Damage analysis of tetragonal perovskite structure ceramics implicated by asymptotic field solutions and boundary conditions

Cracking of ceramics with tetragonal perovskite grain structure is known to appear at different sites and scale level. The multiscale character of damage depends on the combined effects of electromechanical coupling, prevailing physical parameters and boundary conditions. These detail features are exhibited by application of the energy density criterion with judicious use of the mode I asymptotic and full field solution in the range of r/a = 10(-4) to 10(-2) where r and a are, respectively, the distance to the crack tip and half crack length. Very close to the stationary crack tip, bifurcation is predicted resembling the dislocation emission behavior invoked in the molecular dynamics model. At the macroscopic scale, crack growth is predicted to occur straight ahead with two yield zones to the sides. A multiscale feature of crack tip damage is provided for the first time. Numerical values of the relative distances and bifurcation angles are reported for the PZT-4 ceramic subjected to different electric field to applied stress ratio and boundary conditions that consist of the specification of electric field/mechanical stress, electric displacement/mechanical strain, and mixed conditions. To be emphasized is that the multiscale character of damage in piezoceramics does not appear in general. It occurs only for specific combinations of the external and internal field parameters, elastic/piezoelectric/dielectric constants and specified boundary conditions. (C) 2002 Published by Elsevier Science Ltd.

Synchronous chaos in the coupled system of two logistic maps

Synchronous chaos is investigated in the coupled system of two Logistic maps. Although the diffusive coupling admits all synchronized motions, the stabilities of their configurations are dependent on the transverse Lyapunov exponents while independent of the longitudinal Lyapunov exponents. It is shown that synchronous chaos is structurally stable with respect to the system parameters. The mean motion is the pseudo-orbit of an individual local map so that its dynamics can be described by the local map. (C) 2004 Elsevier Ltd. All rights reserved.

Variation of added mass and its application to the calculation of amplitude response for a circular cylinder

In the present study, analyzed are the variation of added mass for a circular cylinder in the lock-in ( synchronization) range of vortex-induced vibration (VIV) and the relationship between added mass and natural frequency. A theoretical minimum value of the added mass coefficient for a circular cylinder at lock-in is given. Developed are semi-empirical formulas for the added mass of a circular cylinder at lock-in as a function of flow speed and mass ratio. A comparison between experiments and numerical simulations shows that the semi-empirical formulas describing the variation of the added mass for a circular cylinder at lock-in are better than the ideal added mass. In addition, computation models such as the wake oscillator model using the present formulas can predict the amplitude response of a circular cylinder at lock-in more accurately than those using the ideal added mass.

Nonlinear dynamics of atomic force microscopy with intermittent contact

When the atomic force microscopy (AFM) in tapping mode is in intermittent contact with a soft substrate, the contact time can be a significant portion of a cycle, resulting in invalidity of the impact oscillator model, where the contact time is assumed to be infinitely small. Furthermore, we demonstrate that the AFM intermittent contact with soft substrate can induce the motion of higher modes in the AFM dynamic response. Traditional ways of modeling AFM (one degree of freedom (DOF) system or single mode analysis) are shown to have serious mistakes when applied to this kind of problem. A more reasonable displacement criterion on contact is proposed, where the contact time is a function of the mechanical properties of AFM and substrate, driving frequencies/amplitude, initial conditions, etc. Multi-modal analysis is presented and mode coupling is also shown. (c) 2006 Published by Elsevier Ltd.

Asymptotic solutions to a class of nonlinear oscillation systems

In this paper, we present an asymptotic method for the analysis of a class of strongly nonlinear oscillators, derive second-order approximate solutions to them expressed in terms of their amplitudes and phases, and obtain the equations governing the amplitudes and phases, by which the amplitudes of the corresponding limit cycles and their behaviour can be determined. As an example, we investigate the modified van der Pol oscillator and give the second-order approximate analytical solution of its limit cycle. The comparison with the numerical solutions shows that the two results agree well with each other.

