Effects of an attached functionally graded layer on the electromechanical behaviors of piezoelectric semiconductor fibers

In this paper, we propose a specific two-layer model consisting of a functionally graded (FG) layer and a piezoelectric semiconductor (PS) layer. Based on the macroscopic theory of PS materials, the effects brought about by the attached FG layer on the piezotronic behaviors of homogeneous n-type PS fibers and PN junctions are investigated. The semi-analytical solutions of the electromechanical fields are obtained by expanding the displacement and carrier concentration variation into power series. Results show that the antisymmetry of the potential and electron concentration distributions in homogeneous n-type PS fibers is destroyed due to the material inhomogeneity of the attached FG layer. In addition, by creating jump discontinuities in the material properties of the FG layer, potential barriers/wells can be produced in the middle of the fiber. Similarly, the potential barrier configuration near the interface of a homogeneous PS PN junction can also be manipulated in this way, which offers a new choice for the design of PN junction based devices.

     

Effects of mechanical loadings on the performance of a piezoelectric hetero-junction

A fully-coupled model for a piezoelectric hetero-junction subjected to a pair of stresses is proposed by discarding the depletion layer approximation. The effect of mechanical loadings on PN junction performance is discussed in detail. Numerical examples are carried out for a p-Si/ZnO-n hetero-junction under a pair of stresses acting on the ntype ZnO portion near the PN interface, where ZnO has the piezoelectric property while Si is not. It is found that the bottom of conduction band is lowered/raised near the two loading points due to the decrease/increase in the electron potential energy there induced by a tensile-stress mode via sucking in majority-carriers from two outside regions, which implies appearance of a potential barrier and a potential well near two loading points. Furthermore, the barrier height and well depth gradually become large with increasing tensile stress such that more and more electrons/holes are inhaled in loading region from the n-/p-zone, respectively. Conversely, rising/dropping of conduction band bottom is brought out near the two loading points by a compressive-stress mode due to the increase/decrease in the potential energy of electrons by pumping out the majority-carriers from the loading region to the two outside regions. Therefore, a potential well and a potential barrier are induced near the two loading points, such that more and more electrons/holes are driven away from the loading region to the n-zone/p-zone, respectively, with the increasing compressive stress. These effects are important to tune the carrier recombination rate near the PN interface. Thus, the present study possesses great referential significance to piezotronic devices.     

Heat production in the windings of the stators of electric machines under stationary condition

In electric machines due to high currents and resistive losses (joule heating) heat is produced. To avoid damages by overheating the design of effective cooling systems is required. Therefore the knowledge of heat sources and heat transfer processes is necessary. The purpose of this paper is to illustrate a good and effective calculation method for the temperature analysis based on homogenization techniques. These methods have been applied for the stator windings in a slot of an electric machine consisting of copper wires and resin. The key quantity here is an effective thermal conductivity, which characterizes the heterogeneous wire resin-arrangement inside the stator slot. To illustrate the applicability of the method, the analysis of a simplified, homogenized model is compared with the detailed analysis of temperature behavior inside a slot of an electric machine according to the heat generation. We considered here only the stationary situation. The achieved numerical results are accurate and show that the applied homogenization technique works in practice. Finally the results of simulations for the two cases, the original model of the slot and the homogenized model chosen for the slot (unit cell), are compared to experimental results.     

压电材料中切口/接头端部平面电弹性场奇异性有限元分析

为了对平面载荷作用下压电材料中切口或接头端部附近电弹性场奇异性问题进行分析，首先以应力平衡方程、Maxwell方程和和边界条件为基础，得到一种求解压电材料特征问题的弱式方程；其次，假定楔形切口或接头端部附近单元内位移和电势沿径向分布为指数形式，而周向方向分布则采用泡函数插值，将其代入弱式方程，建立一种只需对楔形切口或接头端部附近周边进行离散的一维简单有限元方法．压电材料的极化轴可以是任意方向．利用该有限元模型讨论了楔形切口角度、极化轴方向和边界条件对奇性场的影响．通过和其它特定情况下的现有解相比，证实了该文有限元数值方法的有效性，而且精度很高．     

Effect of Maxwell stress on a moving crack with polarization saturation region in ferroelectric solid

The focus of this work is on a generalized two-dimensional problem of a crack moving in a piezoelectric solid subjected to uniform electrical load at infinity. The novel point includes that the electric field inside the crack is taken into account when polarization saturation region exists. Based on the extended Stroh formalism and complex function method, explicit expressions of both the stress fields in the solid and electric fields inside the crack are derived by using semi-permeable crack model, respectively. Effect of Maxwell stress along the crack surface is investigated and the results are illustrated graphically. It is shown that the moving speed of the crack cannot exceed the lowest bulk wave speed. It is also found that the medium properties inside the crack and surrounding the ferroelectric solid at infinity directly affect the Maxwell stress, and as a result the Maxwell stresses are remarkable and cannot be ignored under different electric load.     

