【作者】 关群；

【导师】 王建国；

【作者基本信息】 合肥工业大学 ， 工程力学， 2009， 博士

【摘要】 压电、压磁材料作为传感器和激励器与结构集成在一起,组成一个智能的材料系统,或称为压电、压磁复合材料。研究这一类智能结构的首要工作是建立起能够准确反映压电、压磁传感器和激励器与主体结构之间相互作用的分析模型,这种分析模型既要能够从整体上反映压电智能结构中力电耦合相互作用的内在联系,又要便于运用必要的数学工具进行分析和计算。根据模型适用的研究范围,压电、压磁智能结构的分析模型可分为静态模型和动态模型;根据模型中对弹性场、电场和磁场采用的不同假设,又可划分为精确的理论分析模型、简化模型或者称为低阶分析模型(弹性场、电场和磁场简化为一阶的线性分布)和高阶分析模型。在分析和比较已有压电、压磁材料与智能结构的分析模型时,从压电、压磁器件与结构之间的连接来看,通常有嵌入式和表面粘贴两种方式。但是,这些简化的模型,通常采用了线性或者高阶的位移和电势分布假设,忽略或部分忽略了局部变形的非均匀性,因而不能反映压电、压磁器件与结构结合部的局部应力和局部电场。另外,压电、压磁材料的本构方程中包含了弹性、压电、压磁、介电和磁通率等三套材料常数,使问题的复杂性体现在各场的耦合上。为了能正确描述由三维理论揭示的各种力、电、磁特性,本文提出了一个高阶理论模型,该模型放弃了现有的所有的解析模型采用的几个过于简化的假设,即忽略横向正应变和电势沿横向线性分布等,基于三维线性弹性理论,采用状态空间法、Laplace变换、Hankel变换和级数展开等方法,系统地分析压电、压磁复合材料结构的静态和动态特性。论文突破传统对智能材料的磁、电及机械等微观与聚集观物理性能的局部了解,将压电与压磁材料整合为一系统,进而研究其力学分析模式和理论架构。1)通过引入势函数来研究压电、压磁弹性体在直角坐标系下和在柱坐标系下的空间问题的通解。2)通过利用Almansi定理导出压电、压磁复合材料平面问题的通解,将通解简化为由四个“调和函数”来表示所有的物理量,形式简单,便于应用。3)利用状态空间方法,建立了空间轴对称问题的状态变量方程,然后利用Hankel变换将状态变量方程转换为一组常微分方程,得到了Hankel变换空间中的解,再通过Caylay-Hamilton原理和传递矩阵方法推出压电、压磁复合材料层合结构的状态变量解。4)通过Hankel变换技术,研究压电、压磁复合材料层合结构自由振动的精确解以及压电、压磁复合材料空间球对称结构在外激励作用下的动力稳态解,从而为压电、压磁复合材料的智能控制问题提供良好的理论依据。以上问题的研究旨在探索压电、压磁复合材料智能结构中力-电-磁耦合作用的基本规律,提出分析压电、压磁材料智能结构的一般力学模型和计算方法,其中广泛考虑了板边的各种边界条件。以便较准确地估计该种复合材料组成的结构在各种不同因素作用下的力学行为,为压电、压磁复合材料的智能结构后续研究及其应用研究提供主要的理论基础和分析方法。通过研究发现,压电、压磁复合材料层合结构中的力、电、磁行为特性是非常复杂的,即使是薄压电、压磁结构,其电势、磁势沿厚度方向也不一定是线性分布。综上所述,本文紧紧抓住压电、压磁材料中力电磁耦合作用的物理本质,探索适合于压电、压磁智能结构的数学物理模型,系统性地:1)对压电和压磁复合材料结构的静态和动态特性;2)对压电和压磁复合材料结构中出现的应力、电场分布和磁场分布;3)对压电和压磁复合材料结构与弹性介质的相互作用以及含固定电极压电和压磁体的Green函数等基本问题进行深入和详细的研究。这些研究无论对于压电、压磁材料与智能结构的基础理论研究,还是对将来压电、压磁材料与智能结构的设计和工业化应用都具有重要的理论意义和实际应用价值。更多还原

