智能材料二维问题的状态空间解
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摘要
智能材料是能够感知环境变化并通过自我判断得出结论并执行相关指令的一种功能材料,它是现代高技术新材料发展的重要方向之一,将支撑着未来高新技术的发展,使传统意义下的功能材料和结构材料之间的界限逐渐消失,实现结构的功能化,功能多样化。因此科学家们预言智能材料的研制成功和大规模应用将导致材料科学发展的又一次重大变革。智能材料要求材料体系集感知、自诊断、自适应、自修复等功能早期的智能材料种类极少,而且适应面很窄,功能单一,随着科学技术的发展,人们开始对智能材料的几种功能分别进行处理,并在所使用的材料中融入某种新的材料和器件,使它们具有某种或多种智能特性,从而大大的扩展了智能材料的应用领域由智能材料组成的智能结构系统是在结构中集传感器、控制器及执行器于一体,赋予结构健康自诊断、环境自适应及损伤自愈合等某些智能功能与生命特征,达到增强结构安全、减轻质量、降低能耗、提高性能总目标的一种仿生结构系统。智能结构系统的诞生是信息学科、工程及材料学科相互渗透与融合的结果,并已在一些重要工程和尖端技术领域,如航空航天飞行器、潜艇、高速列车、汽车、桥梁、水坝、河堤、建筑等的结构健康监测,振动、噪声、形状控制及损伤自愈合等方面展现良好的应用前景。本文在文献调研的基础上,简介了压电材料和压电、压磁材料的研究现状以及在土木工程中的应用,推导了压电材料和压电、压磁材料平面问题的状态变量方程。本文先从一般弹性体平面问题的研究出发,抛弃任何有关位移或应力模式的人为假设,引入状态空间理论,利用弹性力学基本方程推导出了一般弹性体平面问题的状态变量方程,得到状态变量空间解。在此基础上,研究压电材料和压电、压磁材料在直角坐标系下,不计体力、体电荷和体电流的情况下,引入状态空间理论,由基本方程导出应力、应变、位移、电位移、电场强度、电位势、磁感强度和磁位势各未知量的状态空间解,此解形式简单,便于应用。
Intelligent materials are able to sense environmental change and, through self-judgment to draw conclusions and implement the relevant directives of the kind of functional material, it is the development of modern high-tech and new materials is one important direction, will support the future development of high-tech, traditional significance under the functional and structural materials, the boundaries between the gradual disappearance of the function of structure, functional diversity. Therefore, scientists predict the successful development of smart materials and large-scale applications will lead to the development of materials science another major change. Smart materials requested material system set perception, self-diagnostic, adaptive, self-repair function of early species are very few smart materials, and adapt to a very narrow face, single function, with the scientific and technological development, people began several smart materials functions are processed, and Among the materials using some new materials and devices, Shi they have one or multiple, significantly the expansion of the field of smart materials for applications. Intelligent structure system which is composed of intelligent materials is a kind of defense structure system. It is sensor、controller and carrier integrated in the structure, provides health self-diagnosing, environment self-adapting, harm self-healing up and some intelligent function and life character, and achieved the objectives of strengthening structure safety, reducing mass, decreasing energy consuming, enhancing performance. The birth of intelligent structure system is the result of permeating and merging in information subject, engineering subject and material subject. It has shown favorable application prospect in some important engineering and tip technology fields such as the structure health monitor of aviation craft, submarine, speed-train, automobile, bridge, dam, bank and building, control of vibration, noise and shape, harm self-healing so on. This paper is based on study, simply introduced the study actuality of piezoelectric piezomagnetic materials and their application in civil engineering. In this paper, discard any displacement or stress patterns on the artificial assumption, the introduction of state-space theory, fundamental equations of the two-dimensional problem for transversely isotropy piezoelectric-piezomagnetic and elastic media were observed. The state vector equation of the transversely isotropic two-dimensional problem in piezoelectric, piezomagnetic and elastic media is established, get the state space solution, Based on this, it studies piezoelectric materials and piezoelectric, piezomagnetic materials in spherical coordinates, not accounting the body force, body electric charge and body electric current, deduces the general solutions of stress、strain、displacement、electro-displacement, electric field strength, electric potential, magnetic strength, magnetic potential and other variables. At the same time considering that under varied boundary conditions, applies the general solutions into stress, electrics short circuit, displacement, electrics open circuit and magnetic field boundary conditions, the solutions under varied conditions are obtained.
