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。     

压电复合材料结构的减振/致动性能优化

压电复合材料由于其优越的机械能-电能转换能力，既可用于吸收结构振动能量进行减振，也可施加电压进行致动，但是针对减振与致动性能的设计异同点未被探讨与研究。针对碳纤维-玻璃纤维-压电纤维组成的多层压电复合材料结构的减振及致动性能进行设计与优化，给出了相应的结构铺层建议及优化结果。所设计的复合材料结构包括多层单向混合纤维复合基底和分布式压电片两个主要部分，基底中碳纤维、压电纤维和玻璃纤维对称铺设，压电片贴于基底最外层。基于Euler-Bernoulli梁理论及Hamilton原理推导了压电复合材料结构的机电耦合模型并分析其动力学特性。通过对比不同铺层顺序下结构的减振与致动性能，得到了混合控制结构的最佳铺层顺序。在此基础上，使用遗传算法对分布式压电片贴附位置和整体复合结构中的铺层角度进行优化，分别提升了结构的减振和致动性能。结果表明，分布式压电贴片在最外层时减振效果最好，压电层在内部时致动能力更优。压电贴片的贴附位置优化后，相比于在高应变区贴附的经验布置策略，前三阶模态减振性能分别提升了0.67 dB、0.77 dB及1.87 dB;碳纤维和玻璃纤维铺层角度分别为90.001 5°、53.06...     

基于ESO和GA的约束阻尼板声辐射优化设计

采用有限元法,建立约束阻尼板的动力学模型;结合瑞利积分方程推导板结构的振动辐射声功率。建立以辐射声功率最小化为目标函数,以约束阻尼材料布置位置和厚度为设计变量的约束阻尼结构声辐射优化模型。提出基于渐进优化算法(ESO)和遗传算法(GA)的约束层阻尼板振动声辐射的分层优化设计策略,获得约束阻尼材料的位置和厚度优化配置。结果表明:在保持附加质量不变的条件下,以约束阻尼材料布置位置最优的约束阻尼板为初始结构,对各区域约束阻尼材料的厚度重新配置,能够获得更好的结构振动辐射声功率的控制效果。     

压电作动器对热变形层合板形状修复研究

基于一阶剪切效应Mindlin板理论,建立了在热载下含分布式压电作动器的复合材料层合板有限元分析模型和控制方程,分别研究了该板在内外表面存在温差的情况下的热变形,以及使用压电作动器对热变形区域进行形状修复的问题;在分析中考虑了压电作动器与复合材料层合板间含有胶接层的影响。由典型算例结果讨论,得到如下结论:1)使用压电作动器可以有效地对复合材料层合板的表面热变形形状进行修复;2)压电作动器的分布位置对修复效果影响很大;3)在电压达到一定数值后,继续增加电压值对修复效果贡献很小。     

含压电片复合材料层合板的高阶计算模型

给出了一种分析含任意内埋压电片复合材料层合板的高阶耦合模型, 板的位移场采用三阶剪切理论, 并提出了压电片中电势场在厚度方向的三次分布模式, 可以更精确地描述力、电耦合作用下电场的非均匀分布。在平面应力的假设下给出了简化的压电材料本构方程, 推导了基于该模型的压电层合板有限元计算公式, 并对双压电片梁的弯曲和层合板的变形控制进行了计算, 压电梁的弯曲计算结果与解析结果吻合良好, 表明本文的模型和公式是精确有效的。     

