智能材料结构的多场耦合问题的基本理论及其应用
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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。
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.
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。
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.
引文
[1]郑哲敏,周恒,张涵信.21世纪的力学发展趋势.力学进展,1995,25(4):433-441
[2] Pak Y E. Force on a piezoelectric screw dislocation. J Appl Mech,1990,57: 863-869
[3] Suo Z G, Kuo C M, Barnett D M. Fracture Mechanics for Piezoelectric solid. J Mech Phys Solids, 1992,40(4):739-965
[4]孙慷,张学福主编.压电学.北京:国防工业出版社,1984
[5]胡明哲,李强,李银祥等.磁致伸缩材料的特性及应用研究(I).稀有金属材料与工程, 2000, 29(6):366-369
[6]胡明哲,李强,李银祥等.磁致伸缩材料的特性及应用研究(II).稀有金属材料与工程, 2001, 30(1):1-4
[7] Moon F C. Magneto-Solid Mechanics. New York. Joh Wiley and Sons. 1984
[8] Harshe G. Magnetoelectric effect in piezoelectric magnetostrictive composit-es. Ph D Thsis. The Pennsylvania State University, University Park, PA, USA
[9] Harshe G, Dougherty J P, Newnham R E. Theoretical modeling of 3-0/0-3 magnetoelectric composites. Int J Intell Mater, 1993,4:161-171
[10]Van Run A M J G, Terrell D R, Scholing J H. An in site grown eutectic magnetoelectric composite material: Part2. Physical properties. J Mater Sci, 1974,9:1710-1714
[11]Benveniste Y. Magnetoelectric effect in fibrous composites with piezoelectric and piezomagnetic phases. Phys Rev B, 1995,51:16424-16427
[12]Huang J H, Kuo W S. The analysis of piezoelectric/piezomagnetic composites materials containing ellipsoidal inclusions. J Appl Phys, 1997,81:4889-4898
[13]Avellaneda M, Harshe G. Mangnetoelectric effect in piezoelectric/magnetostrictive multiplayer (2-2) composites. J Intell Mater Syst Struct, 1994,5:501-513
[14]Nan C W. Magnetoelectric effect in piezoelectric and piezomagnetic phases. Phys Rev B, 1994,50:6082-6088
[15]Huang J H, Kuo W S. The analysis of piezoelectric/piezomagnetic composites materials containing ellipsoidal inclusions. J Appl Phys, 1997,81:4889-4898
[16]Wu T L, Huang J H. Closed-form solutions for the magnetoelectric couping coefficients in fibrous composites with piezoelectric and piezomagnetic phases. Int J Solids Struct, 2000,37:2981-300
[17]E.Pan. Exact Solution for Simply Supported and Multilayered Magneto-Electro-Elastic Plates. Journal of Applied Mechanics.2001,68:608-618
[18]E.Pan. Free Vibrations of Simply Supported and Multilayered Magneto-Electro-Elastic Plates. Journal of Sound Vibration,2002,252(3):429-442
[19]E.PAN. Exact solution for functionally graded and layered magneto-electro-elastic plates. International Journal of Engineering Science,2005,43(3-4):321-339.
