绝对节点坐标法中压电层合板的大变形研究

压电层合板可以通过对作动器施加电压变形为各种形态,在智能可折叠结构领域具有潜在的应用前景。理解这种结构的大变形作动机理是软体智能结构设计的基础。利用等效单层模型,基于绝对节点坐标法（ANCF）,建立了一种柔性压电层合薄板单元。引入了压电材料的本构方程来推导弹性力和压电力,建立了压电层合薄板单元的动力学方程,并对比了在大变形范围内三种曲率表达形式的收敛效果。通过与 ABAQUS 有限元软件求得的结果进行比较,验证了压电层合薄板单元的正确性,并给出了一些大变形算例。结果表明,在压电材料全覆盖、部分覆盖、多段覆盖等情形下,该单元均能得到较为稳定的结果,表明此单元可以与单层线弹性单元进行耦合。此外还研究了压电层合板受集中力状态下的动态响应。该研究有助于理解受智能压电材料驱动的柔性或软体结构的复杂耦合非线性力学行为。     

变截面压电层合梁自由振动分析

考虑压电材料的质量效应和刚度效应,将表面粘贴或埋入式压电悬臂梁看作变截面梁,研究压电材料对智能结构固有特性的影响。基于一阶剪切变形理论导出压电层合梁的抗弯刚度和横向剪切刚度,计及梁的剪切变形和转动惯量,采用Timoshenko理论推导变截面压电层合梁的频率方程。给出了T300/970压电层合梁和硬铝压电层合梁的前3阶固有频率,并和有限元结果、等截面梁的计算结果进行比较。计算表明,压电材料对压电结构固有频率和固有振型的影响显著,在以振动控制为目标的压电结构动力学建模过程中,有必要考虑压电材料的质量和刚度。     

压电驱动器非线性模型研究

本文通过对压电驱动器的软件计算结果与实验结果的差异进行研究总结,利用变形后压电驱动器中各个结构部分的应力应变分布特点,结合复合层合材料力学、梁力学模型和压电材料非线性模型理论构造出压电薄片与基体材料的简化耦合模型,从而建立结构的非线性模型。模型计算结果比软件计算结果更符合实验结果，并且形式比前人的更简单，物理意义清晰明确。再利用该模型对不同结构参数下的压电驱动器性能进行分析，直观地反应出压电驱动器各结构参数对驱动器性能的影响。     

压电层合智能结构冲击损伤自诊断方法的研究

针对压电层合板智能结构,建立了压电阻抗的计算模型,从理论上分析了压电阻抗与结构机械阻抗的相关性,并对冲击损伤试件的压电阻抗进行了实验测试.理论分析和实验研究表明,通过直接测量压电阻抗并提取与冲击损伤相关的特征信息来评价冲击损伤的方法是可行的.该方法基于压电智能结构的机-电动态阻抗特性,不受结构的几何形状限制.测试用的压电元件成本低、且对主体结构刚度的影响很小,测量压电阻抗的方法简单可行,易于实现压电层合智能结构冲击损伤的自诊断功能,有望作为一种新技术在飞行器结构损伤监测方面获得实际应用.     

压电层合板高阶计算模型

压电复合(层合)结构可应用于结构振动控制、形状保持、健康监测等,建立压电层合结构精确的机电耦合计算模型成为了研究的焦点.针对表面粘贴或内部嵌入压电片的压电层合板结构,基于高阶位移场和高阶电势模型,根据Hamilton原理建立了机电耦合高阶有限元模型.该模型适用于薄板和中厚板,并且能够捕捉压电层内沿厚度方向呈抛物线型分布的诱导电势.以压电双晶片简支板为例,进行了作动器构型和开环、闭环状态传感器构型的数值分析.结果指出,诱导电势对压电传感器有重要影响,而压电作动器可忽略这种电势.     

基于模态应变能分布的压电致动器/传感器位置优化遗传算法

本文由线弹性压电结构有限元动力方程,推导了压电智能结构的振动控制方程。建立了准确模拟层合压电结构动力行为的有限元模型。基于主结构模态应变能分布提出了一种新的优化目标函数,将压电致动器/传感器位置编号作为优化变量,建立了离散变量表示的智能结构优化问题,并通过二进制编码的遗传算法（GA）求解了该最优问题。以四边固支复合层合压电智能板为数值算例,采用比例反馈控制, 研究了最优位置配置致动器/传感器智能结构目标模态的控制效果。数值结果表明基于模态应变能分布的遗传算法所得优化解具有较好的振动控制效果。     

压电层合结构力学模型评述

对于存在力场、电场和热场相互耦合的压电层合结构,建立合理的热机电耦合数学模型,是进行结构振动主动控制、形状控制和优化设计的基础.通过假设适当的位移、电势和温度分布模型,根据Hamilton原理或虚功原理导出系统动(静)力学模型是一种有效的建模方法.在推导压电层合结构热机电耦合基本方程的基础上,根据位移、电势和温度分布模型的不同假设,对各种近似力学模型进行评述,指出各种模型的优缺点.最后简单展望该领域今后的发展方向.     

