功能梯度压电微结构力—电耦合特性分析
|
摘要
本文首先基于压电弹性体静力学理论,采用Airy应力函数解法,考虑主要压电参数呈任意变化,给出了多层功能梯度压电曲梁以及连续功能梯度压电曲梁的静力学解析解与数值解,理论解答与数值解答符合很好。其次,在两种不同的边界条件下,对功能梯度压电/弹性复合曲梁进行了解析和数值分析,研究了弹性层参数和压电层参数对复合曲梁整体性能的影响。接着,本文对多层功能梯度压电圆筒以及连续功能梯度压电圆筒进行了静力分析,给出了两种圆筒在同时承受外加电压以及外加压力作用下力学及电学分量的解析解。此外,本文还分别基于弹性薄膜理论和薄壳理论,研究了功能梯度压电弹性筒的动力响应,给出了压电参数沿轴向呈线性分布时,压电弹性筒力学和电学响应的解析解,并对两种理论的优缺点进行了讨论。最后,建立了2-2型水泥基压电机敏器件动力特性的分析模型,采用位移解法给出了其解析解,并与相关文献的实验结果进行了比较和讨论,为水泥基压电机敏器件在土木工程中的应用提供了理论分析方法。
First of all,in consideration of the arbitrary change of the main piezoelectric parameter,exact static solution and numerical solution of the multi-layered graded and continuously graded piezoelectric curved beams were given by using Airy stress function method based on the static theory of the piezoelectric elasticity.Both solutions agreed well with each other.Next,the functionally graded piezoelectric/elastic composite curved beam was analyzed both theoretically and numerically under two different boundary conditions and the influence of the parameters of the elastic layer and the piezoelectric layer on the overall performance of the composite was investigated. Then,the paper presented the static analysis of the multi-layered graded and continuously graded piezoelectric cylinders and the exact solutions of both mechanic and electrical components were obtained when the above two types of cylinders were simultaneously subjected to external voltage and pressure.Moreover,based on the membrane theory of elasticity and the shell theory of elasticity,respectively,the dynamic response of the functionally graded piezoelectric elastic cylinder was investigated.As the piezoelectric parameter changes linearly along the axial direction,the exact solutions of both mechanic and electrical components of the piezoelectric elastic cylinder were given.The merits and drawbacks of the two theories were also discussed.Last,the analysis model of the dynamic properties of 2-2 cement based piezoelectric composite were established and its exact solutions were gaven by using the displacement method;comparison and discussion with the experimental results in related literatures were also presented,which provides theoretical method for the application of the cement based piezoelectric composite in civil engineering.
First of all,in consideration of the arbitrary change of the main piezoelectric parameter,exact static solution and numerical solution of the multi-layered graded and continuously graded piezoelectric curved beams were given by using Airy stress function method based on the static theory of the piezoelectric elasticity.Both solutions agreed well with each other.Next,the functionally graded piezoelectric/elastic composite curved beam was analyzed both theoretically and numerically under two different boundary conditions and the influence of the parameters of the elastic layer and the piezoelectric layer on the overall performance of the composite was investigated. Then,the paper presented the static analysis of the multi-layered graded and continuously graded piezoelectric cylinders and the exact solutions of both mechanic and electrical components were obtained when the above two types of cylinders were simultaneously subjected to external voltage and pressure.Moreover,based on the membrane theory of elasticity and the shell theory of elasticity,respectively,the dynamic response of the functionally graded piezoelectric elastic cylinder was investigated.As the piezoelectric parameter changes linearly along the axial direction,the exact solutions of both mechanic and electrical components of the piezoelectric elastic cylinder were given.The merits and drawbacks of the two theories were also discussed.Last,the analysis model of the dynamic properties of 2-2 cement based piezoelectric composite were established and its exact solutions were gaven by using the displacement method;comparison and discussion with the experimental results in related literatures were also presented,which provides theoretical method for the application of the cement based piezoelectric composite in civil engineering.
引文
[1]张福学.现代压电学[M].北京:科学出版社,2001.
[2]黄尚廉.智能结构--工程学科萌生的一场革命[J].压电与声光,1993,15(1):13-15.
[3]李俊宝,张景绘,任勇生,等.振动工程中智能结构的研究进展[J].力学进展,1999,29(2):165-177.
[4]李传兵,廖昌荣,等.压电智能结构的研究进展[J].压电与声光,2002,24(1):42-46.
[5]向宏军,石志飞.梯度功能压电材料的一组参数识别[J].北京交通大学学报:自然科学版,2006,30(1):30-34.
[6]Wu CCM,Kahn M,Moy W.Piezoelectric ceramics with functional gradients:a new application in material design[J].Journal of the American Ceramic Society,1996,79:809-812.
[7]Zhu XH,Wang Q,Meng ZY.A functionally gradient piezoelectric actuator prepared by powder metallurgical process in PNN-PZ-PT system[J].Journal of Materials Science Letters,1995,14:516-518.
[8]Koizumi M FGM activities in Japan[J].Composites B,1997,28:1-4.
[9]Rabin BH S I.Functionally gradient materials[J].Materials Research Society Bulletin,1995,20:14-18.
[10]余茂黎,魏明坤.功能梯度材料的研究动态[J].功能材料,1992,23:184-191.
[11]李永,宋健,张志民.梯度功能力学[M].北京:清华大学出版社,2003.
[12]王宝林,韩杰才,张幸红.非均匀材料力学[M].北京:科学出版社,2003.