[20]Jianguo Wang, Linfeng Chen, Shisheng Fang. State vector approach analysis of multilayered magneto-electro-elastic plates. Int J Solids and Structures, 2003,40:1669-1680
[21]姚伟岸,李晓川.平面电磁弹性固体的虚边界元—最小二乘配点法.工程力学,2006(10)
[22]F.Garcla-Sanchez, R. Rojas-D?az, A. Saez and etal. Fracture of magnetoelectroelastic composite materials using boundary element method (BEM) .Theoretical and Applied Fracture Mechanics,2007, 47:192–204
[23]周振功,王彪.压电压磁复合材料中一对平行裂纹对弹性波的散射.应用数学和力学, 2006,27(5)
[24]周振功,王彪.压电材料中两个非对称平行裂纹的基本解.应用数学和力学,2007,(4)
[25]张培伟.周振功.王彪不同功能梯度压电压磁层状介质中共线界面裂纹的动态性能析.应用数学和力学,2007,(5)
[26]杨娟,李星.功能梯度压电压磁材料中裂纹对SH波的散射.应用力学学报,2008,(2)
[27]郭丽芳,李星.功能梯度压电压磁材料粘结的Ⅲ型裂纹问题.宁夏大学学报,2008,(1)
[28]郭丽芳,李星.两个功能梯度压电压磁条粘结的Ⅲ型问题.兰州大学学报,2008,(3)
[29]方岱宁,毛贯中,李法新等.功能材料的力、电、磁耦合行为的实验研究.机械强度, 2005,27(2)
[30]周剑平,施展,刘刚等.铁电/铁磁1-3型结构复合材料磁电性能分析.物理学报, 2006,(7)
[31]万红,谢立强,吴学忠等.TbDyFe/PZT层状复合材料的磁电效应研究.物理学报,2005, 54(8)
[32]丁建明,仲崇贵.外电场对层状复合材料磁电效应的影响.苏州大学学报,2007, 23(2)
[33]Van Den Boomgaard J, Terrell D R, Born R A J, Giller H F J I. An in site grown eutectic magnetoelectric composite material: Part1. Composition and unidirectional solidification. J Mater Sci, 1974, 9:1705-1709
[34]闫云聚,姜节胜,顾松年.智能复合材料结构的应用发展前景[J].测控技术,1996, 15(4):3-4
[35]王子昆,陈庚超.压电材料空间轴对称问题的通解及其应用.应用数学与力学,1994, 15(7):587—598
[36]Wang, Z, Zheng, B. The general solution of three-dimensional problems in piezoelectric media. Int J Solids Structures 1995,32:105-115
[37]Wailon M, Coarsant R H, Besnier F. Analysis of piezoelectric structures by a finite elementmethod. Acta Elerctronica. 1983,25(4):341-362
[38]Ray M C, Bhattacharya R, Samanta B. Exact soiutions for static analysis of intelligent structures. AIAA J,1993,31(9):1684-1691
[39]Ray M C, Rao K M, Samanta B. Exact analysis of coupled electroelastic behaviour of a piezoelectric plate under cylindrical bending. Computers and Structures, 1992,45(4):667-677
[40]H.A.Sosa and M.A.Castro. On concentrated loads at the boundary of a piezoelectrichalf-plane, Journal of the Mechanics and Physics of Solids,1994, 42:105-1122
[41]H.A.Sosa and M.A.Castro. Electroelastic analysis of piezoelectric laminated structures, Applied Mechanics Review, 1993, 46:21-28
[42]Tzou H S. Howard R V. A piezothermoelastic thin shell theory applied to active structures. Journal of Vibration and Acoustics,1994,116:295-302
[43]姚林泉,俞焕然.压电材料球对称问题的通解.兰州大学学报,1998,34(1):30-33
[44]王建国.层状压电介质空间轴对称问题的状态空间解.力学学报,2001,33(1):115-120
[45]Wang.J.G,Fang.S.S,Chen Linfeng. The state vector methods for space axisymmetric problem in multilayered piezoelectric media. Int.J.Solids Struct, 2002,39:3959-3970