Intelligent materials are able to sense environmental change and, through self-judgment to draw conclusions and implement the relevant directives of the kind of functional material, it is the development of modern high-tech and new materials is one important direction, will support the future development of high-tech, traditional significance under the functional and structural materials, the boundaries between the gradual disappearance of the function of structure, functional diversity. Therefore, scientists predict the successful development of smart materials and large-scale applications will lead to the development of materials science another major change. Smart materials requested material system set perception, self-diagnostic, adaptive, self-repair function of early species are very few smart materials, and adapt to a very narrow face, single function, with the scientific and technological development, people began several smart materials functions are processed, and Among the materials using some new materials and devices, Shi they have one or multiple, significantly the expansion of the field of smart materials for applications. Intelligent structure system which is composed of intelligent materials is a kind of defense structure system. It is sensor、controller and carrier integrated in the structure, provides health self-diagnosing, environment self-adapting, harm self-healing up and some intelligent function and life character, and achieved the objectives of strengthening structure safety, reducing mass, decreasing energy consuming, enhancing performance. The birth of intelligent structure system is the result of permeating and merging in information subject, engineering subject and material subject. It has shown favorable application prospect in some important engineering and tip technology fields such as the structure health monitor of aviation craft, submarine, speed-train, automobile, bridge, dam, bank and building, control of vibration, noise and shape, harm self-healing so on. This paper is based on study, simply introduced the study actuality of piezoelectric piezomagnetic materials and their application in civil engineering. In this paper, discard any displacement or stress patterns on the artificial assumption, the introduction of state-space theory, fundamental equations of the two-dimensional problem for transversely isotropy piezoelectric-piezomagnetic and elastic media were observed. The state vector equation of the transversely isotropic two-dimensional problem in piezoelectric, piezomagnetic and elastic media is established, get the state space solution, Based on this, it studies piezoelectric materials and piezoelectric, piezomagnetic materials in spherical coordinates, not accounting the body force, body electric charge and body electric current, deduces the general solutions of stress、strain、displacement、electro-displacement, electric field strength, electric potential, magnetic strength, magnetic potential and other variables. At the same time considering that under varied boundary conditions, applies the general solutions into stress, electrics short circuit, displacement, electrics open circuit and magnetic field boundary conditions, the solutions under varied conditions are obtained.
引文
[1]杜善义,冷劲松,王殿富等.智能材料系统和结构[M].科学出版社,2001.
[2]杨大智.智能材料与智能系统[M].天津大学出版社,2000.
[3]Gandhi MV and Thompson BS. Smart Materials and Structures. London:Chapma nHall,1992.
[4]T.Takagi, AC oncept of IntelligentM aterials, U. S. Japan or kshopon Sma-rt Intelligent Materials Systems, Technomic Publishing CompanyI nc.3-10,1990.
[5]孙慷,张学福主编.压电学.北京：国防工业出版社,1984.
[6]靳洪允,压电材料的结构及其性能研究[J].山东陶瓷,2005,28(4)：9-14.
[7]李传兵,廖昌荣,张玉等.压电智能结构的研究进展[J].压电与声光,2002,24(1)：42-46.
[8]江水,李兴丹,吴代华.Smart结构及其应用[J].力学进展,1994,24(3)：53-46.
[9]杨大智,魏中国智能材料-材料科学发展新趋势[J]物39,1997,26(1)：6-11.
[10]刘豹,现代控制理论.机械工业出版社,1983.
[11]K.O gatastates pace Analysis of Control Systems, Prentice-Hall, ING.1967.