[13]Hauke T,Kouvatov A,Steinhausen R,et al.Bending behavior of functionally gradient materials[J].Ferroelectrics,2000,238(1-4):195-202.
[14]伍晓红.儿种新型压电材料中若干力学问题研究[博士].西安:西安交通大学,2003.
[15]Mason WP.Piezoelectricity,Its history and application[J].J.Acoust.Soc.Am.,1981,70:1561-1566.
[16]尹林,沈亚鹏.压电类智能结构的力学行为和工程应用[J].力学进展,1998,28(2):163-172.
[17]Wang ZK,et al.The general solution of three-dimentional problems in piezoelectric media[J].Int.J.Solids Structures,1995,32:105-115.
[18]Ding H J,Chen B,Liang J.General solutions for coupled equations for piezoelectric media[J].International Journal of Solids and Structures,1996,33(16):2283-2298.
[19]Fan H,et al.Two-dimentional contact on a piezoelectric half-space[J].Int.J.Solids Structures,1996,33:1035-1315.
[20]Ding H J,Hou PF,Guo FL.The elastic and electric fields for three-dimensional contact for transversely isotropic piezoelectric materials[J].International Journal of Solids and Structures,2000,37(23):3201-3229.
[21]Wang XM Shen YP.The variational principle for piezoelectric media[J].Acta Mechanica Solida Sinica,1995,8:303-313.
[22]石志飞,周利民.压电材料变分原理逆问题的研究[J].复合材料学报,1998,15(3):119-123.
[23]黄彬彬,石志飞.压电材料变分原理逆问题的研究--动力学中的逆问题[J].复合材料 学报,2000,17(3):103-106.
[24]Ha S,et al.Analysis of laminated composties containing distributed piezoelectric ceramics[J].J.Intell.Mater.Syst.Struct.,1991,2:59-71.
[25]Wailon MC,et al.Analysis of piezoelectric structures by a finite element method[J].Acta Electronica,1983,25:341-362.
[26]Chu WH,Mehregany M,et al.Analysis of tip deflection and force of a bimetallic cantilever microaetuator[J].J.Micromech.Mieroeng.,1993,3:4-7.
[27]Wang QM,et al.Tip deflection and blocking force of soft PZT-based cantilever rainbow actuators[J].Journal of the American Ceramic Society 1999,82:103-110.
[28]Kruusing A.Analysis and optimization of loaded cantilever beam microactuators[J].Smart Materials and Structures,2000,9(2):186-196.
[29]黄彬彬,石志飞.梯度功能压电悬臂梁的几个解析解[J].复合材料学报,2002,19(4):106-113.
[30]张琳楠,石志飞.均布荷载作用下压电材料简支梁的解析解[J].应用数学和力学,2003,24(10):1075-1082.
[31]Fernandes A,Pouget J.An accurate modelling of piezoelectric multi-layer plates[J].European Journal of Mechanics-A/Solids,2002,21(4):629-651.
[32]Fernandes A,Pouget J.Analytical and numerical approaches to piezoelectric bimorph[J].International Journal of Solids and Structures,2003,40(17):4331-4352.
[33]Wu XH,Shen YP,Chen CQ.An exact solution for functionally graded piezothermoelastic cylindrical shell as sensors or actuators[J].Materials Letters,2003,57(22-23):3532-3542.
[34]Chen WQ,Ding H J,Liang J.The exact elasto-electric field of a rotating piezoceramic spherical shell with a functionally graded property[J].International Journal of Solids and Structures,2001,38(38-39):7015-7027.
[35]Chen WQ,Ding HJ.Bending of functionally graded piezoelectric rectangular plates'[J].Acta Mechanica Solida Sinica,2000,13(4):312-319.
[36]Chen WQ,Lu Y,Ye GR,et al.3D electroelastic fields in a functionally graded piezoceramic hollow sphere under mechanical and electric loadings[J].Archive of Applied Mechanics,2002,72(1):39-51.
[37]Kapuria S.An efficient coupled theory for multilayered beams with embedded piezoelectric sensory and active layers[J].International Journal of Solids and Structures,2001,38(50-51):9179-9199.
[38]Ganapathi M,Patel BP,Touratier M.Refined finite element for piezoelectric laminated composite beams[J].Smart Materials & Structures,2004,13(4):57-67.
[39]Wu XH,Chen C,Shen YP,et al.A high order theory for functionally graded piezoelectric shells[J].International Journal of Solids and Structures,2002,39(20):5325-5344.
[40]刘正兴,林启荣.压电-层合梁在非接触电极作用下的二维解析解[J].上海力学,1999,20(3):306-315.
[41]刘正兴,李山青.轴向载荷作用下压电-弹性层合梁段的二维解析解[J].上海力学,1999,20(4):348-356.
[42]章建国,刘正兴,林启荣.压电弹性层合板静力机电耦合特性的解析解[J].32,2000,3:326-333.
[43]林启荣,金占礼.压电弹性层合梁的电场作用下的二维解析解[J].上海交通大学学报,2001,35(4):518-521.
[44]Shen MH,Chen SN,Chen FM.Piezoelectric study on confocally multicoated elliptical inclusion[J].International Journal of Engineering Science,2005,43(17-18):1299-1312.
[45]Zhang C,Cheung YK,Di S,et al.The exact solution of coupled thermoelectroelastic behavior of piezoelectric laminates[J].Computers and Structures,2002,80(13):1201-1212.
[46]Kapuria S,Bhattacharyya M,Kumar AN.Assessment of coupled 1D models for hybrid piezoelectric layered functionally graded beams[J].Composite Structures,2006,72(4):455-468.
