Energy trapping in high-frequency vibrations of piezoelectric plates with partial mass layers under lateral electric field excitation

We study coupled face-shear (FS) and thickness-twist (TT) motions of a piezoelectric plate of monoclinic crystals with mass layers on the central parts of the plate surfaces. The plate is driven by a lateral electric field. Mindlin’s first-order theory of piezoelectric plates is used. An analytical solution is obtained. Numerical results are presented for an AT-cut quartz plate, including the motional capacitance of the plate as a resonator and the vibration modes trapped under the mass layers in the central portion of the plate. The relationship between the dimension of the mass layers and the number of trapped modes is examined.     

Charged dislocations in piezoelectric bimaterials

In some piezoelectric semiconductors and ceramic materials, dislocations can be electrically active and could be even highly charged. However, the impact of dislocation charges on the strain and electric fields in piezoelectric and layered structures has not been presently understood. Thus, in this paper, we develop, for the first time, a charged three-dimensional dislocation loop model in an anisotropic piezoelectric bimaterial space to study the physical and mechanical characteristics which are essential to the design of novel layered structures. We first develop the analytical model based on which a line-integral solution can be derived for the coupled elastic and electric fields induced by an arbitrarily shaped and charged three-dimensional dislocation loop. As numerical examples, we apply our solutions to the typical piezoelectric AlGaN/GaN bimaterial to analyze the fields induced by charged square and elliptic dislocation loops. Our numerical results show that, except for the induced elastic (mechanical) displacement, charges along the dislocation loop could substantially perturb other induced fields. In other words, charges on the dislocation loop could significantly affect the traditional dislocation-induced stress/strain, electric displacement, and polarization fields in piezoelectric bimaterials.     

Fundamental solutions of uniform loads over triangular elements in a three-dimensional piezoelectric medium

In this paper, fundamental solutions of uniform loads over triangular elements in an infinite transversely isotropic piezoelectric three-dimensional space are derived. The triangle element can be parallel or vertical to the plane of isotropy and the uniform load can be mechanical and electric types, oriented in an arbitrary orientation. The solutions are expressed simply as a linear combination of three kinds of elementary functions – linear, trigonometric and logarithm functions. Three methods of superposition are employed to verify the obtained fundamental solutions. Numerical examples are also presented for the extended displacements and stresses induced by both mechanical and electric loads on the vertical and horizontal triangles.     

Analytical solution for the electroelastic dynamics of a nonhomogeneous spherically isotropic piezoelectric hollow sphere

Summary By introduction of a special dependent variable and separation of variables technique, the electroelastic dynamic problem of a nonhomogeneous, spherically isotropic hollow sphere is transformed to a Volterra integral equation of the second kind about a function of time. The equation can be solved by means of the interpolation method, and the solutions for displacements, stresses, electric displacements and electric potential are obtained. The present method is suitable for a piezoelectric hollow sphere with an arbitrary thickness subjected to arbitrary mechanical and electrical loads. Numerical results are presented at the end.The work was supported by the National Natural Science Foundation of China (No. 10172075 and No. 10002016).     

Dynamic response of a crack in a functionally graded interface of two dissimilar piezoelectric half-planes

Summary  In this paper, the dynamic anti-plane crack problem of two dissimilar homogeneous piezoelectric materials bonded through a functionally graded interfacial region is considered. Integral transforms are employed to reduce the problem to Cauchy singular integral equations. Numerical results illustrate the effect of the loading combination parameter λ, material property distribution and crack configuration on the dynamic stress and electric displacement intensity factors. It is found that the presence of the dynamic electric field could impede of enhance the crack propagation depending on the time elapsed and the direction of applied electric impact. Received 4 December 2001; accepted for publication 9 July 2002 This work is supported by the National Natural Science Foundation of China through Grant No. 10132010.     

