extended Lekhnitskii formulation. The piezoelectric material (PZT-4) is polarized in the radial, circular or axial direction, respectively. Similar to the rectilinearly polarized piezoelectric problem, the inplane and antiplane stress fields are uncoupled. The results show the variations of the singularity orders with the changes of the wedge angle, material constants, polarized direction, and the boundary conditions.     

Discussion of Antiplane Singularities of Piezoelectric–Dielectric and Piezoelectric–Conductor Wedges

This technical note deals with two special topics from our previous paper (Chue and Chen in Arch Appl Mech 72 673–685, 2003) in Archive of Applied Mechanics: the effects of electrical conditions imposed on the edges and bonded interfaces of piezoelectric–dielectric and piezoelectric–conductor wedges on antiplane problems. After employing relatively realistic electrical conditions, we found that stress and electric displacement singularities are altered when boundary conditions and/or continuity conditions are changed, and we compared the results with those of previous studies.     

Griffith crack moving in a piezoelectric strip

Summary  The dynamic problem of an impermeable crack of constant length 2a propagating along a piezoelectric ceramic strip is considered under the action of uniform anti-plane shear stress and uniform electric field. The integral transform technique is employed to reduce the mixed-boundary-value problem to a singular integral equation. For the case of a crack moving in the mid-plane, explicit analytic expressions for the electroelastic field and the field intensity factors are obtained, while for an eccentric crack moving along a piezoelectric strip, numerical results are determined via the Lobatto–Chebyshev collocation method for solving a resulting singular integral equation. The results reveal that the electric-displacement intensity factor is independent of the crack velocity, while other field intensity factors depend on the crack velocity when referred to the moving coordinate system. If the crack velocity vanishes, the present results reduce to those for a stationary crack in a piezoelectric strip. In contrast to the results for a stationary crack, applied stress gives rise to a singular electric field and applied electric field results in a singular stress for a moving crack in a piezoelectric strip. Received 14 August 2001; accepted for publication 24 September 2002 The author is indebted to the AAM Reviewers for their helpful suggestions for improving this paper. The work was supported by the National Natural Science Foundation of China under Grant 70272043.