[47]Pan E,Han F.Exact solution for functionally graded and layered magneto-electro-elastic plates[J].International Journal of Engineering Science,2005,43(3-4):321-339.
[48]Pan E.Exact solution for simply supported and multilayered magneto-electro-elastic plates[J].Journal of Applied Mechanics,2001,68:608-618.
[49]Pan E,Heyliger PR.Exact solutions for magneto-electro-elastic laminates in cylindrical bending[J].International Journal of Solids and Structures,2003,40(24):6859-6876.
[50]Vel SS,Batra RC.Generalized plane strain thermopiezoelectric analysis of multilayered plates[J].Journal of Thermal Stresses,2003,26(4):353-377.
[51]Shi ZF,Xiang H J,Spencer JB.Exact analysis of multi-layer piezoelectric/composite cantilevers[J].Smart Materials and Structures,2006,15(5):1447-1458.
[52]Zhang TT,Shi ZF.Elastic solutions of graded piezoelectric hollow cylinders[J].Key Engineering Materials,2006,302-303:658-668.
[53]陈盈,石志飞.梯度功能压电悬臂梁的一组基本解及其应用[J].固体力学学报,2004,25(2):241-245.
[54]石志飞,杜善义,等.功能材料力-电耦合问题的几个基本解:(Ⅰ)悬臂梁受力偶作用[J].复合材料学报,2001,18(1):105-108.
[55]石志飞,杜善义,等.功能材料力-电耦合问题的几个基本解:(Ⅱ)悬臂梁梁端受轴向集中力作用[J].复合材料学报,2001,18(1):109-111.
[56]章梓茂,石志飞,黄彬彬.功能材料力-电耦合问题的几个基本解:(Ⅲ):悬臂梁梁端受轴向集中力[J].复合材料学报,2001,18(1):112-114.
[57]Zhang TT,Shi ZF.Two-dimensional exact analysis for piezoelectric curved actuators[J].Journal of Micromechanics and Microengineering,2006,16(3):640-647.
[58]Chen Y,Shi ZF.Exact solutions of functionally gradient piezothermoelastic cantilevers and parameter identification[J].Journal of Intelligent Materials Systerms and Structures,2005,16(6):531-539.
[59]Liu TT,Shi ZF.Bending behavior of functionally gradient piezoelectric cantilever[J].Ferroelectrics,2004,308:43-51.
[60]Chen Y,Shi ZF.Double-layered piezo-thermoelastic hollow cylinder under some coupled loadings[J].Archive of Applied Mechanics,2006,75(6-7):326-337.
[61]Chen Y,Shi ZF.Double-layered piezothermoelastic hollow cylinder under thermal loading[J].Key Engineering Materials,2006,302-303:684-692.
[62]Almajid A,Taya M,Hudnut S.Analysis of out-of-plane displacement and stress field in a piezocomposite plate with functionally graded microstructure[J].International Journal of Solids and Structures,2001,38(19):3377-3391.
[63]Taya M,Almajid AA,Dunn M,et al.Design of bimorph piezo-composite actuators with functionally graded microstructure[J].Sensors and actuators.A,Physical,2003,107(3):248-260.
[64]Ishihara M,Noda N.Nonlinear dynamic behavior of a piezothermoelastic laminated plate with anisotropic material properties[J].Acta Mechanica,2003,166(1):103-118.
[65]He XQ,Ng TY,Sivashanker S,et al.Active control of FGM plates with integrated piezoelectric sensors and actuators[J].International Journal of Solids and Structures,2001,38(9):1641-1655.
[66]Liew KM,He XQ,Ng TY,et al.Finite element piezothermoelasticity analysis and the active control of FGM plates with integrated piezoelectric sensors and actuators[J].Computational Mechanics,2003,31(3-4):350-358.
[67]Liew KM,He XQ,Kitipornchai S.Finite element method for the feedback control of FGM shells in the frequency domain via piezoelectric sensors and actuators[J].Computer Methods in Applied Mechanics and Engineering,2004,193(3-5):257-273.
[68]Shindo Y,Domon W,Narita F.Dynamic bending of a symmetric piezoelectric laminated plate with a through crack[J].Theoretical and Applied Fracture Mechanics,1998,28(3):175-182.
[69]Dong K,Wang X.Influences of large deformation and rotary inertia on wave propagation in piezoelectric cylindrically laminated shells in thermal environment[J].International Journal of Solids and Structures,2006,43(6):1710-1726.
[70]Chen WQ.Vibration theory of non-homogeneous,spherically isotropic piezoelastic bodies[J].Journal of Sound and Vibration,2000,236(5):833-860.
[71]Chen WQ,Wang LZ.Free vibrations of functionally graded piezoceramic hollow spheres with radial polarization[J].Journal of Sound and Vibration,2002,251(1):103-114.
[72]Huang D,Sun BH.Approximate solution on smart composite beams by using MATLAB[J].Composite Structures,2001,54(2-3):197-205.
[73]Huang D,Sun B.Approximate analytical solutions of smart composite Mindlin beams[J].Journal of Sound and Vibration,2001,244(3):379-394.
[74]Krommer M.Piezoelastic vibrations of composite Reissner-Mindlin-type plates[J].Journal of Sound and Vibration,2003,263(4):871-891.
[75]Varelis D,Saravanos DA.Small amplitude free vibration analysis of piezoelectric composite plates subject to large deflections and initial stresses[J].Journal of Vibration and Acoustics,2006,128:41-49.