Invariant formulation of the electromechanical enthalpy function of transversely isotropic piezoelectric materials

Summary Theoretical and numerical aspects of the formulation of electromechanically coupled, transversely isotropic solids are discussed within the framework of the invariant theory. The main goal is the representation of the governing constitutive equations for reversible material behaviour based on an anisotropic electromechanical enthalpy function, which automatically fulfills the requirements of material symmetry. The introduction of a preferred direction in the argument list of the enthalpy function allows the construction of isotropic tensor functions, which reflect the inherent geometrical and physical symmetries of the polarized medium. After presenting the general framework, we consider two important model problems within this setting: i) the linear piezoelectric solid; and ii) the nonlinear electrostriction. A parameter identification of the invariant- and the common coordinate-dependent formulation is performed for both cases. The tensor generators for the stresses, electric displacements and the moduli are derived in detail, and some representative numerical examples are presented.We thank Dipl.-Ing. H. Romanowski for his support and helpful remarks.     

Phenomenological model for the macroscopical material behavior of ferroelectric ceramics

A thermodynamically consistent phenomenological model for the simulation of the macroscopic behavior of ferroelectric polycrystalline ceramics is presented. It is based on the choice of microscopically motivated internal state variables, which describe the texture and the polarization state of the polycrystal. Saturation states are defined for the internal state variables. The linear material behavior is modelled by a transversely isotropic piezoelectric constitutive law, where the anisotropy is history dependent. For non-linear irreversible processes, a switching function and associated evolution rules are applied, satisfying the principle of maximum ferroelectric dissipation. Saturation is modelled by the use of energy-barrier functions in the electric enthalpy density function. Numerical examples demonstrate the capability of the proposed model, to predict the typical experimental results.     

Optical,piezoelectric and mechanical properties of xylenol orange doped ADP single crystals for NLO applications

Single crystals of pure and xylenol orange (XO; C₃₁H₃₂N₂O₁₃S) dye doped (0.01, 0.05 and 0.1 mol%) ammonium dihydrogen phosphate (ADP; NH₄H₂PO₄) were grown by slow evaporation method with the vision to improve the properties of pure ammonium dihydrogen phosphate crystal. The theoretical morphology of the grown crystals was drawn using Bravais–Friedel–Donnay–Harker (BFDH) law. The selective nature of xylenol orange dye to selectively stain the particular growth sectors of ADP crystal was studied. The structural analysis of as grown crystals was carried out using powder XRD study. The identification of the functional groups present in the ADP material was done using Fourier transform infrared (FTIR) spectroscopy. The linear optical study on pure and dye doped crystals was carried out using UV–vis–NIR spectroscopy. The optical band gap, extinction coefficient, refractive index and optical conductivity were calculated using the transmittance spectra for all the samples. In photoluminescence studies, the blue emission intensity got quenched and an orange emission at 597 nm was seen as a result of XO doping. The thermal stability and decomposition temperature of ADP crystal were found to decrease as an effect of dye doping. The piezoelectric charge coefficient, SHG conversion efficiency, mechanical strength and wettability were also enhanced as a result of XO dye doping.     

Piezomaterials for bone regeneration design—homogenization approach

Relying on the piezoelectric properties of natural bone we propose a new biomaterial made of an inert perforated piezoelectric matrix filled with living osteoblast cells. We expect that this device will help the process of bone regeneration. In this paper we give some conceptual and numerical tools based on homogenization theory as a starting point in the design of such a “smart system”.     

Effects of radially applied angular sector stresses on the frequency of doubly rotated quartz crystal

Summary A theoretical study is presented to determine the sensitivity of a doubly rotated crystal resonator, subject to radial compression along two diametrically opposed zones. The variation of frequency is calculated as a function of the stresses applied to the crystal, then a coefficient of sensitivity is deduced. Some solutions are put forward for obtaining the stability of frequency of a resonator in the particular case where a quartz crystal, stress compensated (SC), is used. Moreover, the particular conditions are described for limiting the influence of possible faults in the construction of such quartz resonators, which must be employed when a very high stability of frequency is needed.