[46]Wang.J.G,Fang.S.S. The state vector methods of axisymmetric problem for multilayered anisotropic elastic system. Mech.Res.Commun, 1999, 26(6):673-678
[47]Wang.J.G. The state space solutions of layered space axisymmetric piezoelectric media. Acta.Mech.Sinica,2001,33(1):115-120
[48]Ding Hao Jiang, Chen Buo, Liang Jian. General solutions for coupled equation for piezoelectric media. Int J Solids Structures,1996,33:2283-2298
[49]Ding Haojiang, Wang Guoqing, Chen Weiqiu. A boundary integral formulation and 2D fundamental solutions for piezoelectric media. Comput Methods Appl.Mech Engrg, 1998, 158:65-80
[50]Ding Hao Jiang, Liang Jian. The fundamental solutions for transversely isotropic piezoelectricity and boundary element method. Computers and Structures,1999,71:447-455
[51]H.J.Ding,H.M.Wang,W.Q.Chen.The general solution of spherically isotropic piezoelectric media and its applications. Mechanics Research Communications, 2001,28(4):389-396
[52]Chen W Q,Ding H J. Exact static analysis of a rotating piezoelectric spherical shell. ACAT Mechanic Sinica, 1998,14(3):257-265
[53]丁浩江,徐荣桥,国风林.轴对称层合横观各向同性压电圆板的精确解.中国科学(E), 1999,29(3):214-221
[54]丁浩江,国凤林,侯鹏飞.横观各向同性热电材料简支矩形板的自由振动.力学学报, 2000,32(4):402-411
[55]丁浩江,陈伟球,徐荣桥.压电板壳自由振动的三维精确分析.力学季刊,2001,22 (1):1-9
[56]陈伟球,梁剑,丁皓江.压电复合材料矩形厚板弯曲的三维分析.复合材料学报, 1997, 14(1):108-115
[57]丁浩江,王国庆,陈伟球.用“调和函数”表示的压电介质平面问题的通解.应用数学和力学,1997,18(8):703-710
[58]丁浩江,国凤林,邹道勤.压电材料圆锥顶端作用集中载荷的解.应用数学与力学, 1999,20(1):11-15
[59]丁浩江,梁剑.横观各向同性压电材料半无限体Green函数解.固体力学学报,1998, 19(2):180-183
[60]丁浩江,陈伟球,徐荣桥.横观各向同性层合矩形板弯曲、振动和稳定的三维精确分析.应用数学和力学,2001,22(1):16-22
[61]丁浩江,王惠明,陈伟球.圆柱壳的轴对称平面应变弹性动力学解.应用数学和力学, 2002, 23(2):128-134
[62]高坚新,沈亚鹏,王子昆.有限长压电层合简支板自由振动的三维精确解.力学学报, 1998, 30(2):168-177
[63]尹林,沈亚鹏.压电类智能结构的力学行为和工程应用.力学进展. 1998,28(2): 163-172
[64]李红云,刘正兴,林启荣.外激励下压电球壳的球对称稳态响应分析.应用数学和力学, 2000, 21(8): 852-860
[65]李山青,刘正兴,章建国等.压电材料静力耦合机理的三维解析及简化分析.上海交通大学学报,1999,33(6):737-741
[66]国凤林.压电热弹性理论中的若干问题.浙江大学博士论文,1999
[67]侯鹏飞.压电体的三维接触和断裂.浙江大学博士论文,2000
[68]马治国.压电智能结构的耦合分析与控制策略研究,东北大学博士论文,1999
[69]吕胜利.压电自适应振动控制结构研究.西北工业大学博士论文,1999
[70]申胜平.压电材料破坏理论.上海交通大学博士论文,1999
[71]尚福林.热压电材料及其层合结构的精确力学分析.西安交通大学博士论文,1996
[72] S.G.Lekhniskii.各向异性板.胡海昌译,北京:科学出版社,1955
[73]胡海昌.弹性力学的变分原理及其应用.北京:科学出版社,1981
[74]Liu J X, Liu X G, Zhao Y B. Green’s functions for anisotropic magneto-electric-elastic solids with an elliptical cavity or a crack. Int J Engng Sci, 2001,39:1405-1418
[75]刘金喜,姜稚清.压电、磁和电磁各向异性弹性介质二维问题的Green函数.工程力学, 2001,18(1):41-45
[76]Martin L. Dunn, H A Wienecke. Green’s functions for transversely isotropic piezoelectricsolids. Int J Solids Structures,1996,33:4571-4581
