一类滞回系统混沌振动的数值分析

在不同参数下,Brouc-Wen滞回模型使系统具有软或硬式响应特性,导致系统有非线性振动特性。利用数值方法,本文给出单自由度滞回系统 稳态振动最大振幅与频率之间的关系曲线。分析了滞回参数对硬式响应特性滞回振动系统的分叉与混沌的影响,发现一些新的现象。     

高强钢及软钢断裂失效行为表征与仿真预测

针对汽车碰撞、结构强度等分析中无法准确模拟高强钢及软钢的断裂失效,研究了高强钢及软钢的断裂失效特性以及其仿真预测方法．以宝钢高强钢HC340/590DP及软钢DC05为研究对象,首先通过不同应变率的拉伸试验和不同应力状态的断裂失效试验,来表征两种钢材的弹塑性及断裂失效行为．并从试验数据中得到LS-DYNA中的Damage Initiation and Evolution Criteria (DIEC)失效模型所需参数,建立失效模型,通过子系统试验及仿真计算对DIEC失效模型进行验证．结果表明基于准确的材料试验数据,正向建立的DIEC失效模型可以准确预测HC340/590D及DC05的断裂失效行为．本研究方法可推广到其他高强钢和软钢的断裂失效仿真预测中．     

含立方刚度和滞回的隔振系统动力学特性分析

包含立方刚度和Bouc–Wen型滞回的隔振系统具有复杂的非线性动力学特性。系统无阻尼响应模型可基于无滞回恢复力建立,利用谐波平衡法和泰勒展开求得近似解析解。系统有阻尼响应模型可利用解析/数值联合方法求解,该方法基于谐波平衡法和Levenberg–Marquardt迭代算法,对于滞回产生的多值非光滑函数项,先计算时域响应再通过快速傅里叶变换求解谐波项系数。上述方法在含水平绞制梁的非线性隔振系统分析中得到有效应用。分析表明,在Bouc–Wen型滞回和立方刚度的综合影响下,隔振系统呈现渐软-渐硬特性,滞回阻尼和线性阻尼都可以有效抑制共振,但前者高频隔振效果优于后者。     

DYNAMIC CHARACTERISTICS OF VIBRATION ISOLATION SYSTEM WITH CUBIC STIFFNESS AND HYSTERESIS 1)

包含立方刚度和Bouc-Wen 型滞回的隔振系统具有复杂的非线性动力学特性。系统无阻尼响应模型可基于无滞回恢复力建立,利用谐波平衡法和泰勒展开求得近似解析解。系统有阻尼响应模型可利用解析/数值联合方法求解,该方法基于谐波平衡法和Levenberg-Marquardt 迭代算法,对于滞回产生的多值非光滑函数项,先计算时域响应再通过快速傅里叶变换求解谐波项系数。上述方法在含水平绞制梁的非线性隔振系统分析中得到有效应用。分析表明,在Bouc-Wen 型滞回和立方刚度的综合影响下,隔振系统呈现渐软–渐硬特性,滞回阻尼和线性阻尼都可以有效抑制共振,但前者高频隔振效果优于后者。     

高细对称结构正交耦合振动响应的试验研究

高细对称结构是指具有较大的高度／直径比,且横向和纵向完全对称的结构形式。由于其典型的对称电磁场特性,在星载天线上得到了一定的应用。有研究发现：高细对称工程结构在振动试验过程中往往表现出正交耦合响应较大的现象,这些现象相当于产品单方向振动激励时在两个互相正交方向同时进行了振动载荷,从而造成了产品的过试验问题。但是,工程实物模型相对较为复杂,无法通过仿真直观地揭示这种特殊现象的本质。本文针对在实践工程高细对称结构中发现的正交耦合振动响应现象,对这类工程结构进行了简化（将某一类星载天线简化为板梁弯曲结构）。在此基础上提出了试验验证模型,并完成了正弦激励载荷下的振动响应试验。通过分析试验数据对比了对称结构和非对称结构的振动耦合响应异同,剖析了各种产生正交耦合振动响应的原因;指出正交耦合振动响应是高细对称结构的一种固有特性,采用非对称设计可以减小正交耦合响应;最后提出了一种针对这种高细对称结构进行准确仿真计算的方法。     