Self-consistent problem about electric fields produced in air by a pulse of gamma quanta

The problem of the radial electric field excited in air by an instantaneous point source of gamma quanta is considered. This problem was solved in [1–3] under the assumption that the Compton electron currents originating during scattering of the gamma quanta are given. Such an approximation is valid if the influence of the originating electric field on the Compton electron motion is neglected. The dimensionless parameter characterizing the influence of the electric field is α = e?1/W (? is the characteristic magnitude of the electric field, and 1 and W are the path and kinetic energy of the Compton electron, W ～ 1 MeV). For α ? 1 deceleration of the electrons by the electric field can be neglected and the model proposed for Compton currents [1] is used to determine the field.     

Persistence and coexistence of infinite attractors in a fractal Josephson junction resonator with unharmonic current phase relation considering feedback flux effect

Josephson junction resonators are the devices which exhibit complex behaviours as a consequence of their inductive properties. Even though the insulating medium between Josephson junctions (JJs) is normally considered homogeneous, the fact that lithography is used to form the layer, it has fractal substrates. Such JJs are identified as fractal Josephson junctions (FJJs). In this paper, a new chaotic oscillator based on memristor and FJJ has been investigated. Superconductor properties can dramatically change its operating points especially voltage and heat that are related to Josephson tunnelling. Some changes in the operating points can cause the Josephson tunnelling junctions to oscillate in different oscillation modes in very high frequencies. This can be achieved by considering the potential across the junction with its flux feedback. In order to model the magnetic flux effect, we use a memristor whose memductance function is considered as an exponential function. By varying the type of the bias current, we could observe the property of infinitely coexisting attractors in the memristor-fractal Josephson junction oscillator, which is considered as a rare phenomenon in physical circuits. The proposed Josephson-Memristor circuit model is developed, and its equilibrium points, bifurcation and Lyapunov exponents are computed. As an engineering application, modelling the trajectories of the moving object has been realized. First, the SURF algorithm, which is not affected by the scale and rotations of the object, is used in the images to identify an object that tracks the states of the proposed Josephson-Memristor circuit. In this way, the coordinates of the orbits on which the object moves were determined on the image. In order to reproduce the orbits of the specified object, the coordinate information of the object has been trained to the artificial neural network model and the orbits of the object have been reproduced.

     

Effect of surface electric current on the electrohydrodynamic flow inside and outside a spherical drop

The problem of electrohydrodynamic flow of a viscous, low-conducting, polarizable liquid inside and outside a spherical drop in an applied homogeneous constant electric field is analytically solved with account for the effect of both surface conduction current and surface convection current. The influence of the drop deformation on the field and the flow is neglected. The solution is obtained in the form of asymptotic expansions in a small parameter corresponding to weak surface convection electric currents.     

Periodic set of limited electrically permeable interface cracks with contact zones

Plane problem for an infinite space composed of two different piezoelectric or piezoelectric/dielectric semi-infinite spaces with a periodic set of limited electrically permeable interface cracks is considered. Uniformly distributed electromechanical loading is applied at infinity. The frictionless contact zones at the crack tips are taken into account. The problem is reduced to the combined Dirichlet–Riemann boundary value problem by means of the electromechanical factors presentation via sectionally analytic functions, assuming that the electric flux is uniformly distributed inside the cracks. An exact solution of the problem is proposed. It permits to find in a closed form all necessary electromechanical characteristics at the interface and to formulate the equation for the determination of the electric flux value. Analysis of this equation confirms the correctness of the assumption concerning the uniform distribution of the electric flux in the crack region.Formulae for stresses, electric displacement vector, elastic displacements and electric potential jump at the interface as well as the intensity factors at the crack tips are given. Equation for the contact zone length determination is presented. Calculations for certain material combinations are carried out. The influence of electric permeability of cracks on electromechanical fields and the fracture mechanical parameters is analyzed.     