[77]Li J Y. Magnetoelectroelastic multi-inclusion and inhomogeneity problems and their applications in composite materials. Int J Engng Sci, 2000,38:1993-2011
[78]范家让.强厚度叠层板壳的精确理论.科学出版社,1996
[79]何滨,章良,宋祖殷.超磁致伸缩薄膜性能测试系统研究.微细加工技术,2007,(4)
[80]K.J.宾斯,P.J.劳伦松.电场与磁场问题的分析与计算[M].北京:人民教育出版社,1981
[81]曹照平,王社良.智能材料结构系统在土木工程中的应用.重庆建筑大学学报,2001, 23(1):108-113
[82]杜彦良,聂景旭.主动探测裂纹和控制裂纹扩展的智能材料结构.力学进展,1994,24 (4)
[83]王社良,沈亚鹏.形状记忆合金的力学特性及其工程应用.工业建筑,1998,28(3)
[84]聂影旭,杜彦良.形状记忆合金在“智能性材料结构”中的应用研究.材料导报,1993, (1)
[85]郭世海,张羊换,王新林.磁性形状记忆合金的研究现状及发展.稀有金属,2005,29(3)
[86]王社良.形状记忆合金在结构抗震控制中的应用.西安建筑科技大学学报,1998,30(2)
[87]瞿伟廉,李卓球,姜德生.智能材料-结构系统在土木工程中的应用.地震工程与工程振动, 1999,19(3):87-95
[88]闫云聚,姜节胜,任礼行.智能材料结构及在振动控制中的应用研究评述和展望.西北工业大学学报,2000,18(1):35-40
[89]闫云聚,姜节胜.智能复合材料结构振动主动控制力学模型[J].固体力学学报,1998, 19(1):64-68
[90]马治国,闻邦椿,颜云辉.智能结构的若干问题与进展.东北大学学报,1998,19(5): 513-516
[91]朱小朋,梁伟,麦汉超.电磁复合材料层合板自由振动的三维解.复合材料学报,2005, (6): 130-134
[92]Pak Y E, Herrmann G. Conservation laws and the material momentum tensor for the elastic dielectric. Int J Engng Sci, 1986,24:1365-1374
[93][美]D.尤金著,邓建松,彭冉冉译.Mathematica使用指南[M].北京:科学出版社,2002
[94]朱衡君.MATLAB语言与实践教程[M].北京:清华大学出版社,2005
[95]求是科技.MATLAB7.0从入门到精通[M].北京:人民邮电出版社,2006
[96]Luo En,Zhu Huijian,Yuan Lei.Unconventional Hamilton-type variational principles for electromagnetic eiastodynamics.中国科学G辑(英文版),2006,(1)
[97]姚伟岸.电磁弹性固体三维问题的广义变分原理.计算力学学报,2003,20(4)
[98]罗恩,朱慧坚,原磊.电磁弹性动力学的非传统Hamilton型变分原理.中国科学G辑, 2005(6)
[99]黄彬彬,石志飞,章梓茂.压电材料中Gurtin型变分原理.北方交通大学学报,1999, 23(4):114-117
[100]石志飞,赵世瑛,周利民等.压电材料变分原理逆问题的研究.复合材料学报,1998, 15(3):119-123
[101]奚定平.贝塞尔函数[M].北京:高等教育出版社,1998
[102]R.A.Eubanks and E.Sternberg, On the axisymmetric problem of elastic theory for a medium with transverse isotropy. Journal of Rational Mechanics Analysis, 1954, 3: 89-101
[103]Fan J R, Ye J Q. An exact solution for the statics and dynamics of laminated thick plate with orthotropic layers.Int J Solids Struct,1990,26(5/6): 655-662
[104]盛宏玉,范家让.集中荷载作用下层合厚圆板的轴对称弯曲.应用数学和力学, 2000,21(1):87-93
[105]关群.层状压电、压磁介质轴对称问题的状态空间解.合肥工业大学学报, 2003, 26(1): 117-122
[106]Paul Heyliger, Stephen Brooks. Free Vibration of Piezoelectric Laminates in Cylindrical Benging. Int.J.Solids Structures,1995,32(20):2945-2960
[107]杨帆,文玉梅,李平等.考虑损耗的磁致/压电层合材料谐振磁电响应分析.物理学报, 2007,(6)
[108]杨帆,文玉梅,郑敏等.磁致/压电/磁致层合材料磁电响应分析.传感技术学报, 2006,(6)
[109]卿光辉,徐建新,邱家俊.考虑阻尼的状态向量方程和层合板的振动分析.应用数学和学,2007,(2)
[110]代海涛,程伟,李明志.哈密顿体系下功能梯度压电板/管静动力三维解.北京航空航天大学学报,2008,(1)
[111]周又和,郑晓静,王省哲.悬臂铁磁板磁弹性耦合作用的力学分析.固体力学学报, 1998,19(3):239-245
[112]周又和,何琴淑,郑晓静.带铁磁薄膜悬臂板的磁场微感应器磁弹性特征研究.固体力学学报,2000,21(4):283-289
[113]周又和,郑晓静.电磁固体结构力学.北京:科学出版社,2007
[114]熊锐,周忠坡.发展中的磁电材料.信息记录材料,2006,7(6)
[115]薛大为.板壳理论.北京:北京工业学院出版社,1988