[12]J.J.DA ZZOC. H. Houpis Linear Control System Analysis and Design McGrawH-ill,1975.
[13]F. CSAKI Modern Control Theorieskadmiai Kiad 1975. Nonlinear optimal and Adaptive System Akadmiai.
[14]L. M. Silverman Realization of Linear Dynamics Systems MPrTransA G-16. No.6. 1971.
[15]范家让,强厚度叠层板壳的精确理论,北京：科学技术出版社.1996.
[16]钟万勰,弹性力学求解新体系,大连理工大学出版社,1993.
[17]钟万勰,结构动力方程的精细积分法,大连理工大学学报,1994：34(2)131-136.
[18]沈鹏程等,状态空间法分析结构的动力响应,安徽建筑工业学院学报,1995：3(2)：1-50
[19]沈小璞,肖卓,高层建筑结构动力时程响应分析的状态空间法,建筑结构报,1998(5),8-160.
[20]沈小璞等,基于状态空间理论的结构动力响应解法,工程力学增刊,1996,492-496.
[21]张爱社等,高耸结构驰振临界风速分析的精细时程积分法,工程力学,2004(1),98-101.
[22]张华,变截面框架—剪力墙—薄壁筒斜交结构简化计算研究,河北工程学院硕士学位论文,2004.
[23]徐芝纶.弹性力学(上册)[M].第3版.北京：人民教育出版社,1992：48—68.
[24]杨桂通.弹性力学[M].北京：高等教育出版社,1998：40—66.
[25]范家让.强厚度叠层板壳的精确理论[M].北京：科学出版社,1998：48—168.
[26]FanJiarang, Yejianqiao.An exact solution for the static and dynamics of laminated thick plates with orthotropie layers [J].Int Solids Structures, 1990,26(5/6):655-662.
[27]Fanjiarang, YeJianqiao. A series solution of the exact equation for thick orthothopic plates [J]. hat J Solids Struetures,1990,26(7):773-778.
[28]Fanjiarang, Yejianqiao. Exact solutions of buckling for simply supported thick laminates[J]. Composite Structures,1993,24:23—28.
[29]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,15(7)：587-598,1994.
[30]孙慷,张学福.压电学[M].北京：国防工业出版社,1984.
[31]Lekhniskii S G.向异性板[M].海昌译.北京：科学出版社,1955.
[32]范家让.强厚度叠层板壳的精确理论(第2版)[M].北京.科学出社,1998.226-330
[33]盛宏玉,董朝文.任意厚度压电层合闭口柱壳的精确解.合肥工业大学学报,2003,26(5)：118-121.
[34]盛宏玉,王慧.压电层合板的三维有限元分析.合肥工业大学学报.2004,27(7)
[35]关群,层状压电压磁弹性介质轴对称问题的状态空间解[J].合肥工业大学学报,2003,26(1)：117—122.
[36]关群.压电、压磁弹性体平面问题的通解[J].上海交通大学学报,2004,38(8).
[37]ETAN.FREE VIBRATIONS OF SIMPLY SUPPORTED AND MULTI LAYERED MAGNETO-ELECTRO ELASTIC PLATES[J]. Journal of Sound Vibration.2002,2 52(3):429-442.
[38]F. Garcla-Sanchez, R. Rojas-Diaz, A. Saez and etal. Fracture of magnet oelectroelastic composite materials using boundary element method [J]. Theoretical and Applied Fracture Mechanics,2007,47(3):192-204.
[2]杨大智.智能材料与智能系统[M].天津大学出版社,2000.
[3]Gandhi MV and Thompson BS. Smart Materials and Structures. London:Chapma nHall,1992.
[4]T.Takagi, AC oncept of IntelligentM aterials, U. S. Japan or kshopon Sma-rt Intelligent Materials Systems, Technomic Publishing CompanyI nc.3-10,1990.
[5]孙慷,张学福主编.压电学.北京：国防工业出版社,1984.
[6]靳洪允,压电材料的结构及其性能研究[J].山东陶瓷,2005,28(4)：9-14.