采用分布式压电驱动器升力面的颤振主动抑制

对采用分布式压电驱动器升力面的颤振主动抑制进行了理论与试验研究。应用LQG最优控制法设计了主动控制律，在控制律降阶时提出了平衡实现与LK法结合使用的新途径，在对不定常气动力进行有理函数拟合时对LS法进行了改进。试验中利用激光测速仪非接触测量模型的速度响应并在地面共振试验中用压电驱动器激振模型。颤振风洞试验结果表明，理论计算合理并与试验结果吻合良好。

压电材料椭圆切口的力学分析

在线性压电本构方程框架下，用复势函数方法对椭圆切口模型进行了精确的数值计算。完整地考虑了各向异性力电耦合效应以及切口内不同电介质的介电性质。给出了切口内部不同介电性质对压电材料内部应力的影响。指出了Sosa文章里的一些计算错误。由于现在文献中很小有关于电导通边界条件政府解的数值结果，所以本文同时提供了不同电边界条件下的理论解的数值结果。最后通过最小势能原理建立了8结点有限元模型，对椭圆切口问题进行了计算并与理论解进行了仔细比较。

Piezoelectricity of ZnO films prepared by sol-gel method

ZnO piezoelectric thin films were prepared on crystal substrate Si(111) by sol-gel technology, then characterized by scanning electron microscopy, X-ray diffraction and atomic force microscopy (AFM). The ZnO films characterized by X-ray diffraction are highly oriented in (002) direction with the growing of the film thickness. The morphologies, roughness and grain size of ZnO film investigated by AFM show that roughness and grain size of ZnO piezoelectric films decrease with the increase of the film thickness. The roughness dimension is 2.188-0.914 nm. The piezoelectric coefficient d(33) was investigated with a piezo-response force microscope (PFM). The results show that the piezoelectric coefficient increases with the increase of thickness and (002) orientation. When the force reference is close to surface roughness of the films, the piezoelectric coefficient measured is inaccurate and fluctuates in a large range, but when the force reference is big, the piezoelectric coefficient d(33) changes little and ultimately keeps constant at a low frequency.

线性压电材料的有限元分析

本文利用线性压电学理论，编制了线性压电材料四结点等参有限元程序，进行了校核，并对PZT-5A材料压电智能元件和压电材料标准断裂试进行了计算，计算包括：①采用实际工程应用的压电智能元件尺寸，计算了元件的压电响应；并针对元件内部电极尖端区域容易引起破坏的现象，计算了该区域的奇异应力、应变场及电场。②计算了加力和加电两种情况下压电材料标准断裂试件应力强度因子影响系数F_I和电位移强度因子影响系数F_D。裂纹面边界条件采用D-P条件，试件包括紧凑拉伸标准试件和三点弯曲标准试件。③应用Lagrange乘子法将Parton裂纹边界条件加于有限元程序中，计算了上述两种标准断裂试件的F_I和F_D，计算结果与采用D-P裂纹边界条件的计算结果有很大差异。

带压电陶瓷片梁的力学分析和二类变量广义变分原理

对于采用贴有压电陶瓷片作为作动元件的智能结构，在进行自适应控制时，往往要分析压电陶瓷片所引起的结构中的应力、应变和位移。对于带有压电陶瓷片梁的力学分析，文献中大多采用Euler-Bernoulli模型，即不考虑梁中的剪力，且假定梁沿厚度方向满足直法线假定。考虑到压电陶瓷片对梁的作用主要是通过粘贴层以剪力的形式传递到梁上，梁截面上的剪应力和剪应变一般很大，其影响不能忽略。本文采用Hellinger-Reissner二类变分广义余能原理，导出考虑梁截面上剪应力和剪应变影响的方程式，其中采用吉尔法求解非齐次常微分方程组。并将求得的解与相同条件的有限元解进行比较。结果证明该方法很有效。本文还对二类广义变分法进行了一般的讨论，发现，在使用二类广义变分法求解时，随着应力和位移所取项数的增加，结果有时反而变坏。并对二类广义变分法的使用提出了一些建议。

Energy Functions And Basic Equations For Ferroelectrics

Energy functions (or characteristic functions) and basic equations for ferroelectrics in use today are given by those for ordinary dielectrics in the physical and mechanical communications. Based on these basic equations and energy functions, the finite element computation of the nonlinear behavior of the ferroelectrics has been carried out by several research groups. However, it is difficult to process the finite element computation further after domain switching, and the computation results are remarkably deviating from the experimental results. For the crack problem, the iterative solution of the finite element calculation could not converge and the solutions for fields near the crack tip oscillate. In order to finish the calculation smoothly, the finite element formulation should be modified to neglect the equivalent nodal load produced by spontaneous polarization gradient. Meanwhile, certain energy functions for ferroelectrics in use today are not compatible with the constitutive equations of ferroelectrics and need to be modified. This paper proposes a set of new formulae of the energy functions for ferroelectrics. With regard to the new formulae of the energy functions, the new basic equations for ferroelectrics are derived and can reasonably explain the question in the current finite element analysis for ferroelectrics.