[116]刘彦菊,冷劲松,王殿富.智能材料系统与结构的研究进展.纤维复合材料,1999,1: 43-47
[117]孙东亚,陈祖煜,汪小刚.光纤测量技术及其在土木工程中的应用.中国水利水电科学研究院, 1996
[118]熊瑞生.智能材料与智能建筑结构.信阳师范学院学报,1998,11(4):413-416
[2] Pak Y E. Force on a piezoelectric screw dislocation. J Appl Mech,1990,57: 863-869
[3] Suo Z G, Kuo C M, Barnett D M. Fracture Mechanics for Piezoelectric solid. J Mech Phys Solids, 1992,40(4):739-965
[4]孙慷,张学福主编.压电学.北京:国防工业出版社,1984
[5]胡明哲,李强,李银祥等.磁致伸缩材料的特性及应用研究(I).稀有金属材料与工程, 2000, 29(6):366-369
[6]胡明哲,李强,李银祥等.磁致伸缩材料的特性及应用研究(II).稀有金属材料与工程, 2001, 30(1):1-4
[7] Moon F C. Magneto-Solid Mechanics. New York. Joh Wiley and Sons. 1984
[8] Harshe G. Magnetoelectric effect in piezoelectric magnetostrictive composit-es. Ph D Thsis. The Pennsylvania State University, University Park, PA, USA
[9] Harshe G, Dougherty J P, Newnham R E. Theoretical modeling of 3-0/0-3 magnetoelectric composites. Int J Intell Mater, 1993,4:161-171
[10]Van Run A M J G, Terrell D R, Scholing J H. An in site grown eutectic magnetoelectric composite material: Part2. Physical properties. J Mater Sci, 1974,9:1710-1714
[11]Benveniste Y. Magnetoelectric effect in fibrous composites with piezoelectric and piezomagnetic phases. Phys Rev B, 1995,51:16424-16427
[12]Huang J H, Kuo W S. The analysis of piezoelectric/piezomagnetic composites materials containing ellipsoidal inclusions. J Appl Phys, 1997,81:4889-4898
[13]Avellaneda M, Harshe G. Mangnetoelectric effect in piezoelectric/magnetostrictive multiplayer (2-2) composites. J Intell Mater Syst Struct, 1994,5:501-513
[14]Nan C W. Magnetoelectric effect in piezoelectric and piezomagnetic phases. Phys Rev B, 1994,50:6082-6088
[15]Huang J H, Kuo W S. The analysis of piezoelectric/piezomagnetic composites materials containing ellipsoidal inclusions. J Appl Phys, 1997,81:4889-4898
[16]Wu T L, Huang J H. Closed-form solutions for the magnetoelectric couping coefficients in fibrous composites with piezoelectric and piezomagnetic phases. Int J Solids Struct, 2000,37:2981-300
[17]E.Pan. Exact Solution for Simply Supported and Multilayered Magneto-Electro-Elastic Plates. Journal of Applied Mechanics.2001,68:608-618
[18]E.Pan. Free Vibrations of Simply Supported and Multilayered Magneto-Electro-Elastic Plates. Journal of Sound Vibration,2002,252(3):429-442
[19]E.PAN. Exact solution for functionally graded and layered magneto-electro-elastic plates. International Journal of Engineering Science,2005,43(3-4):321-339.
[20]Jianguo Wang, Linfeng Chen, Shisheng Fang. State vector approach analysis of multilayered magneto-electro-elastic plates. Int J Solids and Structures, 2003,40:1669-1680