Re-examination of the PKHS crack model in piezoelectric materials

In this paper, the PKHS crack model is re-examined in detail. Some novel features and better understandings are presented. It is found that the normal crack opening displacement jump (NCODJ) across the crack is always extremely small, whereas the electric potential drop (EPD) across the crack is very large for PZT-4 or PZT-5H under 20 MPa and a varying electric field from −0.5 MV/m to 0.5 MV/m. It is also found that the permittivities of the medium inside the crack gap influence the NCODJ and the EPD significantly. Of great significance is that the crack tip energy release rate (ERR) does not always show an even functional dependence on the applied electric field as previous researchers reported. Its variable tendencies (even or odd) depend on the mechanical loading levels, which are called as the load dependence feature here. In PZT-4, this load-dependence feature induced from the increasing mechanical loading may lead to a transformation of the crack tip ERR from an even functional dependence to an odd one when the applied electric loading varies within the range mentioned above, whereas in PZT-5H no such feature exists. This implies that different mechanical loading levels may yield different fracture behaviors when using the crack tip ERR as a fracture criterion. Moreover, the permittivities of medium inside the PKHS crack gap influence the variable tendencies of the ERR significantly. Thus, a useful addition to previous works is provided and a reasonable explanation for the fundamental discrepancy between previous theoretical predictions and experimental observations in piezoelectric fracture can be given. That is, previous experiments were performed for quite different piezoelectric materials, under quite different mechanical loading levels, and with quite different media inside crack gaps.     

管道联接件参数识别的行波法

基于结构振动的行波理论,提出了一种管道联接件物理参数识别的新方法.以未充液直管在平面内的弯曲振动为例,建立了入射波和出射波在联接件处的散射关系,并结合波模式幅值系数的识别,得到一组包含待识别参数的非线性方程组.在每一个频率下求解该方程组得到联接件的动刚度,最后采用最小二乘法一次识别得到联接件的物理参数.数值仿真结果表明,行波法在管道联接件参数辨识中,识别精度高,而且采用矩阵条件数小的传感器阵列,可以提高参数辨识的精度.     

A confrontation of 1D and 2D RKDG numerical simulation of transitional flow at open‐channel junction

In this study, a comparison between the 1D and 2D numerical simulation of transitional flow in open‐channel networks is presented and completely described allowing for a full comprehension of the modeling water flow. For flow in an open‐channel network, mutual effects exist among the channel branches joining at a junction. Therefore, for the 1D study, the whole system (branches and junction) cannot be treated individually. The 1D Saint Venant equations calculating the flow in the branches are then supplemented by various equations used at the junction: a discharge flow conservation equation between the branches arriving and leaving the junction, and a momentum or energy conservation equation. The disadvantages of the 1D study are that the equations used at the junction are of empirical nature due to certain parameters given by experimental results and moreover they often present a reduced field of validity. On the contrary, for the 2D study, the entire network is considered as a single unit and the flow in all the branches and junctions is solved simultaneously. Therefore, we simply apply the 2D Saint Venant equations, which are solved by a second‐order Runge–Kutta discontinuous Galerkin method. Finally, the experimental results obtained by Hager are used to validate and to compare the two approaches 1D and 2D. Copyright © 2009 John Wiley & Sons, Ltd.     

广西航运枢纽工程建设中的极软岩研究

广西郁江桂平至上游百色规划有10个千吨级航运枢纽梯级,其中老口、鱼梁、那吉处在南宁、百色第三纪盆地。盆地内泥质岩石属软~极软泥岩,它具有低强度、对环境敏感、弱改造等特性,反映在工程设计中地基承载力不足、地基应力及变形超标,抗剪强度低、抗滑稳定问题突出等方面;在工程施工中体现在岩体工程稳定性差,施工保护要求高等。根据那吉等工程勘探试验研究成果,提出针对软岩工程地质问题评价及基础验收、建基面保护、地基处理等应注意的问题和采取的对策。     

Asymptotic approach to analyze singular stress state in anisotropic multi-material: Application to the rivets

The problem of stress singularities due to multi-material junctions is described in this paper. A semi-analytical approach is proposed based on an asymptotic model in the case of anisotropic linear elasticity in three dimensions. The advantage of the present method is the quasi-explicit knowledge of the stress and displacement fields around the junctions. Thus, after a brief explanation of the approach leading to the mechanical fields around the singular line at the junction between different materials, numerical results are presented concerning various configurations of an assembly with rivets included in a bi-layer composite that illustrate this method.     