[76]伍晓红,沈亚鹏.压电功能梯度板自由振动的三维解[J].固体力学学报,2003,24(1):75-82.
[77]Lee H J,Saravanos DA.A mixed multi-field finite element formulation for thermopiezoelectric composite shells[J].International Journal of Solids and Structures,2000,37(36):4949-4967.
[78]Ganesan N,Kadoli R.Semianalytical finite element analysis of piezothermoelastic shells of revolution[J].Computers & Structures,2005,83(15-16):1305-1319.
[79]Liu X,Wang Q,Quek ST.Analytical solution for free vibration of piezoelectric coupled moderately thick circular plates[J].International Journal of Solids and Structures,2002,39(8):2129-2151.
[80]董兴建,孟光,李鸿光.变截面压电层合梁自由振动分析[J].振动工程学报,2005,18(2):243-247.
[81]Ishihara M,Noda N.Nonlinear dynamic behavior of a piezothermoelastic laminate considering the effect of transverse shear[J].Journal of Thermal Stresses,2003,26(11): 1093-1112.
[82]Mukherjee A,Chaudhuri AS.Nonlinear dynamic response of piezolaminated smart beams[J].Computers & Structures,2005,83(15-16):1298-1304.
[83]Kapuria S,Dumir PC,Ahmed A.Exact 2D piezoelasticity solution of hybrid beam with damping under harmonic electromechanical load[J].ZAMM,2004,84(6):391-402.
[84]Kapuria S,Aehary GG.Exact 3D piezothermoelasticity solution for buckling of hybrid cross-ply plates using state space approach[J].ZAMM,2005,85(3):189-201.
[85]Kapuria S,Ahmed A,Dumir PC.Static and dynamic thermo-electro-mechanical analysis of angle-ply hybrid piezoelectric beams using an efficient coupled zigzag theory[J].Composites Science and Technology,2004,64(16):2463-2475.
[86]Zhang TT,Shi ZF,Spencer BF.Vibration analysis of a functionally graded piezoelectric cylindrical actuator[J].Smart Materials and Structures,2008,17(0250182):.
[87]刘艳红,卿光辉,张焕铜.压电材料修正后的变分原理及智能板的精确解[J].中国民航学院学报,2006,24(1):13-17.
[88]Lim CW,He LH.Three-dimensional exact solutions for the electromechanical response of triple-layer piezoelectric actuators[J].Smart Materials and Structures,2004,13(5):1050-1058.
[89]Lim CW,Cheng ZQ,Reddy JN.Natural frequencies of laminated piezoelectric plates with internal electrodes[J].ZAMM,2006,86(5):410-420.
[90]Cheng ZQ,Reddy JN.Three dimensional dolutions of dmart functionally graded plates[J].Journal of Applied Mechanics,2001,68:234-241.
[91]Pan E,Heyliger PR.Free vibrations of simply supported and multilayered magneto-electro-elastic plates[J].Journal of Sound and Vibration,2002,252(3):429-442.
[92]Vel SS,Mewer RC,Batra RC.Analytical solution for the cylindrical bending vibration of piezoelectric composite plates[J].International Journal of Solids and Structures,2004,41(5-6):1625-1643.
[93]王永龄,俞大畏,董显林.智能材料与器件的发展设想[J].无机材料学报,1999,14(2):211-217.
[94]Tanaka T.Piezoelectric devices in Japan[J].Ferroelectrics,1982,40:167-187.
[95]Cross LE.Dielectric,piezoelectric and ferroelectric components[J].American Ceramics Society Bulletin,1984,63:586-590.
[96]Xu Y.Ferroelectric materials and their application[M].Amsterdam,1991.
[97]Wada Y.Piezoelectricity and pyroelectricity of polymers[J].Japan Journal of Applied Physics,1976,15:2041-2057.
[98]Furukawa T.Piezoelectricity and pyroelectricity in polymers[J].IEEE Transaction on Electrical Insulation,1989,24(3):375-394.
[99]Dias CJ,Das-Gupta DK.Inorganic ceramic/polymer ferroelectric composite electrets[J].IEEE Transactions on Dielectrics and Electrical Insulation,1996,3(5):706-734.
[100]郑占申,曲远方,马卫兵.陶瓷/聚合物复合材料的电性能及应用[J].复合材料学报,1998,15(4):14-19.
[101]王数彬,韩杰才,杜善义.压电陶瓷/聚合物复合材料的制备工艺及其性能研究[J].功能材料,1999,30(2):113-117.
[102]Huston DR,Fuhr PL Ambrose T P.Intelligent civil structures-activities in vermont[J].Smart Materials and Structures,1994,3(2):129-139.
[103]Ansari F,Maji A,Leung C.Intelligent civil engineering materials and structures:A collection of state-of-the-art papers in the application of emerging technologies to civil structures and materials[M].New York:American Society of Civil Engineers(ASCE),1997.
[104]Chang F.Structural health monitoring 2000[M].Pennsylvania:Technomic Publishing Co Inc.,1999.
[105]AizawaSkakizawa T,Higasino M.Case studios of smart materials for civil structures[J].Smart Materials and Structures,1998,7(5):617-626.
[106]Wang ML,Heo G,Satpathi D.A health monitoring system for large structural systerms[J].Smart Materials and Structures,1998,7(5):606-616.
[107]Wang XD.Coupled electromechanical behaviour of piezoelectric actuators in smart structures[J].Journal of Intelligent Material Systems and Structures,1999,10(3):232-241.
[108]张东,李宗津.水泥基压电机敏复合材料的可行性分析和研究[J].建筑材料学报,2002,5(2):141-146.