[21]姚伟岸,李晓川.平面电磁弹性固体的虚边界元—最小二乘配点法.工程力学,2006(10)
[22]F.Garcla-Sanchez, R. Rojas-D?az, A. Saez and etal. Fracture of magnetoelectroelastic composite materials using boundary element method (BEM) .Theoretical and Applied Fracture Mechanics,2007, 47:192–204
[23]周振功,王彪.压电压磁复合材料中一对平行裂纹对弹性波的散射.应用数学和力学, 2006,27(5)
[24]周振功,王彪.压电材料中两个非对称平行裂纹的基本解.应用数学和力学,2007,(4)
[25]张培伟.周振功.王彪不同功能梯度压电压磁层状介质中共线界面裂纹的动态性能析.应用数学和力学,2007,(5)
[26]杨娟,李星.功能梯度压电压磁材料中裂纹对SH波的散射.应用力学学报,2008,(2)
[27]郭丽芳,李星.功能梯度压电压磁材料粘结的Ⅲ型裂纹问题.宁夏大学学报,2008,(1)
[28]郭丽芳,李星.两个功能梯度压电压磁条粘结的Ⅲ型问题.兰州大学学报,2008,(3)
[29]方岱宁,毛贯中,李法新等.功能材料的力、电、磁耦合行为的实验研究.机械强度, 2005,27(2)
[30]周剑平,施展,刘刚等.铁电/铁磁1-3型结构复合材料磁电性能分析.物理学报, 2006,(7)
[31]万红,谢立强,吴学忠等.TbDyFe/PZT层状复合材料的磁电效应研究.物理学报,2005, 54(8)
[32]丁建明,仲崇贵.外电场对层状复合材料磁电效应的影响.苏州大学学报,2007, 23(2)
[33]Van Den Boomgaard J, Terrell D R, Born R A J, Giller H F J I. An in site grown eutectic magnetoelectric composite material: Part1. Composition and unidirectional solidification. J Mater Sci, 1974, 9:1705-1709
[34]闫云聚,姜节胜,顾松年.智能复合材料结构的应用发展前景[J].测控技术,1996, 15(4):3-4
[35]王子昆,陈庚超.压电材料空间轴对称问题的通解及其应用.应用数学与力学,1994, 15(7):587—598
[36]Wang, Z, Zheng, B. The general solution of three-dimensional problems in piezoelectric media. Int J Solids Structures 1995,32:105-115
[37]Wailon M, Coarsant R H, Besnier F. Analysis of piezoelectric structures by a finite elementmethod. Acta Elerctronica. 1983,25(4):341-362
[38]Ray M C, Bhattacharya R, Samanta B. Exact soiutions for static analysis of intelligent structures. AIAA J,1993,31(9):1684-1691
[39]Ray M C, Rao K M, Samanta B. Exact analysis of coupled electroelastic behaviour of a piezoelectric plate under cylindrical bending. Computers and Structures, 1992,45(4):667-677
[40]H.A.Sosa and M.A.Castro. On concentrated loads at the boundary of a piezoelectrichalf-plane, Journal of the Mechanics and Physics of Solids,1994, 42:105-1122
[41]H.A.Sosa and M.A.Castro. Electroelastic analysis of piezoelectric laminated structures, Applied Mechanics Review, 1993, 46:21-28
[42]Tzou H S. Howard R V. A piezothermoelastic thin shell theory applied to active structures. Journal of Vibration and Acoustics,1994,116:295-302
[43]姚林泉,俞焕然.压电材料球对称问题的通解.兰州大学学报,1998,34(1):30-33
[44]王建国.层状压电介质空间轴对称问题的状态空间解.力学学报,2001,33(1):115-120
[45]Wang.J.G,Fang.S.S,Chen Linfeng. The state vector methods for space axisymmetric problem in multilayered piezoelectric media. Int.J.Solids Struct, 2002,39:3959-3970
[46]Wang.J.G,Fang.S.S. The state vector methods of axisymmetric problem for multilayered anisotropic elastic system. Mech.Res.Commun, 1999, 26(6):673-678
