压电陶瓷驱动器力学模型理论与试验研究
|
摘要
近年来,压电陶瓷中的锆钛酸铅(Lead Zirconate Titanate,简称PZT)以体积小、响应速度快、频响范围宽且输出力大等一系列优点广泛应用于多种用途的驱动器中。通过对PZT物理、力学性能的深入研究,建立基于力学等效原理的PZT驱动力学模型,使PZT的驱动性能得到了更直观的描述,同时也使PZT驱动特性在工程上的应用得到简化。
由于PZT特殊的压电效应使其在驱动方面的研究与应用得到快速发展。在以往的研究成果中发现,对PZT驱动器的理论研究多运用静力学方法,即把压电陶瓷片和基体耦合,假设接触面处的应变相等来计算PZT驱动力。然而这种理论上的研究方法既没有考虑PZT的动力特性,又没有考虑PZT与基体之间粘接层的影响问题。因此,这种理论研究并不完善。本文通过动力学思想并结合PZT的逆压电效应,建立不同振动模式的PZT驱动器力学模型,并根据所建立的驱动器力学模型对PZT的驱动特性进行深入研究。这种方法所提取的力学模型简单易行,便于工程应用,无论在理论方面还是实际应用都具有一定的指导意义。
本文采用理论推导与试验相结合的方式进行研究,主要研究内容如下:
(1)介绍本文的研究背景,目的及意义。简单介绍智能材料的基础知识及其在驱动方面的广阔应用前景。
(2)深入研究压电陶瓷的物理及力学性能,对压电陶瓷的驱动机理进行剖析,对压电方程进行详细介绍。
(3)建立埋入式PZT驱动器的驱动力学模型。通过对压电陶瓷逆压电效应的研究,根据质量集总法,建立PZT等效力学模型。结合算例并利用软件Matlab / Simulink对建立的驱动模型进行数值分析。结果表明:PZT输入信号与输出信号具有良好的线性关系;PZT的几何尺寸,输入信号的频率及粘结层性能对PZT的输出均有影响。
(4)建立粘贴式PZT驱动器的驱动力学模型。通过力学等效原理以及弹性动力学理论建立等效力学模型。利用软件Matlab / Simulink对建立的模型进行参数分析,并深入研究粘结层厚度及材料属性对PZT输出性能的影响。
(5)通过试验对建立的粘贴式PZT驱动器力学模型及粘结层性能对PZT驱动力的影响进行验证,所得结果与理论分析基本吻合,表明所建立的PZT驱动模型是合理的且具有一定的通用性。
(6)总结本文的主要工作,对得到的结论进行整理,并对今后的研究内容提出建议。
In recent years, piezoelectric ceramic (such as Lead Zirconate Titanate, PZT) with advantages of small size, fast response, wide responding frequency and great output force are widely used as multi-purpose actuators. Through studying the physical and mechanical properties of PZT material, an equivalence principle based on the mechanical model of the PZT actuator performance was established, resulting in making it more intuitive description and simply applying the actuating properties of the PZT in engineering.
Due to the special aspects of PZT piezoelectric effect, the research and application for the PZT actuator have rapidly developed. In previous research, the theory of PZT actuator usually used static method which made a coupling between the piezoelectric ceramic plate and the substrate, assuming that the strains at the contact surface of the PZT actuator and the structure are equal during calculation. However, the theory did not take into account both the dynamic characteristics of PZT material and the influence of the bond layer. Therefore, the previous theory about the modeling of PZT actuator needs to be further developing. By combining PZT dynamic ideas and the inverse piezoelectric effect, the different vibration modes of PZT mechanical model were created and further research on the mechanical properties of the PZT actuator using the developed model was conducted in the paper. The developed model for the PZT actuating performance was simple and convenient for engineering application, which was of certain significance in both theory and application.
In this paper, the combination of theoretical analysis and experimental research was used and the main contents were as follows:
(1) The research background, purpose and significance of the paper were firstly introduced, and the basic knowledge of smart materials and their wide application in the field of actuators were also briefly introduced.
(2) The physical and mechanical properties of piezoelectric ceramics were further researched. The actuating mechanism for the PZT actuators was carefully developed and the piezoelectric equations which were one of bases for the theoretical analysis were also introduced in detail.
(3) An actuating model for the embedded-type PZT actuators was established. A PZT equivalent mechanical model was set up by the lumped mass method through the research on the converse piezoelectric effect of piezoelectric ceramics. A numerical example was used to numerically analyze by using the Matlab / Simulink software. The results of the numerical simulation showed that the input and output signals of the PZT actuators had a linear relationship, and the geometry of the PZT patch and the input signal frequency as well as the cohesive layer had influenced on the output of the PZT actuators.