Nonlinear Fluid Damping In Structure-Wake Oscillators In Modeling Vortex-Induced Vibrations

A Nonlinear Fluid Damping (NFD) in the form of the square-velocity is applied in the response analysis of Vortex-induced Vibrations (VIV). Its nonlinear hydrodynamic effects oil the coupled wake and structure oscillators are investigated. A comparison between the coupled systems with the linear and nonlinear fluid dampings and experiments shows that the NFD model can well describe response characteristics, such as the amplification of body displacement at lock-in and frequency lock-ill, both at high and low mass ratios. Particularly, the predicted peak amplitude of the body in the Griffin plot is ill good agreement with experimental data and empirical equation, indicating the significant effect of the NFD on the structure motion.

Flow-induced vibrations of long circular cylinders modeled by coupled nonlinear oscillators

The dynamics of long slender cylinders undergoing vortex-induced vibrations (VIV) is studied in this work. Long slender cylinders such as risers or tension legs are widely used in the field of ocean engineering. When the sea current flows past a cylinder, it will be excited due to vortex shedding. A three-dimensional time domain model is formulated to describe the response of the cylinder, in which the in-line (IL) and cross-flow (CF) deflections are coupled. The wake dynamics, including in-line and cross-flow vibrations, is represented using a pair of non-linear oscillators distributed along the cylinder. The wake oscillators are coupled to the dynamics of the long cylinder with the acceleration coupling term. A non-linear fluid force model is accounted for to reflect the relative motion of cylinder to current. The model is validated against the published data from a tank experiment with the free span riser. The comparisons show that some aspects due to VIV of long flexible cylinders can be reproduced by the proposed model, such as vibrating frequency, dominant mode number, occurrence and transition of the standing or traveling waves. In the case study, the simulations show that the IL curvature is not smaller than CF curvature, which indicates that both IL and CF vibrations are important for the structural fatigue damage.

压电驱动器的气动弹性应用

随着压电智能材料与结构的发展,压电驱动器在气动弹性控制领域占据重要地位.使用压电驱动器控制翼面变形,利用而不是抵抗气动弹性效应可以控制升力、力矩以及它们的分布.采用基本相同的智能结构翼面控制系统,根据不同的控制目标需求,使用压电智能材料驱动器可以达到多种目的,包括静态的形状控制与动态的颤振抑制、抖振控制与阵风响应控制.静态控制方面例如改变翼面形状获得附加空气动力以增加升力、提供横滚力矩、改变升力分布以减小诱导阻力或减小翼根弯矩等;动态控制例如利用改变翼面形状产生的附加空气动力作为控制载荷,改变气动弹性系统的耦合程度,根据控制效果要求可作为气动阻尼、气动刚度或气动质量.这种控制方法可以减轻结构重量,提高操纵效率,扩大飞行包线,提高材料利用率,已成为可变形飞行器的重要研究内容.本文主要阐述压电驱动器气动弹性应用的动机与机理、发展与成就以及问题与展望.

Regenerative amplifier with continuously variable pulse duration used in an optical parametric chirped-pulse amplification laser system for synchronous pumping

A Nd:glass regenerative amplifier has been set up to generate the pumping pulse with variable pulse width for an optical parametric chirped-pulse amplification (OPCPA) laser system. Each pulse of the pulse train from a cw self-mode-locking femtosecond Ti:sapphire oscillator is stretched to approximate to300 ps at 1062 nm to be split equally and injected into a nonlinear crystal and the Nd:glass regenerative amplifier, as the chirped signal pulse train and the seed pulse train of the pumping laser system, respectively. By adjusting the cavity length of the regenerative amplifier directly, the width of amplified pulse could be varied continuously from approximate to300 ps to approximate to3 ns. The chirped signal pulse for the OPCPA laser system and the seed pulse for the pumping laser system come from the same oscillator, so that the time jitter between the signal pulse and the pumping pulse in optical parametric amplification stages could be <10 ps. (C) 2003 Society of Photo-Optical Instrumentation Engineers.