【Abstract】 Piezoelectric、piezomagnetic materials which are used as sensor and actuator integrating with structure form a intelligent material system, which can also be called piezoelectric、piezomagnetic composite materials.。The primary work for the research in this kind of intelligent structure is to establish analytical model which can accurately indicate the interaction between piezoelectric、piezomagnetic sensor and actuator and body structure. This model is not only able to exhibit the internal relation of mechanics-electricity coupling interaction in piezoelectric intelligent structure from the global aspect, but also easy to analyze and calculate with necessary mathematical tools. According to the study domains which are appropriate to the models, the analytical models of piezoelectric、piezomagnetic intelligent structure can be divided into static and dynamic models; On the basis of the different assumptions of the elastic、electric and magnetic fields in the models, they can be divided into precise theory analytical model and simplified model or low- order analytical model i.e. elastic、electric and magnetic fields are simplified as one-order linear distribution and high-order analytical model. When analyzing and comparing the existing analytical models of piezoelectric、piezomagnetic material and intelligent structure, the correlations of piezoelectric、piezomagnetic apparatus and structure can be divided into embedding and surface pasting. However, these simplified models usually adopt linear or high-order distribution assumptions of displacement and electricity potential and neglect or partly neglect the nonuniformity of local deformation, thus can not demonstrate the local stress and electric field of the joint part of piezoelectric、piezomagnetic apparatus and the structure. In order to correctly describe the characteristics of different forces、electricity and magnetism demonstrated by three-dimensional theory, a high-order theory model is developed in this paper, which gives up several excessively simplified assumptions applied in all existing analytical models, that is to say, which neglects the linear distribution of transverse positive strain and electric potential along transverse direction. Based on three-dimensional linear elastic theory, adopting state space method、Laplace transform、Hankel transform and series expansion methods, etc. the static and dynamic characteristics of piezoelectric、piezomagnetic composite structure are systematically analyzed in this paper.This paper breaks through the local knowledge in micro and macro physical properties of magnetism、electricity and mechanism involving intelligent material, integrating piezoelectric and piezomagnetic material, and further studies the mechanics analytical model and theory frame. 1) By means of drawing the potential function the general solution for three- dimensional transversely isotropic magneto-electro-elastic is derived.2) By means of using Almansi’s theorem the general solution for two- dimensional transversely isotropic magneto-electro-elastic is derived. Then is used to simplify the general solution and all physicals quantity are expressed by fou“r harmnic function”. This general solution is easy and convenient for application.3)The methodology is based on a state space formulation . The state vector equation of transversely isotropic space for thick laminated circular plate is established. By the use of the Hankel integral transform and the Caylay-Hamilton theorem, the solutions of state vector equation for thick laminated circular plate are obtained which are the product of initial state variables and transfer matrix. 4) By the use of the Hankel integral transform to study vibration of the piezoelectric、piezomagnetic materials in spherical symmetry and free vibration of piezoelectric、piezomagnetic and elastic circular plate of single layer and multilayered , in order to provid theoretical basis for dynamic control of piezo-electric-magnetic material in space spherical symmetry.The investigation in this paper aims to explore the basic law of mechanics-electricity-magnet- ism coupling action in piezoelectric、pizomagnetic composite structure and systematically proposes general mechanics model and calculating method of analyzing piezoelectric、piezomagnetic composite materials structure with considering a variety of boundary conditions, thus relatively accurately estimates the mechanics behaviors of structure made up of this composite materials influenced by all kinds of elements, accordingly provides elementary theory basis and analytical method for the following research and application research in intelligent structure composed of piezoelectric、piezomagnetic composite materials. It can be found from the study result that the behavior characteristics of mechanics、electricity、magnetism in laminar structure involving piezoelectric、piezomagnetic composite materials are quite complex, even for the thin piezoelectric、piezomagnetic structure, the electric potential、magnetic potential are not necessarily linear distributions along the thickness direction.In a word, the physical nature of mechanics-electricity-magnetism coupling action in piezoelectric、piezomagnetic composite materials is closely grasped, and mathematical physical model which is appropriate to piezoelectric、piezomagnetic structure is explored in this paper. Several fundamental problems, including static and dynamic characteristics of piezoelectric、piezomagnetic composite materials structure, the distributions of stress、electric and magnetic fields occurred in piezoelectric、piezomagnetic composite materials structure , the interaction of piezoelectric、piezomagnetic structure and viscosity elastic medium and the Green function of piezoelectric、piezomagnetic structure containing fixed electrode, etc. are researched deeply and in detail here. These researches show important theoretical significance and practical application value not only for the basic theory study but also for the design and industrial application in the future about piezoelectric、piezomagnetic materials and intelligent structure.更多还原