[47]Wang.J.G. The state space solutions of layered space axisymmetric piezoelectric media. Acta.Mech.Sinica,2001,33(1):115-120
[48]Ding Hao Jiang, Chen Buo, Liang Jian. General solutions for coupled equation for piezoelectric media. Int J Solids Structures,1996,33:2283-2298
[49]Ding Haojiang, Wang Guoqing, Chen Weiqiu. A boundary integral formulation and 2D fundamental solutions for piezoelectric media. Comput Methods Appl.Mech Engrg, 1998, 158:65-80
[50]Ding Hao Jiang, Liang Jian. The fundamental solutions for transversely isotropic piezoelectricity and boundary element method. Computers and Structures,1999,71:447-455
[51]H.J.Ding,H.M.Wang,W.Q.Chen.The general solution of spherically isotropic piezoelectric media and its applications. Mechanics Research Communications, 2001,28(4):389-396
[52]Chen W Q,Ding H J. Exact static analysis of a rotating piezoelectric spherical shell. ACAT Mechanic Sinica, 1998,14(3):257-265
[53]丁浩江,徐荣桥,国风林.轴对称层合横观各向同性压电圆板的精确解.中国科学(E), 1999,29(3):214-221
[54]丁浩江,国凤林,侯鹏飞.横观各向同性热电材料简支矩形板的自由振动.力学学报, 2000,32(4):402-411
[55]丁浩江,陈伟球,徐荣桥.压电板壳自由振动的三维精确分析.力学季刊,2001,22 (1):1-9
[56]陈伟球,梁剑,丁皓江.压电复合材料矩形厚板弯曲的三维分析.复合材料学报, 1997, 14(1):108-115
[57]丁浩江,王国庆,陈伟球.用“调和函数”表示的压电介质平面问题的通解.应用数学和力学,1997,18(8):703-710
[58]丁浩江,国凤林,邹道勤.压电材料圆锥顶端作用集中载荷的解.应用数学与力学, 1999,20(1):11-15
[59]丁浩江,梁剑.横观各向同性压电材料半无限体Green函数解.固体力学学报,1998, 19(2):180-183
[60]丁浩江,陈伟球,徐荣桥.横观各向同性层合矩形板弯曲、振动和稳定的三维精确分析.应用数学和力学,2001,22(1):16-22
[61]丁浩江,王惠明,陈伟球.圆柱壳的轴对称平面应变弹性动力学解.应用数学和力学, 2002, 23(2):128-134
[62]高坚新,沈亚鹏,王子昆.有限长压电层合简支板自由振动的三维精确解.力学学报, 1998, 30(2):168-177
[63]尹林,沈亚鹏.压电类智能结构的力学行为和工程应用.力学进展. 1998,28(2): 163-172
[64]李红云,刘正兴,林启荣.外激励下压电球壳的球对称稳态响应分析.应用数学和力学, 2000, 21(8): 852-860
[65]李山青,刘正兴,章建国等.压电材料静力耦合机理的三维解析及简化分析.上海交通大学学报,1999,33(6):737-741
[66]国凤林.压电热弹性理论中的若干问题.浙江大学博士论文,1999
[67]侯鹏飞.压电体的三维接触和断裂.浙江大学博士论文,2000
[68]马治国.压电智能结构的耦合分析与控制策略研究,东北大学博士论文,1999
[69]吕胜利.压电自适应振动控制结构研究.西北工业大学博士论文,1999
[70]申胜平.压电材料破坏理论.上海交通大学博士论文,1999
[71]尚福林.热压电材料及其层合结构的精确力学分析.西安交通大学博士论文,1996
[72] S.G.Lekhniskii.各向异性板.胡海昌译,北京:科学出版社,1955
[73]胡海昌.弹性力学的变分原理及其应用.北京:科学出版社,1981
[74]Liu J X, Liu X G, Zhao Y B. Green’s functions for anisotropic magneto-electric-elastic solids with an elliptical cavity or a crack. Int J Engng Sci, 2001,39:1405-1418
[75]刘金喜,姜稚清.压电、磁和电磁各向异性弹性介质二维问题的Green函数.工程力学, 2001,18(1):41-45
[76]Martin L. Dunn, H A Wienecke. Green’s functions for transversely isotropic piezoelectricsolids. Int J Solids Structures,1996,33:4571-4581
[77]Li J Y. Magnetoelectroelastic multi-inclusion and inhomogeneity problems and their applications in composite materials. Int J Engng Sci, 2000,38:1993-2011
[78]范家让.强厚度叠层板壳的精确理论.科学出版社,1996