压电层合薄壳振动主动控制的有限元分析

本文采用广义协调平板型壳元对两侧贴有压电薄膜的层合薄壳的振动控制问题进行了数值分析，推导出这种智能结构的主动控制方程，通过对一压电柱壳的计算，分析了主动振动控制的效果。     

类石墨烯单层结构ZnO和GaN的压电特性对比研究

本研究采用基于密度泛函理论的第一性原理计算了类石墨烯单层结构ZnO(g-ZnO) 和GaN(g-GaN)的力学、电学和压电性质, 重点研究了施加应变后原子坐标弛豫与否的Clamped-ion和Relaxed-ion两种模式的弹性刚度系数和压电张量。结果表明单层g-ZnO和g-GaN均具有半导体属性和较好的弹性。单层g-ZnO和g-GaN的压电系数分别约为9.4和2.2 pm·V^-1, 预测这类单层材料在极薄器件中可能具有压电效应, 且g-ZnO的压电性能更好。因此, 类石墨烯单层ZnO有望用于压力传感器、制动器、换能器及能量收集器等纳米尺度器件。     

压电悬臂梁的动力学建模与主动控制

为计及压电层的刚度特性,基于一阶剪切变形理论推导压电层合梁的抗弯刚度,由Hamilton变分原理建立压电层合梁的有限元模型,采用模态叠加方法对有限元模型降阶。在应变最大处配置制动器和传感器,基于鲁棒极点配置算法对低阶系统设计状态反馈,配置极点至期望位置。把针对低阶系统设计的控制器作用于原系统以实现振动主动控制。数值算例验证了这种力学建模方法和控制器设计方法的有效性。     

正交压电复合材料层板各类边界的解析解

压电复合材料层板由压电片与纤维层叠合而成。基于等效单层理论的位移场和电势场,针对正交铺层压电复合材料层板柱面弯曲问题,建立了力电耦合平衡方程,获得了一般边界的解析解。解析解由特解和通解两部分组成,特解对应于简支边界条件,通解由其他各类边界条件确定。平衡方程的变量仅4个,且不随层数变化。如采用相应的位移和电势分布函数,可以得到一阶理论、高阶理论、指数型理论等多种理论的解析解。算例中给出了各种边界条件下位移、应力和电势的解,讨论了各种理论的精度,观察到了固支边界的应力奇异现象。     

An efficient finite element with layerwise mechanics for smart piezoelectric composite and sandwich shallow shells

In this work, we present a new efficient four-node finite element for shallow multilayered piezoelectric shells, considering layerwise mechanics and electromechanical coupling. The laminate mechanics is based on the zigzag theory that has only seven kinematic degrees of freedom per node. The normal deformation of the piezoelectric layers under the electric field is accounted for without introducing any additional deflection variables. A consistent quadratic variation of the electric potential across the piezoelectric layers with the provision of satisfying the equipotential condition of electroded surfaces is adopted. The performance of the new element is demonstrated for the static response under mechanical and electric potential loads, and for free vibration response of smart shells under different boundary conditions. The predictions are found to be very close to the three dimensional piezoelasticity solutions for hybrid shells made of not only single-material composite substrates, but also sandwich substrates with a soft core for which the equivalent single layer (ESL) theories perform very badly.     

On refined nonlinear theories of laminated composite structures with piezoelectric laminae

In this paper geometrically nonlinear theories of laminated composite plates with piezoelectric laminae are developed. The formulations are based on thermopiezoelectricity, and include the coupling between mechanical deformations, temperature changes, and electric displacements. Two different theories are presented: one based on an equivalent-single-layer third-order theory and the other based on the layerwise theory, both of which were developed by the senior author for composite laminates without piezoelectric laminae. In the present study, they are extended to include piezoelectric laminae. In both theories, the electric field is expanded layerwise through the laminate thickness. The dynamic version of the principle of virtual displacements (or Hamilton’s principle) is used to derive the equations of motion and associated boundary conditions of the two theories. These theories may be used to accurately determine the response of laminated plate structures with piezoelectric laminae and subjected to thermomechanical loadings.     

压电层合板层间应力新研究

综述了压电层合板数值分析方面的一些进展，在一般层合板理论的基础上提出一个多层压电层合板单元，依据线性压电理论建立压电层合板单元的杂交元模型，利用三维8节点块状单元建立多层压电层合板的有限元列式，解决了压电层合板层间应力的连续性。     

一种基于Layerwise理论的压电复合材料层合圆柱壳机电耦合有限单元

基于Reddy的Layerwise理论,对含压电铺层的复合材料层合壳的静力响应特性进行了理论研究。基于Layerwise理论,推导了含压电层的复合材料层合壳的应变分量与电场强度表达式。利用Hamilton原理和变分法,推导了压电智能层合壳的欧拉-拉格朗日方程,并采用有限元解法,建立了相应的有限元控制方程及其机电耦合刚度矩阵。通过算例结果与文献中的精确解和试验值进行了对比,表明相较于传统的经典层合板壳理论,本文理论方法的有效性和优势性;并分析了径厚比等参量对两端简支压电智能层合壳静力响应值的影响规律。      