[109]Li Z,Zhang D,Wu K.Cement-Based 0-3 Piezoelectric Composites[J].Journal of the American Ceramic Society,2002,85(2):305-313.
[110]Zhang D,Li ZJ,Wu KR.2-2 piezoelectric cement matrix composite:Part Ⅱ.Actuator effect[J].Cement and Concrete Research,2002,32(5):825-830.
[111]Li ZJ,Zhang D Wu KR.Cement matrix 2-2 piezoelectric composite:Part Ⅰ.Sensory effect[J].Mater.Struct.,2001,13(242):506-512.
[112]Huang S,Chang J,Xu R,et al.Piezoelectric properties of 0-3 PZT/sulfoaluminate cement composites[J].Smart Materials and Structures,2004,13(2):270-274.
[113]F H S.Poling process and piezoelectric properties of lead zirconate titanate/sulphoaluminate cement composites[J].Journal of materials science,2004,39:6975-6979.
[114]Cheng X,Huang SF,et al.Piezoelectric,dielectric and ferroelectric properties of 0-3ceramic/cement composites[J].Journal of applied physics,2007,101,094110:.
[115]Ruan X,Danforth SC,Safari A,et al.Saint-Venant end effects in piezoceramic materials[J].International Journal of Solids and Structures,2000,37(19):2625-2637.
[116]Shi ZF.Bending behavior of piezoelectric curved actuator[J].Smart Materials & Structures,2005,14(4):835-842.
[117]Kouvatov A,Steinhausen R,Seifert W,et al.Comparison between bimorphic and polymorphic bending devices[J].Journal of the European Ceramic Society,1999,19(6):1153-1156.
[118]Haskins JF,et al.Vibrations of ferroelectric cylinderical shells with transverse isotropy[J].J.Acoust.Soc.Am.,1957,29(2):729-734.
[119]张东,李宗津等.2-2型水泥基压电机敏复合材料的研制[J].压电与声光,2002,03:217-04
[2]黄尚廉.智能结构--工程学科萌生的一场革命[J].压电与声光,1993,15(1):13-15.
[3]李俊宝,张景绘,任勇生,等.振动工程中智能结构的研究进展[J].力学进展,1999,29(2):165-177.
[4]李传兵,廖昌荣,等.压电智能结构的研究进展[J].压电与声光,2002,24(1):42-46.
[5]向宏军,石志飞.梯度功能压电材料的一组参数识别[J].北京交通大学学报:自然科学版,2006,30(1):30-34.
[6]Wu CCM,Kahn M,Moy W.Piezoelectric ceramics with functional gradients:a new application in material design[J].Journal of the American Ceramic Society,1996,79:809-812.
[7]Zhu XH,Wang Q,Meng ZY.A functionally gradient piezoelectric actuator prepared by powder metallurgical process in PNN-PZ-PT system[J].Journal of Materials Science Letters,1995,14:516-518.
[8]Koizumi M FGM activities in Japan[J].Composites B,1997,28:1-4.
[9]Rabin BH S I.Functionally gradient materials[J].Materials Research Society Bulletin,1995,20:14-18.
[10]余茂黎,魏明坤.功能梯度材料的研究动态[J].功能材料,1992,23:184-191.
[11]李永,宋健,张志民.梯度功能力学[M].北京:清华大学出版社,2003.
[12]王宝林,韩杰才,张幸红.非均匀材料力学[M].北京:科学出版社,2003.
[13]Hauke T,Kouvatov A,Steinhausen R,et al.Bending behavior of functionally gradient materials[J].Ferroelectrics,2000,238(1-4):195-202.
[14]伍晓红.儿种新型压电材料中若干力学问题研究[博士].西安:西安交通大学,2003.
[15]Mason WP.Piezoelectricity,Its history and application[J].J.Acoust.Soc.Am.,1981,70:1561-1566.
[16]尹林,沈亚鹏.压电类智能结构的力学行为和工程应用[J].力学进展,1998,28(2):163-172.
[17]Wang ZK,et al.The general solution of three-dimentional problems in piezoelectric media[J].Int.J.Solids Structures,1995,32:105-115.
[18]Ding H J,Chen B,Liang J.General solutions for coupled equations for piezoelectric media[J].International Journal of Solids and Structures,1996,33(16):2283-2298.
[19]Fan H,et al.Two-dimentional contact on a piezoelectric half-space[J].Int.J.Solids Structures,1996,33:1035-1315.
[20]Ding H J,Hou PF,Guo FL.The elastic and electric fields for three-dimensional contact for transversely isotropic piezoelectric materials[J].International Journal of Solids and Structures,2000,37(23):3201-3229.
[21]Wang XM Shen YP.The variational principle for piezoelectric media[J].Acta Mechanica Solida Sinica,1995,8:303-313.
[22]石志飞,周利民.压电材料变分原理逆问题的研究[J].复合材料学报,1998,15(3):119-123.
[23]黄彬彬,石志飞.压电材料变分原理逆问题的研究--动力学中的逆问题[J].复合材料 学报,2000,17(3):103-106.
[24]Ha S,et al.Analysis of laminated composties containing distributed piezoelectric ceramics[J].J.Intell.Mater.Syst.Struct.,1991,2:59-71.
[25]Wailon MC,et al.Analysis of piezoelectric structures by a finite element method[J].Acta Electronica,1983,25:341-362.
[26]Chu WH,Mehregany M,et al.Analysis of tip deflection and force of a bimetallic cantilever microaetuator[J].J.Micromech.Mieroeng.,1993,3:4-7.