基于几何因子的复合材料气动弹性剪裁设计

实现了基于几何因子的复合材料层合板建模,解决了几何因子与Natran的参数输入问题,并根据工艺约束中的最小铺层比例对几何因子可行空间进行了推导补充。在此基础上,提出了一种基于几何因子和Nastran的复合材料气动弹性剪裁优化设计方法。首先以总厚度和几何因子作为设计变量以及以Nastran作为求解器,以强度、刚度、颤振和发散速度以及几何因子相关性约束作为约束条件进行结构寻优,得到最优的铺层总厚度和几何因子。其次,以最优几何因子作为目标,进行铺层结构逆问题求解,约束条件为复合材料铺层工艺约束。因几何因子为铺层厚度和铺层顺序的表达式,与传统的多级优化相比,以几何因子作为设计变量可以避免铺层厚度和铺层顺序的解耦,进而获得更大的设计空间,且得到的铺层结构可以满足工艺约束。最后,对一矩形悬臂复合材料层合板进行剪裁设计,使得铺层结构满足气动弹性约束且质量最小。结果显示,运用该优化方法可以得到质量更小且满足工艺约束的铺层结构。     

航空发动机复合材料主轴优化方案设计方法

提出了航空发动机复合材料主轴优化设计方法,建立了以质量最轻为目标函数,以强度、临界转速和外径尺寸为约束,以轴芯厚度、复合材料层数、各层厚度和各层铺设角度为优化设计变量的优化数学模型。基于ANSYS软件,建立了发动机复合材料主轴优化方案设计平台,着重解决了可同时进行离散和连续设计变量优化的问题。以低压涡轮主轴为例,进行了金属基复合材料主轴优化设计,设计的复合材料主轴质量比同负荷金属轴减少36.16%。     

压电复合材料层合板的热压电弹性简化模型研究

为有效分析压电复合材料层合板在热、电和载荷下的单向耦合热电弹性问题,基于变分渐近方法(VAM)建立热电弹性简化模型。首先根据虚功原理推导三维压电复合板总势能泛函。然后基于变分渐近法,利用板固有的小参数将三维总势能泛函渐近扩展为系列二维泛函,同时将近似泛函转换为Reissner形式以便实际工程应用。最后建立三维场重构关系以正确预测沿厚度方向的应力分布。计算结果显示:基于该模型重构的沿厚度方向横向剪切应力较古典层合理论和一阶剪切变形理论精确度更好,与三维有限元精确解相一致,表明该模型在压电复合材料层合板应力预测上的有效性。     

基于铺层设计特征的碳纤维增强复合材料悬架控制臂结构优化

基于铺层设计特征,提出一种使用碳纤维复合材料对承载结构件进行结构优化设计的方法和流程.该方法综合考虑结构几何特征、材料铺层方式、铺层厚度及铺层角度在设计环节中的序列关系,通过几何设计空间构建、离散变量多目标优化、基于工艺可行性的最优决策等方法实现结构设计.以碳纤维增强复合材料悬架控制臂的轻量化设计为例:首先,以钢质控制臂结构为参考建立复合材料控制臂的几何设计空间;然后,以复合材料铺层便利性为原则对其进行结构设计,采用准各向同性铺层对控制臂的铺层厚度进行设计;进而,以提高控制臂刚度和1阶固有频率为目标,使用优化算法对铺层角度进行多目标优化设计;最后,以工艺可行性为约束对优化结果进行筛选并最终完成结构设计.结果表明,所设计复合材料结构具有更大的刚度和1阶固有频率,并且与钢质结构相比减重47.9%.所提出的方法能够较好地兼顾结构特征和复合材料设计要求之间的关系,为复合材料结构优化设计理论与方法的发展提供有益参考.     

悬臂梁压电复合材料振动发电功率与应变的关系研究

设计制备了压电陶瓷片分布植入的玻璃纤维复合材料,建立了悬臂梁振动发电结构模型,计算了悬臂梁模型的应变分布,测试了植入到复合材料不同位置、不同厚度的压电陶瓷片的振动发电功率,研究表明,应变提高2倍,振动发电功率提高4倍以上。     

Modeling and characterization of piezoelectrically actuated bistable composites

This paper develops and validates a finite-element model to predict both the cured shape and snap-through of asymmetric bistable laminates actuated by piezoelectric macro fiber composites attached to the laminate. To fully describe piezoelectric actuation, the three-dimensional compliance [s(ij)], piezoelectric [d(ij)], and relative permittivity [ε(ij)] matrices were formulated for the macro fiber actuator. The deflection of an actuated isotropic aluminum beam was then modeled and compared with experimental measurements to validate the data. The model was then extended to bistable laminates actuated using macro fiber composites. Model results were compared with experimental measurements of laminate profile (shape) and snap-through voltage. The modeling approach is an important intermediate step toward enabling design of shape-changing structures based on bistable laminates.     