(4) A mechanical model for the paste-type PZT actuators was established. An equivalent mechanical model for the PZT actuators was set up by using the principle of equivalence and elastic dynamic theory. A parameter analysis for the developed model was conducted by using the Matlab / Simulink software, and the influence for the thick of the bonding layer and the material performance on the output characteristics of the PZT actuators was further developed.
(5) The developed paste-type model of the PZT actuator and the impact for the cohesive layer on the actuating force of the PZT driver were validated by experiments. The experimental results and that of the theoretical analysis matched well, it showed that the proposed model for the PZT actuator was reasonable and had some versatility.
(6) The main work was summarized at the end and some conclusions were made, and the future research contents were also recommended.
由于PZT特殊的压电效应使其在驱动方面的研究与应用得到快速发展。在以往的研究成果中发现,对PZT驱动器的理论研究多运用静力学方法,即把压电陶瓷片和基体耦合,假设接触面处的应变相等来计算PZT驱动力。然而这种理论上的研究方法既没有考虑PZT的动力特性,又没有考虑PZT与基体之间粘接层的影响问题。因此,这种理论研究并不完善。本文通过动力学思想并结合PZT的逆压电效应,建立不同振动模式的PZT驱动器力学模型,并根据所建立的驱动器力学模型对PZT的驱动特性进行深入研究。这种方法所提取的力学模型简单易行,便于工程应用,无论在理论方面还是实际应用都具有一定的指导意义。
本文采用理论推导与试验相结合的方式进行研究,主要研究内容如下:
(1)介绍本文的研究背景,目的及意义。简单介绍智能材料的基础知识及其在驱动方面的广阔应用前景。
(2)深入研究压电陶瓷的物理及力学性能,对压电陶瓷的驱动机理进行剖析,对压电方程进行详细介绍。
(3)建立埋入式PZT驱动器的驱动力学模型。通过对压电陶瓷逆压电效应的研究,根据质量集总法,建立PZT等效力学模型。结合算例并利用软件Matlab / Simulink对建立的驱动模型进行数值分析。结果表明:PZT输入信号与输出信号具有良好的线性关系;PZT的几何尺寸,输入信号的频率及粘结层性能对PZT的输出均有影响。
(4)建立粘贴式PZT驱动器的驱动力学模型。通过力学等效原理以及弹性动力学理论建立等效力学模型。利用软件Matlab / Simulink对建立的模型进行参数分析,并深入研究粘结层厚度及材料属性对PZT输出性能的影响。
(5)通过试验对建立的粘贴式PZT驱动器力学模型及粘结层性能对PZT驱动力的影响进行验证,所得结果与理论分析基本吻合,表明所建立的PZT驱动模型是合理的且具有一定的通用性。
(6)总结本文的主要工作,对得到的结论进行整理,并对今后的研究内容提出建议。
In recent years, piezoelectric ceramic (such as Lead Zirconate Titanate, PZT) with advantages of small size, fast response, wide responding frequency and great output force are widely used as multi-purpose actuators. Through studying the physical and mechanical properties of PZT material, an equivalence principle based on the mechanical model of the PZT actuator performance was established, resulting in making it more intuitive description and simply applying the actuating properties of the PZT in engineering.
Due to the special aspects of PZT piezoelectric effect, the research and application for the PZT actuator have rapidly developed. In previous research, the theory of PZT actuator usually used static method which made a coupling between the piezoelectric ceramic plate and the substrate, assuming that the strains at the contact surface of the PZT actuator and the structure are equal during calculation. However, the theory did not take into account both the dynamic characteristics of PZT material and the influence of the bond layer. Therefore, the previous theory about the modeling of PZT actuator needs to be further developing. By combining PZT dynamic ideas and the inverse piezoelectric effect, the different vibration modes of PZT mechanical model were created and further research on the mechanical properties of the PZT actuator using the developed model was conducted in the paper. The developed model for the PZT actuating performance was simple and convenient for engineering application, which was of certain significance in both theory and application.
In this paper, the combination of theoretical analysis and experimental research was used and the main contents were as follows:
(1) The research background, purpose and significance of the paper were firstly introduced, and the basic knowledge of smart materials and their wide application in the field of actuators were also briefly introduced.
(2) The physical and mechanical properties of piezoelectric ceramics were further researched. The actuating mechanism for the PZT actuators was carefully developed and the piezoelectric equations which were one of bases for the theoretical analysis were also introduced in detail.