[27]Wang QM,et al.Tip deflection and blocking force of soft PZT-based cantilever rainbow actuators[J].Journal of the American Ceramic Society 1999,82:103-110.
[28]Kruusing A.Analysis and optimization of loaded cantilever beam microactuators[J].Smart Materials and Structures,2000,9(2):186-196.
[29]黄彬彬,石志飞.梯度功能压电悬臂梁的几个解析解[J].复合材料学报,2002,19(4):106-113.
[30]张琳楠,石志飞.均布荷载作用下压电材料简支梁的解析解[J].应用数学和力学,2003,24(10):1075-1082.
[31]Fernandes A,Pouget J.An accurate modelling of piezoelectric multi-layer plates[J].European Journal of Mechanics-A/Solids,2002,21(4):629-651.
[32]Fernandes A,Pouget J.Analytical and numerical approaches to piezoelectric bimorph[J].International Journal of Solids and Structures,2003,40(17):4331-4352.
[33]Wu XH,Shen YP,Chen CQ.An exact solution for functionally graded piezothermoelastic cylindrical shell as sensors or actuators[J].Materials Letters,2003,57(22-23):3532-3542.
[34]Chen WQ,Ding H J,Liang J.The exact elasto-electric field of a rotating piezoceramic spherical shell with a functionally graded property[J].International Journal of Solids and Structures,2001,38(38-39):7015-7027.
[35]Chen WQ,Ding HJ.Bending of functionally graded piezoelectric rectangular plates'[J].Acta Mechanica Solida Sinica,2000,13(4):312-319.
[36]Chen WQ,Lu Y,Ye GR,et al.3D electroelastic fields in a functionally graded piezoceramic hollow sphere under mechanical and electric loadings[J].Archive of Applied Mechanics,2002,72(1):39-51.
[37]Kapuria S.An efficient coupled theory for multilayered beams with embedded piezoelectric sensory and active layers[J].International Journal of Solids and Structures,2001,38(50-51):9179-9199.
[38]Ganapathi M,Patel BP,Touratier M.Refined finite element for piezoelectric laminated composite beams[J].Smart Materials & Structures,2004,13(4):57-67.
[39]Wu XH,Chen C,Shen YP,et al.A high order theory for functionally graded piezoelectric shells[J].International Journal of Solids and Structures,2002,39(20):5325-5344.
[40]刘正兴,林启荣.压电-层合梁在非接触电极作用下的二维解析解[J].上海力学,1999,20(3):306-315.
[41]刘正兴,李山青.轴向载荷作用下压电-弹性层合梁段的二维解析解[J].上海力学,1999,20(4):348-356.
[42]章建国,刘正兴,林启荣.压电弹性层合板静力机电耦合特性的解析解[J].32,2000,3:326-333.
[43]林启荣,金占礼.压电弹性层合梁的电场作用下的二维解析解[J].上海交通大学学报,2001,35(4):518-521.
[44]Shen MH,Chen SN,Chen FM.Piezoelectric study on confocally multicoated elliptical inclusion[J].International Journal of Engineering Science,2005,43(17-18):1299-1312.
[45]Zhang C,Cheung YK,Di S,et al.The exact solution of coupled thermoelectroelastic behavior of piezoelectric laminates[J].Computers and Structures,2002,80(13):1201-1212.
[46]Kapuria S,Bhattacharyya M,Kumar AN.Assessment of coupled 1D models for hybrid piezoelectric layered functionally graded beams[J].Composite Structures,2006,72(4):455-468.
[47]Pan E,Han F.Exact solution for functionally graded and layered magneto-electro-elastic plates[J].International Journal of Engineering Science,2005,43(3-4):321-339.
[48]Pan E.Exact solution for simply supported and multilayered magneto-electro-elastic plates[J].Journal of Applied Mechanics,2001,68:608-618.
[49]Pan E,Heyliger PR.Exact solutions for magneto-electro-elastic laminates in cylindrical bending[J].International Journal of Solids and Structures,2003,40(24):6859-6876.
[50]Vel SS,Batra RC.Generalized plane strain thermopiezoelectric analysis of multilayered plates[J].Journal of Thermal Stresses,2003,26(4):353-377.
[51]Shi ZF,Xiang H J,Spencer JB.Exact analysis of multi-layer piezoelectric/composite cantilevers[J].Smart Materials and Structures,2006,15(5):1447-1458.
[52]Zhang TT,Shi ZF.Elastic solutions of graded piezoelectric hollow cylinders[J].Key Engineering Materials,2006,302-303:658-668.
[53]陈盈,石志飞.梯度功能压电悬臂梁的一组基本解及其应用[J].固体力学学报,2004,25(2):241-245.
[54]石志飞,杜善义,等.功能材料力-电耦合问题的几个基本解:(Ⅰ)悬臂梁受力偶作用[J].复合材料学报,2001,18(1):105-108.
[55]石志飞,杜善义,等.功能材料力-电耦合问题的几个基本解:(Ⅱ)悬臂梁梁端受轴向集中力作用[J].复合材料学报,2001,18(1):109-111.
[56]章梓茂,石志飞,黄彬彬.功能材料力-电耦合问题的几个基本解:(Ⅲ):悬臂梁梁端受轴向集中力[J].复合材料学报,2001,18(1):112-114.
[57]Zhang TT,Shi ZF.Two-dimensional exact analysis for piezoelectric curved actuators[J].Journal of Micromechanics and Microengineering,2006,16(3):640-647.