Higher order shear deformation effects on analysis of laminates with piezoelectric fibre reinforced composite actuators

A complete analytical solution for cross-ply composite laminates integrated with piezoelectric fiber-reinforced composite (PFRC) actuators under bi-directional bending is presented in this paper. A higher order shear and normal deformation theory (HOSNT12) is used to analyze such hybrid or smart laminates subjected to electromechanical loading. The displacement function of the present model is approximated by employing Taylor’s series in the thickness coordinate, while the electro-static potential is assumed to be layer wise (LW) linear through the thickness of PFRC. The equations of equilibrium are obtained using principle of minimum potential energy and solution is by Navier’s technique. Transverse shear stresses are presented at the interface of PFRC actuator and laminate under the action of electrostatic potentials. Results are compared with first order shear deformation theory (FOST) and exact solution.     

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.     

传递矩阵法分析复合材料层合板的传声损失

为了得到不同频率下正交各向异性复合材料层合板的传声损失,基于传递矩阵的方法,推导出层合板的传声损失计算公式。通过建立复合材料层合板的传声计算模型,研究了层合板铺设角度、板厚度和板密度等结构参数对层合板的传声损失影响。计算结果表明：复合材料的密度与传声损失之间没有明显的线性关系,而是随着频率的增加而上升;层合板的总厚度越大,传声损失也越大,而且各层之间厚度不同,也会引起传声损失的较大改变;层合板铺层角度越大,传声损失也越大。采用传递矩阵法能充分考虑复合材料层合板的铺设方式和铺层角度等因素的影响,利用层合板层间的速度和应力连续边界条件,准确的反应复合材料层合板隔声性能。     

HSDT-layerwise analytical solution for rectangular piezoelectric laminated plates

The present paper develops a formulation for laminated plates with extensional distributed piezoelectric sensors/actuators. This formulation is based on linear electroelasticity, and an equivalent single layer is used for the mechanical displacement field, applying a Higher-Order Shear Deformation Theory (HSDT), whereas a layerwise discretization is used in the thickness direction for the electric potential. The electric and mechanical local equilibrium equations and local constitutive equations for the problem are identified. The Principle of Virtual Work is used to derive the dynamic equilibrium equations in terms of generalized forces and the consistent boundary conditions. The piezoelectric laminate constitutive equations are built and used to write the equations of motion in terms of generalized displacements. Finally, analytical solutions for simply supported square laminates with piezoelectric layers are developed. The entire laminate, composed of the base structure and piezoelectric layers, can be arbitrary orthotropic. The solution is adequate for an arbitrary number of piezoelectric layers and stacking positions. Moreover, the solution takes into account all material coefficients, whether mechanical, piezoelectric or dielectric. Analytical results are obtained for static bending, both in sensor and actuation modes, and for free vibration of symmetric cross-ply laminates with piezoelectric layers externally bonded to the plate.     

Analytical solutions for the transverse deflection of a piezoelectric circular axisymmetric unimorph actuator

This paper presents analytical solutions to the transverse deformation shape of a circular axisymmetric piezoelectric-metal composite unimorph actuator. The solutions account for both the influence of an applied electric field and a concentrated or uniformly distributed mechanical load. Using piezoelectric constitutive equations, combined with thin plate and small bending elastic theory, the generalized equation of motion for bending of thin piezoelectric-metal composite plates has been derived. Our approach predicts that there is an optimum thickness ratio between the piezoelectric and metal plates, which leads to a maximum combination of deflection and load carrying capabilities. Derived formulas are very simple that offer a quick method for engineering design and optimization of a circular unimorph piezoelectric actuator.     