(3) An actuating model for the embedded-type PZT actuators was established. A PZT equivalent mechanical model was set up by the lumped mass method through the research on the converse piezoelectric effect of piezoelectric ceramics. A numerical example was used to numerically analyze by using the Matlab / Simulink software. The results of the numerical simulation showed that the input and output signals of the PZT actuators had a linear relationship, and the geometry of the PZT patch and the input signal frequency as well as the cohesive layer had influenced on the output of the PZT actuators.
(4) A mechanical model for the paste-type PZT actuators was established. An equivalent mechanical model for the PZT actuators was set up by using the principle of equivalence and elastic dynamic theory. A parameter analysis for the developed model was conducted by using the Matlab / Simulink software, and the influence for the thick of the bonding layer and the material performance on the output characteristics of the PZT actuators was further developed.
(5) The developed paste-type model of the PZT actuator and the impact for the cohesive layer on the actuating force of the PZT driver were validated by experiments. The experimental results and that of the theoretical analysis matched well, it showed that the proposed model for the PZT actuator was reasonable and had some versatility.
(6) The main work was summarized at the end and some conclusions were made, and the future research contents were also recommended.
引文
1叶云岳.现代驱动技术综述[J].电机技术,2005(1):3-7.
2陶宝祺.智能材料结构[M].北京:国防工业出版社,1997.
3王金斗,宋颖.压电传感技术的研究及应用[J].电子技术应用,2008(8):89-93.
4李宏男,赵晓燕.压电智能传感结构在土木工程中的研究和应用[J].地震工程与工程振动,2004,24(6):165-172.
5姚康德,成国祥.智能材料[M].北京:化学工业出版社,2002.
6 Roger C A. Intelligent Material System-The Down of a New Materials Age [J]. Intell. Mater. Syst and Struct, 1993, 4(1):4-12.
7陶宝棋,熊克.智能材料结构的定义及应用前景[J].中国科学基金,1995(2):40-46.
8杨亲民.智能材料的研究与开发[J].功能材料,1999,30(6):575-581.
9 Crawley E F. Intelligent structures for aerospace: A technologyoverview and assessment. AIAA J, 1994, 32(2): 1689-1699.
10 Newnhanm R E, Ruschau G R. Smart Electroceramics [J]. Am Ceram Soc, 1991, 74(3):
463-480.
11 Chopra I. Review of state of art of smart structures and integrated systems [J]. AIAA Journal, 2002, 40(11): 2145-2187.
12陈定球.压电梁柱构件的动力方程及其在结构振动控制中的应用[D].[硕士学位论文]上海:同济大学,2007.
13周智,欧进萍.用于土木工程的智能监测传感材料性能及比较研究[J].建筑技术,2002,33(4):270-272.
14李宏男,李军,宋钢兵.采用压电智能材料的土木工程结构控制研究进展[J].建筑结构学报,2005,26(3):1-8.
15 STRANB F K. Development of a piezoelectric actuator for trailing edge flap control of full scale rotor blades [J]. Smart Material and Structure, 2001, 10(1): 25-34.
16王志国.形状记忆合金双向记忆效应及驱动特性研究[D].[博士学位论文]成都:四川大学,2002.
17刘畅.形状记忆合金(SMA)驱动模型及其在结构位置控制中应用[D].[硕士学位论文]沈阳:沈阳建筑大学,2009.
18曹照平,史庆轩,王社良.智能材料结构系统在土木工程中的应用研究[J].西北建筑工程学院学报(自然科学版),2000,17(3):1-4.
19佟荣光,赵建林,成振龙等.磁致伸缩材料弱磁场响应特性的实验研究[J].光子学报,2009,38(2):311-314.
20欧进萍,关新春.土木工程智能结构体系的研究与发展[J].地震工程与工程振动,1996,19(2):21-28.
21杜善义,冷劲松,王殿富.智能材料系统和结构[M].北京:科学出版社,2001.
22 William F Pickard, Michael Knoblauch, Winfried S Peters, et al. Prospective energy densities in the forisome, a new smart material [J]. Materials Science and Engineering C, 2006, 26: 104-112.
23周喜.基于多次压电效应的可作动传感器的研制[D].[硕士学位论文]大连:大连理工大学,2008.
24孙慷,张福学.压电学[M].国防工业出版社,1984.
25张皓.利用压电陶瓷的柔性结构智能主动控制[D].[硕士学位论文]沈阳:沈阳建筑大学,2008.
26李传兵,廖昌荣.压电智能结构的研究进展[J].压电与声光,2002,24(2):42-46.
27杨浩.基于智能算法的结构系统辨识及MR阻尼器半主动控制[D].[硕士学位论文]沈阳:沈阳建筑工程学院,2003.