MEMS加速度计温漂预测补偿模型

温度漂移是影响MEMS加速度计实用效能的关键问题,为提高加速度计的精度和使用范围,需对温漂进行建模和补偿.首先通过温度循环试验对MEMS加速度计温漂特性进行了分析,然后分别采用曲面拟合法、SVM模型和RVM模型建立了温漂预测补偿模型,最后应用环境温度试验数据对模型进行检验和验证.结果表明:三种方法均能够有效的预测加速度计温漂,补偿后的温漂滞环开口由60 mg分别下降到5 mg、10 mg、1 5 mg.曲面拟合法简单、精度高,但对系统重复性要求高,且对噪声比较敏感;SVM模型法计算能力强,但计算量较大,模型参数较多;RVM模型法模型参数较少,计算量小,但训练时间校长,且预测精度不如其他两种方法高.     

考虑参数随机性的压实黄土蠕变变形不确定性分析

现有蠕变模型的计算值为确定值,未能考虑岩土材料和参数评估过程中的随机性。为反映岩土材料的变形随机特性,基于多次重复的一维固结蠕变试验,本文研究了分级和分别加载条件下压实黄土的蠕变特性,建立了考虑参数随机性的改进Merchant模型,提出了一种蠕变变形的不确定性预测方法,并通过延安高填方工程进行了验证。结果表明,压实黄土具有明显的衰减蠕变特性,引入非线性元件的Merchant模型能更好描述土体的应变时间关系,考虑参数随机性的模型计算值近似服从正态分布;通过不确定性预测方法可以获得蠕变变形值的概率云图,且工程实测蠕变变形值落在预测范围的95%的置信区间内,说明了考虑参数随机性的蠕变变形不确定性预测方法的有效性。     

基于贝叶斯信息融合的岸桥有限元模型修正研究

为建立精确的岸桥有限元模型,研究了基于贝叶斯信息融合的模型修正方法．通过方差分析,确定待修正参数,利用中心复合试验设计获取样本点,根据有限元计算结果与实测的结果残差为目标函数获得响应样本．拟合样本点和响应样本值构建二阶多项式响应面模型,并检验响应面模型的精度．基于贝叶斯理论更新融合系数来优化响应面参数,从而获得修正模型．以宁波大榭3号岸桥为工程背景,对比修正后的模态频率和实测频率,最大频率相对误差不超过5%,进而验证了基于贝叶斯信息融合的动力学有限元模型修正方法的有效性．修正后的有限元模型可进一步应用于岸桥的健康监测和安全评估．     

独立失效模式多自由度随机滞回系统可靠性分析

基于Bouc-Wen滞回模型,研究了由滞回环本身的随机性导致的多自由度非线性随机系统可靠性分析问题。基于结构失效的首次穿越模型,应用四阶矩技术和Edgeworth级数逼近技术,对独立失效模式下多自由度随机滞回系统的可靠性问题进行分析。数值算例表明,由独立随机参数表征的随机结构,系统随机响应之间不再独立,存在协方差;系统响应之间相关系数不唯一,具有随时间连续变化的动态、强相关特性。分析计算结果与Monte-Carlo模拟结果吻合较好,表明算法能够满足工程计算精度要求。     

随机激励下滞迟系统的稳态响应闭合解

滞迟系统属于一类典型的强非线性系统,滞迟力不仅取决于系统的瞬时变形,还与变形历程有关.虽然滞迟系统的随机振动问题已被广泛研究,但至今尚未得到滞迟系统随机响应概率密度函数的精确闭合解.本文运用迭代加权残值法获得了高斯白噪声激励下Bouc-Wen滞迟系统稳态响应概率密度函数的近似闭合解.首先,运用等效线性化法求出系统的稳态高斯概率密度函数;然后以此构造权函数,应用加权残值法求得了系统指数多项式形式的非高斯概率密度函数;最后引入迭代的过程,逐步优化权函数,提高计算所得结果的精度.以随机地震激励下钢纤维陶粒混凝土结构的稳态响应作为算例,其中Bouc-Wen模型的参数是基于拟静力学试验数据,并应用最小二乘法辨识获得.与Monte Carlo模拟结果相比,等效线性化法得到的结果精度较差;由加权残值法得到的结果能够表现出非线性特征,但其精度依然无法令人满意;采用迭代加权残值法得到的近似闭合解与Monte Carlo模拟的结果吻合非常好;对于较强随机激励情形,采用渐进迭代加权残值法具有较高的求解效率,所获得的理论解析解具有较高的精度.结果表明,所获得的近似闭合解不仅对于土木工程领域具有重要的实际应用价值,而且还可作为检验其他非线性系统随机响应预测方法的精度的标准.     