Control of mechanical deformation of a laminate by electrical load to piezoelectric actuator considering the effects of damping and transverse shear

In this paper, we treat the control of dynamic deformation of a laminate by applying electrical load to piezoelectric actuators. Dynamic behavior of the laminate is analyzed considering the effect of damping due to interlaminar shear and the effect of transverse shear. The analytical model is a rectangular laminate composed of fiber-reinforced laminae and piezoelectric layers. The model is assumed to be a symmetric cross-ply laminate with all edges simply supported and to be subjected to unavoidable mechanical load and to electrical loads to piezoelectric actuators. Behavior of the laminate is analyzed based on the first-order shear deformation theory. The effect of damping due to interlaminar shear is incorporated into our analysis by introducing the interlaminar shear stresses which satisfy the Newton’s law of viscosity. The following quantities are obtained: (1) natural frequencies of the laminate, (2) weight functions for the deflection and rotations and (3) transient deflection due to loads varying arbitrarily with time. Moreover, the methods to control the deflection due to mechanical load by applying electrical voltage to the piezoelectric actuator are shown.     

Longitudinal and transverse magnetoelectric voltage coefficients of magnetostrictive/piezoelectric laminate composite: theory

This paper presents a novel, long-type of magnetostrictive and piezoelectric laminate composite design in which the layers are, respectively, magnetized/poled along their length axes, and a theory for modeling its behavior. Using piezoelectric and magnetostrictive constitutive equations, and an equation of motion, a magneto-elasto-electric bieffect equivalent circuit is developed. The circuit is used to predict the longitudinal and transverse magnetoelectric (ME) voltage coefficients of our Terfenol-D/Pb(Zr/sub 1-x/Ti/sub x/)O/sub 3/ laminate design. It is found that the longitudinal ME voltage coefficient is significantly higher (/spl sim/5x) than the transverse one, and that our new laminate design has significantly higher ME voltage coefficients under small applied direct current (DC) magnetic bias fields than designs reported previously by other groups. Experimental values were found to be coincidental with predicted ones.     

Giant magneto-electric effect in laminate composites

It has been discovered that laminate composites of longitudinally magnetized magnetostrictive and transversely poled piezoelectric layers (a L-T laminate composite) have a giant magneto-electric (ME) effect under a low magnetic bias. The ME voltage coefficient is over 110 mV/Oe at a magnetic bias H=500 Oe. This value is 5-10 times higher than that previously reported for transverse magnetized/transverse polarized (T-T) laminates of the same layer compositions at the same bias. In this paper, we also report the magneto-elasto-electric bieffect equivalent circuit of the L-T laminate composite and the corresponding theoretical formula of the magneto-electric voltage coefficient.     

Non-linear coupled multi-field mechanics and finite element for active multi-stable thermal piezoelectric shells

In this paper, a coupled multi-field mechanics framework is presented for analyzing the non-linear response of shallow doubly curved adaptive laminated piezoelectric shells undergoing large displacements and rotations in thermal environments. The mechanics incorporate coupling between mechanical, electric and thermal fields and encompass geometric non-linearity effects due to large displacements and rotations. The governing equations are formulated explicitly in orthogonal curvilinear coordinates and are combined with the kinematic assumptions of a mixed-field shear-layerwise shell laminate theory. A finite element methodology and an eight-node coupled non-linear shell element are developed. The discrete coupled non-linear equations of motion are linearized and solved, using an extended cylindrical arc-length method together with a Newton–Raphson technique, to enable robust numerical predictions of non-linear active shells transitioning between multiple stable equilibrium paths. Validation and evaluation cases on laminated cylindrical strips and cylindrical panels demonstrate the accuracy of the method and its robust capability to predict non-linear response under thermal and piezoelectric actuator loads. Moreover, the results illustrate the capability of the method to model piezoelectric shells undergoing large shape changes by actively jumping between stable equilibrium states and quantify the strong relationship between shell curvature, applied electric potential, applied temperature differential and induced shape change. Copyright © 2008 John Wiley & Sons, Ltd.     

层合板中压电作动器最优厚度和嵌入位置研究

研究了压电结构中压电片厚度和嵌入深度的优化问题。首先给出了压电层合板的高阶耦合分析模型;然后以不受约束的含压电铺层复合材料板为代表,在压电层厚度方向施加电场时板自由变形,假设板任意微元横截面上内力为零,以其弯(扭)曲曲率最大为优化目标,建立了求解压电片最优厚度和嵌入深度问题的约束优化模型。最后分别以各向同性板中嵌入各项同性压电片和复合材料板中嵌入各向异性压电片为例进行了分析,绘出了目标函数的三维曲面图及等高线图,结果表明压电片的作动效能与其厚度和嵌入位置密切相关,而最优厚度和嵌入位置是由压电片和基体的材料特性决定的。