[58]Chen Y,Shi ZF.Exact solutions of functionally gradient piezothermoelastic cantilevers and parameter identification[J].Journal of Intelligent Materials Systerms and Structures,2005,16(6):531-539.
[59]Liu TT,Shi ZF.Bending behavior of functionally gradient piezoelectric cantilever[J].Ferroelectrics,2004,308:43-51.
[60]Chen Y,Shi ZF.Double-layered piezo-thermoelastic hollow cylinder under some coupled loadings[J].Archive of Applied Mechanics,2006,75(6-7):326-337.
[61]Chen Y,Shi ZF.Double-layered piezothermoelastic hollow cylinder under thermal loading[J].Key Engineering Materials,2006,302-303:684-692.
[62]Almajid A,Taya M,Hudnut S.Analysis of out-of-plane displacement and stress field in a piezocomposite plate with functionally graded microstructure[J].International Journal of Solids and Structures,2001,38(19):3377-3391.
[63]Taya M,Almajid AA,Dunn M,et al.Design of bimorph piezo-composite actuators with functionally graded microstructure[J].Sensors and actuators.A,Physical,2003,107(3):248-260.
[64]Ishihara M,Noda N.Nonlinear dynamic behavior of a piezothermoelastic laminated plate with anisotropic material properties[J].Acta Mechanica,2003,166(1):103-118.
[65]He XQ,Ng TY,Sivashanker S,et al.Active control of FGM plates with integrated piezoelectric sensors and actuators[J].International Journal of Solids and Structures,2001,38(9):1641-1655.
[66]Liew KM,He XQ,Ng TY,et al.Finite element piezothermoelasticity analysis and the active control of FGM plates with integrated piezoelectric sensors and actuators[J].Computational Mechanics,2003,31(3-4):350-358.
[67]Liew KM,He XQ,Kitipornchai S.Finite element method for the feedback control of FGM shells in the frequency domain via piezoelectric sensors and actuators[J].Computer Methods in Applied Mechanics and Engineering,2004,193(3-5):257-273.
[68]Shindo Y,Domon W,Narita F.Dynamic bending of a symmetric piezoelectric laminated plate with a through crack[J].Theoretical and Applied Fracture Mechanics,1998,28(3):175-182.
[69]Dong K,Wang X.Influences of large deformation and rotary inertia on wave propagation in piezoelectric cylindrically laminated shells in thermal environment[J].International Journal of Solids and Structures,2006,43(6):1710-1726.
[70]Chen WQ.Vibration theory of non-homogeneous,spherically isotropic piezoelastic bodies[J].Journal of Sound and Vibration,2000,236(5):833-860.
[71]Chen WQ,Wang LZ.Free vibrations of functionally graded piezoceramic hollow spheres with radial polarization[J].Journal of Sound and Vibration,2002,251(1):103-114.
[72]Huang D,Sun BH.Approximate solution on smart composite beams by using MATLAB[J].Composite Structures,2001,54(2-3):197-205.
[73]Huang D,Sun B.Approximate analytical solutions of smart composite Mindlin beams[J].Journal of Sound and Vibration,2001,244(3):379-394.
[74]Krommer M.Piezoelastic vibrations of composite Reissner-Mindlin-type plates[J].Journal of Sound and Vibration,2003,263(4):871-891.
[75]Varelis D,Saravanos DA.Small amplitude free vibration analysis of piezoelectric composite plates subject to large deflections and initial stresses[J].Journal of Vibration and Acoustics,2006,128:41-49.
[76]伍晓红,沈亚鹏.压电功能梯度板自由振动的三维解[J].固体力学学报,2003,24(1):75-82.
[77]Lee H J,Saravanos DA.A mixed multi-field finite element formulation for thermopiezoelectric composite shells[J].International Journal of Solids and Structures,2000,37(36):4949-4967.
[78]Ganesan N,Kadoli R.Semianalytical finite element analysis of piezothermoelastic shells of revolution[J].Computers & Structures,2005,83(15-16):1305-1319.
[79]Liu X,Wang Q,Quek ST.Analytical solution for free vibration of piezoelectric coupled moderately thick circular plates[J].International Journal of Solids and Structures,2002,39(8):2129-2151.
[80]董兴建,孟光,李鸿光.变截面压电层合梁自由振动分析[J].振动工程学报,2005,18(2):243-247.
[81]Ishihara M,Noda N.Nonlinear dynamic behavior of a piezothermoelastic laminate considering the effect of transverse shear[J].Journal of Thermal Stresses,2003,26(11): 1093-1112.
[82]Mukherjee A,Chaudhuri AS.Nonlinear dynamic response of piezolaminated smart beams[J].Computers & Structures,2005,83(15-16):1298-1304.
[83]Kapuria S,Dumir PC,Ahmed A.Exact 2D piezoelasticity solution of hybrid beam with damping under harmonic electromechanical load[J].ZAMM,2004,84(6):391-402.
[84]Kapuria S,Aehary GG.Exact 3D piezothermoelasticity solution for buckling of hybrid cross-ply plates using state space approach[J].ZAMM,2005,85(3):189-201.
[85]Kapuria S,Ahmed A,Dumir PC.Static and dynamic thermo-electro-mechanical analysis of angle-ply hybrid piezoelectric beams using an efficient coupled zigzag theory[J].Composites Science and Technology,2004,64(16):2463-2475.
[86]Zhang TT,Shi ZF,Spencer BF.Vibration analysis of a functionally graded piezoelectric cylindrical actuator[J].Smart Materials and Structures,2008,17(0250182):.