A micromechanics method to study the effect of domain switching on fracture behavior of polycrystalline ferroelectric ceramics

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Modelling the viscoplastic response of polyethylene in uniaxial loading–unloading tests

Two series of uniaxial cyclic tests are performed on low-density polyethylene at room temperature. In the first series of experiments, injection-molded specimens are stretched to several maximal strains ε_max in the region of sub-yield deformations with a constant cross-head speed, mm/min, and retracted down to the zero stress with the same strain rate. In the other series, loading–unloading tests are carried out with the maximal strain ε_max=0.10 and cross-head speeds ranging from 5 to 200 mm/min. A constitutive model is derived for the viscoplastic behavior of a semicrystalline polymer at small strains. A polymer is modelled as an equivalent network of chains bridged by permanent junctions (entanglements, physical cross-links on the surfaces of crystallites and lamellar blocks). The network is treated as an ensemble of meso-regions connected by links (crystalline lamellae). Deformation of a specimen induces sliding of junctions with respect to their reference positions both at active loading and unloading (this process reflects sliding of junctions in amorphous regions and fine slip of crystalline lamellae). At retraction, sliding of junctions is accompanied by mutual displacements of meso-domains (that reflects coarse slip and fragmentation of lamellar blocks). The constitutive equations are determined by 5 adjustable parameters that are found by matching the experimental stress–strain curves.     

含双侧分支受限空间油气爆炸火焰行为与超压特性大涡模拟

为研究含分支结构狭长受限空间油气爆炸特性规律,基于大涡模拟WALE模型和Zimont预混火焰模型,对横截面为100 mm×100 mm的含双侧分支管道受限空间油气泄压爆炸特性进行了数值模拟。通过对火焰形态、火焰传播速度和动态超压3个物理量的对比,验证了所建立模型对于含分支结构受限空间油气爆炸计算的适用性。基于数值模拟结果,对爆炸过程中的流场结构、火焰形态和超压变化规律进行了分析,指出了“浪花状”火焰的形成原因。结果表明:（1）火焰传播进入分支管道前,在主管道和分支管道交界处会产生旋转方向相反的对称涡旋结构,并随着火焰传播不断向分支管道内部发展;（2）当火焰传播进入分支管道后,分支管道内部前期已建立流场决定了火焰的形态,火焰锋面在涡旋结构作用下呈“浪花状”,此后火焰和流场相互影响,流场向湍流转捩,火焰锋面褶皱变形;（3）爆炸超压升压过程可划分为4个阶段,受到火焰锋面面积和分支管道泄压共同作用,表明爆炸流场、火焰行为和动态超压呈现出显著耦合性。     

Subsonic electrically quasi-neutralweakly-ionized gas flow past a spherical probe

The electric characteristics of a sphere located in a flow of viscous, electrically quasi-neutral weakly-ionized gas containing electrons and monovalent ions are investigated theoretically and numerically. As in the majority of applications, the electrogasdynamic (EGD) interaction parameter is assumed to be small. This makes it possible to solve the gasdynamic and electric equations successively. The spherical surface is assumed to be conducting and heat-insulated. At low free-stream Mach numbers the gas temperature is almost constant in the region of flow past the sphere. This makes it possible to use the model of a viscous incompressible medium. The flow past a sphere is analyzed for gasdynamic Reynolds numbers varying over the interval 0 ≤ Re ≤ 1000. The electrodynamic equations in which the convection and diffusion of the electrons and ions and their electrical drift are taken into account are reduced to three elliptic equations for the electron and ion concentrations and the electric potential. A constant potential is assigned on the boundary of the computation region simulating infinity. The entire problem is simulated numerically using specially constructed grids. The charged-component, potential, and electric current fields are determined and the volt-ampere characteristics of the sphere are constructed for various gas velocities. The results obtained generalize the available data on the voltampere characteristics of a sphere (probe) in a weakly-ionized medium at rest.     

Three-dimensional analysis of defects in a piezoelectric material

In this paper, the Green's function technique is used to develop a solution of an infinite, piezoelectric medium containing either an ellipsoidal cavity or a flat elliptical crack. The coupled elastic and electric fields both inside the cavity and on the boundary of the cavity are obtained, and the stress intensity factor and the electric field intensity factor are also obtained for an elliptical crack. It is found that; (1) the coupled elastic and electric fields inside the cavity keep uniform when the external elastic field and electric field are constant; (2) the behavior of the stress and electric field components in the neighborhood of the crack tip shows the classical type of singularity. The project supported by National Natural Science Foundation of China     

On unique kinematics for the branching shells

We construct the unique two-dimensional (2D) kinematics which is work-conjugate to the exact, resultant local equilibrium conditions of the non-linear theory of branching shells. It is shown that the compatible shell displacements consist of the translation vector and rotation tensor fields defined on the regular parts of the shell base surface as well as independently on the singular surface curve modelling the shell branching. Discussing relations between limits of the translation vector and rotation tensor fields when approaching the singular curve, and analogous fields given only along the singular curve itself, several types of the junctions are described. Among them are the stiff, entirely simply connected and partly simply supported junction as well as the elastically and dissipatively deformable junction, and the non-local elastic junction. For each type of junction the explicit form of the principle of virtual work is derived.