Some studies on free vibration of composite laminates

Free vibration analysis is carried out to study the vibration characteristics of composite laminates using the modified shear deformation, layered, composite plate theory and employing the Rayleigh-Ritz energy approach. The analysis is presented in a unified form so as to incorporate all different combinations of laminate boundary conditions and with full coverage with regard to the various design parameters of a laminated plate. A parametric study is made using a beam characteristic function as the admissible function for the numerical calculations.The numerical results presented here are for an example case of fully clamped boundary conditions and are compared with previously published results. The effect of parameters, such as the aspect ratio of plates, ply-angle, number of layers and also the thickness ratios of plies in laminates on the frequencies of the laminate, is systematically studied. It is found that for anti-symmetric angle-ply or cross-ply laminates unique numerical values of the thickness ratios exist which improve the vibration characteristics of such laminates. Numerical values of the non-dimensional frequencies and nodal patterns, using the thickness ratio distribution of the plies, are then obtained for clamped laminates, fabricated out of various commonly used composite materials, and are presented in the form of the design curves.     

Analysis of unsymmetric CFRP–metal hybrid laminates for use in adaptive structures

The potential of using multistable composite materials for adaptive structures is currently receiving interest from the aerospace community because they possess more than one single equilibrium configuration. Unsymmetric CFRP laminates are studied which have an inner isotropic metallic layer. These hybrid laminates are studied using analytical, finite element and experimental techniques. The thermal contraction of the isotropic layer upon cool down from cure induces large in-plane thermal loads which act remotely from the laminate’s neutral plane, increasing snap-through moments and out-of-plane displacements. The curvatures of the hybrid laminates can be doubled compared to pure unsymmetric CFRP laminates.     

An adhesively laminated plate element for PZT smart plates

An adhesively laminated element taking into consideration peel stress is developed for a piezoelectric smart plate. In this novel finite element analysis formulation, a four node piezoelectric element is firstly derived, and an adhesive element of finite thickness with both shear and peel stiffness is sandwiched between two collocated four node plate elements to form an adhesively laminated element for a piezoelectric smart plate. In this framework of finite element analysis, because the displacement filed in this adhesively laminated element is continuous and a plate element is derived based on the Reissner–Mindlin plate theory, and thus it can be accurately applied to a thin or moderately thick host plate with bonded or debonded piezoelectric actuators and sensors. The formulation is performed for an isotropic host plate and a fiber reinforced laminate plate. Numerical results are presented to compare with those of the exact solutions for smart beams, and validate with the experimental results of the isotropic and composite host plates available in the literature. Using the present finite element analysis formulation, energy transfer stresses in the adhesive and equivalent forces induced in the host plate are investigated. The present formulation is demonstrated to allow debondings of piezoelectric patches and the debonding detection.The authors are grateful to the support of the Australian Research Council via a Discovery Projects grant (grant No: DP0346419).     

基于改进模拟退火算法的复合材料层合板频率优化

针对复合材料层合板频率优化问题,结合可行规则法和直接搜索模拟退化算法,提出了一种自适应模拟退火(SA)改进算法。层合板优化目标是基频、频率带隙以及给定基频和带隙约束的层合板厚度。设计变量包括铺层角度和铺层数两种离散变量。改进算法的自适应新点产生模块采用依赖温度的动态调整搜索半径,改善了直接搜索模拟退化(DSA)算法易陷入局部极值的缺陷,而可行规则法的引入提高了SA算法求解约束问题的效率和简易性。采用Ritz法进行频率响应分析以考虑弯扭耦合影响。不同铺层数、角度增量和长宽比时的层合板3类算例结果显示:改进算法能有效求解层合板频率优化,可获得更多或更好的铺层顺序全局优化解。