28 Kamada T, Fujita T, Hatayama T, et al. Active Vibration Control of Frame Structure with Smart Structures Using Piezoelectric Actuators(Vibration Control by Control of Bending Moments of Columns) [J]. Smart Materials and Structures, 1997, No.6: 448-456.
29欧进萍.结构振动控制—主动、半主动和智能控制[M].北京:科学出版社,2003.
30 John W Ayres, Frederic Lalande, Zaffir Chaudhry, et al. Qualitative impedance-based health monitoring of civil infrastructures [J]. Smart Mater Struct, 1998, 7: 599-605.
31 Sun F, Chaudhry Z, Liang C, Rogers C A. Truss structure integrity identification using PZT sensor-actuator [J]. J of Intelligent Material Systems and Structures, 1995, 16(2): 134-139.
32 Park G, Cudney H H, Inman D J. Impedance-based health monitoring of civil structural componsents [J]. Journal of Infrastructure Systems, 2000(4): 353-354.
33赵晓燕,李宏男.基于压电陶瓷的混凝土裂缝损伤监测[J].压电与声光,2009,31(3):437-443.
34 Song G, Mo Y L, Otero K. Health monitoring and rehabilitation of a concrete structyre using intelligent materials [J]. Smart Mater Struct, 2006, 15(2): 309-314.
35文玉梅,李平,刘双临等.压电机敏混凝土原理[J].压电与声光,2002,24(3):196-198.
36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.
37 Saravanos D A, Heyliger P R. Mechanics and computational models for laminated piezoelectic beams, plates, and shells [J]. Applied Mechanics Review, 1999, 52(10): 305-319.
38 Yang J S, Batra R C, Liang X Q. The cylindrical bending vibration of a laminated elastic plate due to piezoelectric actuators [J]. Smart Material and Structures, 1994, (3): 485-493.
39 Vel S S, Batra R C. Cylindrical bending of laminated plates with distributed and segmented piezoelectric actuators / sensors [J]. AIAA Journal, 2000, 38(5): 857-867.
40 Heyliger P. Exact solutions for simply supported laminated piezoelectric plates [J]. Journal ofapplied mechanics, 1997, 64: 299-306.
41丁皓江,陈伟球,徐荣桥.压电板壳自由振动的三维精确分析[J].力学季刊,2001,22(1):1-9.
42蔡金标,叶贵如,陈伟球等.横观各向同性层合压电矩形板稳定问题的三维精确分析[J].复合材料学报,2002,19(1):69-73.
43盛宏玉,张伟林,高荣誉.一般边界条件下压电层合厚板的精确解[J].安徽建筑工业学院学报.2002,10(4):1-6.
44高坚新,沈亚鹏,王子昆.压电层合板的结构特性及优化分析[J].西安交通大学学报,1998,32(9):76-80.
45 Padma Akella. Modeling, analysis, control of flexible and smart structures [D]. Rensselaer Polytechnic Institue, 1997.
46 Crawley E F, J de Luis. Use Piezoelectric Actuator as Elements of Intelligent Structures [J]. AIAA Journal 1987(10): 1373-1385.
47孙东昌,王大均.梁振动控制的分布压电单元法[J].北京大学学报:自然科学版,1996,32(5):585-593.
48 Lines M.E. and Glass A.M. Principles and Applications of Ferroelectrics and Related Materials [M]. Oxford: Clarendon Press, 1977.中译本:钟维烈译,王华馥校.铁电体及有关材料的原理和应用[M].北京:科学出版社,1989.
49崔玉国.压电陶瓷自感知执行器及其驱动微动工作台控制方法的研究[D].大连:大连理工大学,2003.
50 Griffiths R B. Dependence of critical indices on a parameter [C]. Phys. Rev. Lett, 1970, 24(26): 1479-1482.
51张建雄.自感知二维微动工作台及其控制方法的研究[D].[硕士学位论文]大连:大连理工大学,2005.
52张福学,王丽坤.现代压电学(上)[M].北京:科学出版社,2001.
53 Wickramasinghe V K, Hagood N W. Durability Characterization of Active Fiber Composite Actuators for Helicopter Rotor Blade Applications [C]. 44thAIAA/ASME/ASCE/AHS Structures, Structural Dynamics, and Materials Con, 2003, 4:7-10.
54 W P Mason. Piezoelectric Crystals and Their Application to Ultrasonics [M]. D Van Nostrand Company Inc, New York, 1955.
55 W P Mason. Physical Acoustics-Principles and Methods. Vol.I, New York and London, 1964.
56 Landau L D, Lifshits E M. Statistical Physics [M]. Oxford: Pergamon Press, 1980.
57杨大智.智能材料与智能系统[M].天津:天津大学出版社,2000.