[87]刘艳红,卿光辉,张焕铜.压电材料修正后的变分原理及智能板的精确解[J].中国民航学院学报,2006,24(1):13-17.
[88]Lim CW,He LH.Three-dimensional exact solutions for the electromechanical response of triple-layer piezoelectric actuators[J].Smart Materials and Structures,2004,13(5):1050-1058.
[89]Lim CW,Cheng ZQ,Reddy JN.Natural frequencies of laminated piezoelectric plates with internal electrodes[J].ZAMM,2006,86(5):410-420.
[90]Cheng ZQ,Reddy JN.Three dimensional dolutions of dmart functionally graded plates[J].Journal of Applied Mechanics,2001,68:234-241.
[91]Pan E,Heyliger PR.Free vibrations of simply supported and multilayered magneto-electro-elastic plates[J].Journal of Sound and Vibration,2002,252(3):429-442.
[92]Vel SS,Mewer RC,Batra RC.Analytical solution for the cylindrical bending vibration of piezoelectric composite plates[J].International Journal of Solids and Structures,2004,41(5-6):1625-1643.
[93]王永龄,俞大畏,董显林.智能材料与器件的发展设想[J].无机材料学报,1999,14(2):211-217.
[94]Tanaka T.Piezoelectric devices in Japan[J].Ferroelectrics,1982,40:167-187.
[95]Cross LE.Dielectric,piezoelectric and ferroelectric components[J].American Ceramics Society Bulletin,1984,63:586-590.
[96]Xu Y.Ferroelectric materials and their application[M].Amsterdam,1991.
[97]Wada Y.Piezoelectricity and pyroelectricity of polymers[J].Japan Journal of Applied Physics,1976,15:2041-2057.
[98]Furukawa T.Piezoelectricity and pyroelectricity in polymers[J].IEEE Transaction on Electrical Insulation,1989,24(3):375-394.
[99]Dias CJ,Das-Gupta DK.Inorganic ceramic/polymer ferroelectric composite electrets[J].IEEE Transactions on Dielectrics and Electrical Insulation,1996,3(5):706-734.
[100]郑占申,曲远方,马卫兵.陶瓷/聚合物复合材料的电性能及应用[J].复合材料学报,1998,15(4):14-19.
[101]王数彬,韩杰才,杜善义.压电陶瓷/聚合物复合材料的制备工艺及其性能研究[J].功能材料,1999,30(2):113-117.
[102]Huston DR,Fuhr PL Ambrose T P.Intelligent civil structures-activities in vermont[J].Smart Materials and Structures,1994,3(2):129-139.
[103]Ansari F,Maji A,Leung C.Intelligent civil engineering materials and structures:A collection of state-of-the-art papers in the application of emerging technologies to civil structures and materials[M].New York:American Society of Civil Engineers(ASCE),1997.
[104]Chang F.Structural health monitoring 2000[M].Pennsylvania:Technomic Publishing Co Inc.,1999.
[105]AizawaSkakizawa T,Higasino M.Case studios of smart materials for civil structures[J].Smart Materials and Structures,1998,7(5):617-626.
[106]Wang ML,Heo G,Satpathi D.A health monitoring system for large structural systerms[J].Smart Materials and Structures,1998,7(5):606-616.
[107]Wang XD.Coupled electromechanical behaviour of piezoelectric actuators in smart structures[J].Journal of Intelligent Material Systems and Structures,1999,10(3):232-241.
[108]张东,李宗津.水泥基压电机敏复合材料的可行性分析和研究[J].建筑材料学报,2002,5(2):141-146.
[109]Li Z,Zhang D,Wu K.Cement-Based 0-3 Piezoelectric Composites[J].Journal of the American Ceramic Society,2002,85(2):305-313.
[110]Zhang D,Li ZJ,Wu KR.2-2 piezoelectric cement matrix composite:Part Ⅱ.Actuator effect[J].Cement and Concrete Research,2002,32(5):825-830.
[111]Li ZJ,Zhang D Wu KR.Cement matrix 2-2 piezoelectric composite:Part Ⅰ.Sensory effect[J].Mater.Struct.,2001,13(242):506-512.
[112]Huang S,Chang J,Xu R,et al.Piezoelectric properties of 0-3 PZT/sulfoaluminate cement composites[J].Smart Materials and Structures,2004,13(2):270-274.
[113]F H S.Poling process and piezoelectric properties of lead zirconate titanate/sulphoaluminate cement composites[J].Journal of materials science,2004,39:6975-6979.
[114]Cheng X,Huang SF,et al.Piezoelectric,dielectric and ferroelectric properties of 0-3ceramic/cement composites[J].Journal of applied physics,2007,101,094110:.
[115]Ruan X,Danforth SC,Safari A,et al.Saint-Venant end effects in piezoceramic materials[J].International Journal of Solids and Structures,2000,37(19):2625-2637.
[116]Shi ZF.Bending behavior of piezoelectric curved actuator[J].Smart Materials & Structures,2005,14(4):835-842.
[117]Kouvatov A,Steinhausen R,Seifert W,et al.Comparison between bimorphic and polymorphic bending devices[J].Journal of the European Ceramic Society,1999,19(6):1153-1156.
[118]Haskins JF,et al.Vibrations of ferroelectric cylinderical shells with transverse isotropy[J].J.Acoust.Soc.Am.,1957,29(2):729-734.
[119]张东,李宗津等.2-2型水泥基压电机敏复合材料的研制[J].压电与声光,2002,03:217-04