[7]李传兵,廖昌荣,张玉等.压电智能结构的研究进展[J].压电与声光,2002,24(1)：42-46.
[8]江水,李兴丹,吴代华.Smart结构及其应用[J].力学进展,1994,24(3)：53-46.
[9]杨大智,魏中国智能材料-材料科学发展新趋势[J]物39,1997,26(1)：6-11.
[10]刘豹,现代控制理论.机械工业出版社,1983.
[11]K.O gatastates pace Analysis of Control Systems, Prentice-Hall, ING.1967.
[12]J.J.DA ZZOC. H. Houpis Linear Control System Analysis and Design McGrawH-ill,1975.
[13]F. CSAKI Modern Control Theorieskadmiai Kiad 1975. Nonlinear optimal and Adaptive System Akadmiai.
[14]L. M. Silverman Realization of Linear Dynamics Systems MPrTransA G-16. No.6. 1971.
[15]范家让,强厚度叠层板壳的精确理论,北京：科学技术出版社.1996.
[16]钟万勰,弹性力学求解新体系,大连理工大学出版社,1993.
[17]钟万勰,结构动力方程的精细积分法,大连理工大学学报,1994：34(2)131-136.
[18]沈鹏程等,状态空间法分析结构的动力响应,安徽建筑工业学院学报,1995：3(2)：1-50
[19]沈小璞,肖卓,高层建筑结构动力时程响应分析的状态空间法,建筑结构报,1998(5),8-160.
[20]沈小璞等,基于状态空间理论的结构动力响应解法,工程力学增刊,1996,492-496.
[21]张爱社等,高耸结构驰振临界风速分析的精细时程积分法,工程力学,2004(1),98-101.
[22]张华,变截面框架—剪力墙—薄壁筒斜交结构简化计算研究,河北工程学院硕士学位论文,2004.
[23]徐芝纶.弹性力学(上册)[M].第3版.北京：人民教育出版社,1992：48—68.
[24]杨桂通.弹性力学[M].北京：高等教育出版社,1998：40—66.
[25]范家让.强厚度叠层板壳的精确理论[M].北京：科学出版社,1998：48—168.
[26]FanJiarang, Yejianqiao.An exact solution for the static and dynamics of laminated thick plates with orthotropie layers [J].Int Solids Structures, 1990,26(5/6):655-662.
[27]Fanjiarang, YeJianqiao. A series solution of the exact equation for thick orthothopic plates [J]. hat J Solids Struetures,1990,26(7):773-778.
[28]Fanjiarang, Yejianqiao. Exact solutions of buckling for simply supported thick laminates[J]. Composite Structures,1993,24:23—28.
[29]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,15(7)：587-598,1994.
[30]孙慷,张学福.压电学[M].北京：国防工业出版社,1984.
[31]Lekhniskii S G.向异性板[M].海昌译.北京：科学出版社,1955.
[32]范家让.强厚度叠层板壳的精确理论(第2版)[M].北京.科学出社,1998.226-330
[33]盛宏玉,董朝文.任意厚度压电层合闭口柱壳的精确解.合肥工业大学学报,2003,26(5)：118-121.
[34]盛宏玉,王慧.压电层合板的三维有限元分析.合肥工业大学学报.2004,27(7)
[35]关群,层状压电压磁弹性介质轴对称问题的状态空间解[J].合肥工业大学学报,2003,26(1)：117—122.
[36]关群.压电、压磁弹性体平面问题的通解[J].上海交通大学学报,2004,38(8).
[37]ETAN.FREE VIBRATIONS OF SIMPLY SUPPORTED AND MULTI LAYERED MAGNETO-ELECTRO ELASTIC PLATES[J]. Journal of Sound Vibration.2002,2 52(3):429-442.
[38]F. Garcla-Sanchez, R. Rojas-Diaz, A. Saez and etal. Fracture of magnet oelectroelastic composite materials using boundary element method [J]. Theoretical and Applied Fracture Mechanics,2007,47(3):192-204.
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