Time dependent behavior of ferroelectric materials undergoing changes in their material properties with electric field and temperature

This paper presents a time dependent polarization constitutive model suitable for predicting nonlinear polarization and electro-mechanical strain responses of ferroelectric materials subject to various histories of electric fields. The constitutive model is derived based on a single integral form with nonlinear (electric field and temperature dependent) integrand. The total polarization consists of the time-dependent and residual components. The residual component of the polarization is due to polarization switching in the ferroelectric materials. We use an ‘internal clock’ concept to incorporate the effect of electric field on the rate of polarization. The corresponding strain response is determined through the use of third order piezoelectric constant and/or fourth order electrostrictive constant that vary with polarization stage. It is assumed that in absence of polarization, both piezoelectric and electrostrictive constants are zero. To incorporate the effect of temperature on the overall polarization behavior all material parameters in the constitutive model are allowed to change with the ambient temperature. We present numerical studies on the effect of time, temperature, and electric field on the response of ferroelectric material followed by verification of the constitutive model. Experimental data on lead zirconate titanate (PZT) materials available in the literature are used to verify the model.     

Effect of electric displacement saturation on the hysteretic behavior of ferroelectric ceramics and the initiation and propagation of cracks in piezoelectric ceramics

This paper presents a computational investigation of a proposed simplified account for electric displacement saturation on the hysteretic behavior of initially unpoled ferroelectric ceramics as well as on the initiation and propagation of cracks in poled ferroelectric ceramics within the linear regime of piezoelectricity. For the latter case, experimental observations suggest an odd dependency of the onset of crack initiation in these brittle materials on the orientation of the applied electric field with respect to their poling direction which contradicts theoretical results which propose an even dependency of the energy release rate on the applied electric field within the framework of anisotropic linear piezoelectricity. Electric non-linearities arising at regions of inhomogeneities such as inclusions or at the crack tip are proposed in the literature to avoid this discrepancy. Electric displacement saturation is one such non-linear effect which is investigated in this work. A simplified account of this effect is proposed based on an exponential saturation model of the identified material parameters which can be related to this non-linearity. Its advantage over the superposition of a complex function onto the singular solution of a crack within the framework of linear piezoelectricity lies in the straightforward extension of the proposed approach to problems where no analytical solutions exist. This is outlined based on its incorporation into a rate-dependent ferroelectric model accounting for polarization switching as well as based on its incorporation into a finite element framework capable of simulating the initiation and propagation of cracks in piezoelectric ceramics through strong discontinuities in the displacement field and the electric potential. It is shown that besides the determination of the crack initiation onset also the crack propagation direction is influenced by the appearance of saturation zones arising at the crack tip normal to the polarization direction. The numerically obtained crack paths are found to be close to the experimentally reported results.     

Macroscopical non-linear material model for ferroelectric materials inside a hybrid finite element formulation

A new approach for modeling hysteretic non-linear ferroelectric ceramics is presented, based on a fully ferroelectric/ferroelastic coupled macroscopic material model. The material behavior is described by a set of yield functions and the history dependence is stored in internal state variables representing the remanent polarization and the remanent strain. For the solution of the electromechanical coupled boundary value problem, a hybrid finite element formulation is used. Inside this formulation the electric displacement is available as nodal quantity (i.e. degree of freedom) which is used instead of the electric field to determine the evolution of remanent polarization. This involves naturally the electromechanical coupling. A highly efficient integration technique of the constitutive equations, defining a system of ordinary differential equations, is obtained by a customized return mapping algorithm. Due to some simplifications of the algorithm, an analytical solution can be calculated. The automatic differentiation technique is used to obtain the consistent tangent operator. Altogether this has been implemented into the finite element code FEAP via a user element. Extensive verification tests are performed in this work to evaluate the behavior of the material model under pure electrical and mechanical as well as coupled and multi-axial loading conditions.     

A ferroelectric and ferroelastic 3D hexahedral curvilinear finite element

An isoparametric 3D electromechanical hexahedral finite element integrating a 3D phenomenological ferroelectric and ferroelastic constitutive law for domain switching effects is proposed. The model presents two internal variables which are the ferroelectric polarization (related to the electric field) and the ferroelastic strain (related to the mechanical stress). An implicit integration technique of the constitutive equations based on the return-mapping algorithm is developed. The mechanical strain tensor and the electric field vector are expressed in a curvilinear coordinate system in order to handle the transverse isotropy behavior of ferroelectric ceramics. The hexahedral finite element is implemented into the commercial finite element code Abaqus® via the subroutine user element. Some linear (piezoelectric) and non linear (ferroelectric and ferroelastic) benchmarks are considered as validation tests.     