[79]何滨,章良,宋祖殷.超磁致伸缩薄膜性能测试系统研究.微细加工技术,2007,(4)
[80]K.J.宾斯,P.J.劳伦松.电场与磁场问题的分析与计算[M].北京:人民教育出版社,1981
[81]曹照平,王社良.智能材料结构系统在土木工程中的应用.重庆建筑大学学报,2001, 23(1):108-113
[82]杜彦良,聂景旭.主动探测裂纹和控制裂纹扩展的智能材料结构.力学进展,1994,24 (4)
[83]王社良,沈亚鹏.形状记忆合金的力学特性及其工程应用.工业建筑,1998,28(3)
[84]聂影旭,杜彦良.形状记忆合金在“智能性材料结构”中的应用研究.材料导报,1993, (1)
[85]郭世海,张羊换,王新林.磁性形状记忆合金的研究现状及发展.稀有金属,2005,29(3)
[86]王社良.形状记忆合金在结构抗震控制中的应用.西安建筑科技大学学报,1998,30(2)
[87]瞿伟廉,李卓球,姜德生.智能材料-结构系统在土木工程中的应用.地震工程与工程振动, 1999,19(3):87-95
[88]闫云聚,姜节胜,任礼行.智能材料结构及在振动控制中的应用研究评述和展望.西北工业大学学报,2000,18(1):35-40
[89]闫云聚,姜节胜.智能复合材料结构振动主动控制力学模型[J].固体力学学报,1998, 19(1):64-68
[90]马治国,闻邦椿,颜云辉.智能结构的若干问题与进展.东北大学学报,1998,19(5): 513-516
[91]朱小朋,梁伟,麦汉超.电磁复合材料层合板自由振动的三维解.复合材料学报,2005, (6): 130-134
[92]Pak Y E, Herrmann G. Conservation laws and the material momentum tensor for the elastic dielectric. Int J Engng Sci, 1986,24:1365-1374
[93][美]D.尤金著,邓建松,彭冉冉译.Mathematica使用指南[M].北京:科学出版社,2002
[94]朱衡君.MATLAB语言与实践教程[M].北京:清华大学出版社,2005
[95]求是科技.MATLAB7.0从入门到精通[M].北京:人民邮电出版社,2006
[96]Luo En,Zhu Huijian,Yuan Lei.Unconventional Hamilton-type variational principles for electromagnetic eiastodynamics.中国科学G辑(英文版),2006,(1)
[97]姚伟岸.电磁弹性固体三维问题的广义变分原理.计算力学学报,2003,20(4)
[98]罗恩,朱慧坚,原磊.电磁弹性动力学的非传统Hamilton型变分原理.中国科学G辑, 2005(6)
[99]黄彬彬,石志飞,章梓茂.压电材料中Gurtin型变分原理.北方交通大学学报,1999, 23(4):114-117
[100]石志飞,赵世瑛,周利民等.压电材料变分原理逆问题的研究.复合材料学报,1998, 15(3):119-123
[101]奚定平.贝塞尔函数[M].北京:高等教育出版社,1998
[102]R.A.Eubanks and E.Sternberg, On the axisymmetric problem of elastic theory for a medium with transverse isotropy. Journal of Rational Mechanics Analysis, 1954, 3: 89-101
[103]Fan J R, Ye J Q. An exact solution for the statics and dynamics of laminated thick plate with orthotropic layers.Int J Solids Struct,1990,26(5/6): 655-662
[104]盛宏玉,范家让.集中荷载作用下层合厚圆板的轴对称弯曲.应用数学和力学, 2000,21(1):87-93
[105]关群.层状压电、压磁介质轴对称问题的状态空间解.合肥工业大学学报, 2003, 26(1): 117-122
[106]Paul Heyliger, Stephen Brooks. Free Vibration of Piezoelectric Laminates in Cylindrical Benging. Int.J.Solids Structures,1995,32(20):2945-2960
[107]杨帆,文玉梅,李平等.考虑损耗的磁致/压电层合材料谐振磁电响应分析.物理学报, 2007,(6)
[108]杨帆,文玉梅,郑敏等.磁致/压电/磁致层合材料磁电响应分析.传感技术学报, 2006,(6)
[109]卿光辉,徐建新,邱家俊.考虑阻尼的状态向量方程和层合板的振动分析.应用数学和学,2007,(2)
[110]代海涛,程伟,李明志.哈密顿体系下功能梯度压电板/管静动力三维解.北京航空航天大学学报,2008,(1)
[111]周又和,郑晓静,王省哲.悬臂铁磁板磁弹性耦合作用的力学分析.固体力学学报, 1998,19(3):239-245
[112]周又和,何琴淑,郑晓静.带铁磁薄膜悬臂板的磁场微感应器磁弹性特征研究.固体力学学报,2000,21(4):283-289
[113]周又和,郑晓静.电磁固体结构力学.北京:科学出版社,2007
[114]熊锐,周忠坡.发展中的磁电材料.信息记录材料,2006,7(6)
[115]薛大为.板壳理论.北京:北京工业学院出版社,1988
[116]刘彦菊,冷劲松,王殿富.智能材料系统与结构的研究进展.纤维复合材料,1999,1: 43-47
[117]孙东亚,陈祖煜,汪小刚.光纤测量技术及其在土木工程中的应用.中国水利水电科学研究院, 1996
[118]熊瑞生.智能材料与智能建筑结构.信阳师范学院学报,1998,11(4):413-416