铁电陶瓷PZT53复杂力电耦合行为的实验研究

通过实验研究了平行和垂直于极化方向的正应力对铁电陶瓷锆钛酸铅(PZT53)的电滞回线(E3-P3)和电致应变曲线(E-ε)的影响. 实验发现平行于极化方向的压应力对PZT53陶瓷的电滞回线、电致应变曲线形状以及矫顽场大小都有明显的影响,但是垂直于极化方向的拉、压应力只对PZT53陶瓷的电致应变曲线形状有明显的影响,但对电滞回线形状和矫顽场大小都没有显著影响. 采用畴翻转的模型详细解释了观察到的实验现象,所得结果为建立铁电陶瓷的多轴力、电耦合本构模型,提供了物理基础.     

The shift of Curie temperature and evolution of ferroelectric domain in ferroelectric crystals

A micromechanics-based thermodynamic model for the phase transition of ferroelectric crystals is developed and, with it, the shift of Curie temperature and evolution of ferroelectric phase upon cooling are examined. This approach differs from the classical phenomenological one in that the evolution of new domain concentration can be predicted. We start out by formulating the Gibbs free energy of a generic, two-phase crystal consisting of the parent paraelectric phase and the transformed ferroelectric phase, at a given level of temperature, stress, and electric field. The thermodynamic driving force for domain growth is then derived and, together with the resistance force, a kinetic equation is established. The derived driving force is found to arise from three different sources of Gibbs free energy: (i) the interaction energy due to the heterogeneity of electromechanical moduli of the parent and product phases, (ii) the energy dissipation due to spontaneous polarization, and (iii) the self-energy of the dual-phase system due to the existence of polarization strain and electric polarization. For a BaTiO₃ crystal the electromechanical heterogeneity is found to play a rather significant role that seems not to have been recognized before. The derived shift recovers to the Clausius-Clapeyron relation if such heterogeneity disappears. We have examined in detail several factors that affect the shift of Curie temperature, and calculated the evolution of overall polarization and dielectric constant of a BaTiO₃ crystal. The results are found to be consistent with available test data.     

Three dimensional phase field study on the thickness effect of ferroelectric polymer thin film

The electromechanical behavior of poly(vinylidene fluoride-trifluoroethylene) [P(VDF-TrFE)] ferroelectric thin film was investigated using the three dimensional (3D) phase-field method. Various energetic contributions, including elastic, electrostatic, and domain wall energy were taken into account in the variational functional of the phase field model. Evolution of the microscopic domain structures of P (VDF-TrFE) polymer film was simulated. Effects of the in-plane residual stress, the film thickness and externally applied electric bias field on the electromechanical properties of the film were explored. The obtained numerical results showed that the macroscopic responses of the electric hysteresis loops are sensitive to the residual stress and electric bias field. It was also found that thickness has a great effect on the electric hysteresis loops and remanent polarization.     

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.     

Three-dimensional finite element simulations of ferroelectric polycrystals under electrical and mechanical loading

Complex, non-linear, irreversible, hysteretic behavior of polycrystalline ferroelectric materials under a combined electro-mechanical loading is a result of domain wall motion, causing simultaneous expansion and contraction of unlike domains, grain sub-divisions that have distinct spontaneous polarization and strain. In this paper, a 3-dimensional finite element method is used to simulate such a polycrystalline ferroelectric under electrical and mechanical loading. A constitutive law due to Huber et al. [1999. A constitutive model for ferroelectric polycrystals. J. Mech. Phys. Solids 47, 1663-1697] for switching by domain wall motion in multidomain ferroelectric single crystals is employed in our model to represent each grain, and the finite element method is used to solve the governing conditions of mechanical equilibrium and Gauss's law. The results provide the average behavior for the polycrystalline ceramic. We compare the outcomes predicted by this model with the available experimental data for various electromechanical loading conditions. The qualitative features of ferroelectric switching are predicted well, including hysteresis and butterfly loops, the effect on them of mechanical compression, and the response of the polycrystal to non-proportional electrical loading.     

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

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