58王矜奉,姜祖桐,石瑞大.压电振动[M].北京:科学出版社,1989.
59吴克恭.埋入压电材料的智能复合材料结构振动主动控制理论和实验研究[D].西安:西北工业大学,2003.
60盛宏玉.结构动力学(第二版)[M].合肥:合肥工业大学出版社,2007.
61胡海岩.机械振动基础[M].北京:北京航空航天大学出版社,2005.
62隋华.压电效应的有限元分析及压电悬置控制方法的研究[D].[硕士学位论文]长春:吉林大学,2003.
63李俊宝,吕刚.智能桁架结构振动控制中压电主动构件的研究:(三)压电主动构件动力学建模[J].压电与声光,1998,20(5):237-241.
64张奔牛,张俊乾,黄尚廉.层合机敏结构的变形传递和层间应力分析[J].重庆大学学报:自然科学版,2002,25(2):134-138.
65孙威.基于波动法的压电智能混凝土结构主动健康监测技术[D].[博士学位论文]大连:大连理工大学,2009.
2陶宝祺.智能材料结构[M].北京:国防工业出版社,1997.
3王金斗,宋颖.压电传感技术的研究及应用[J].电子技术应用,2008(8):89-93.
4李宏男,赵晓燕.压电智能传感结构在土木工程中的研究和应用[J].地震工程与工程振动,2004,24(6):165-172.
5姚康德,成国祥.智能材料[M].北京:化学工业出版社,2002.
6 Roger C A. Intelligent Material System-The Down of a New Materials Age [J]. Intell. Mater. Syst and Struct, 1993, 4(1):4-12.
7陶宝棋,熊克.智能材料结构的定义及应用前景[J].中国科学基金,1995(2):40-46.
8杨亲民.智能材料的研究与开发[J].功能材料,1999,30(6):575-581.
9 Crawley E F. Intelligent structures for aerospace: A technologyoverview and assessment. AIAA J, 1994, 32(2): 1689-1699.
10 Newnhanm R E, Ruschau G R. Smart Electroceramics [J]. Am Ceram Soc, 1991, 74(3):
463-480.
11 Chopra I. Review of state of art of smart structures and integrated systems [J]. AIAA Journal, 2002, 40(11): 2145-2187.
12陈定球.压电梁柱构件的动力方程及其在结构振动控制中的应用[D].[硕士学位论文]上海:同济大学,2007.
13周智,欧进萍.用于土木工程的智能监测传感材料性能及比较研究[J].建筑技术,2002,33(4):270-272.
14李宏男,李军,宋钢兵.采用压电智能材料的土木工程结构控制研究进展[J].建筑结构学报,2005,26(3):1-8.
15 STRANB F K. Development of a piezoelectric actuator for trailing edge flap control of full scale rotor blades [J]. Smart Material and Structure, 2001, 10(1): 25-34.
16王志国.形状记忆合金双向记忆效应及驱动特性研究[D].[博士学位论文]成都:四川大学,2002.
17刘畅.形状记忆合金(SMA)驱动模型及其在结构位置控制中应用[D].[硕士学位论文]沈阳:沈阳建筑大学,2009.
18曹照平,史庆轩,王社良.智能材料结构系统在土木工程中的应用研究[J].西北建筑工程学院学报(自然科学版),2000,17(3):1-4.
19佟荣光,赵建林,成振龙等.磁致伸缩材料弱磁场响应特性的实验研究[J].光子学报,2009,38(2):311-314.
20欧进萍,关新春.土木工程智能结构体系的研究与发展[J].地震工程与工程振动,1996,19(2):21-28.
21杜善义,冷劲松,王殿富.智能材料系统和结构[M].北京:科学出版社,2001.
22 William F Pickard, Michael Knoblauch, Winfried S Peters, et al. Prospective energy densities in the forisome, a new smart material [J]. Materials Science and Engineering C, 2006, 26: 104-112.
23周喜.基于多次压电效应的可作动传感器的研制[D].[硕士学位论文]大连:大连理工大学,2008.
24孙慷,张福学.压电学[M].国防工业出版社,1984.
25张皓.利用压电陶瓷的柔性结构智能主动控制[D].[硕士学位论文]沈阳:沈阳建筑大学,2008.
26李传兵,廖昌荣.压电智能结构的研究进展[J].压电与声光,2002,24(2):42-46.
27杨浩.基于智能算法的结构系统辨识及MR阻尼器半主动控制[D].[硕士学位论文]沈阳:沈阳建筑工程学院,2003.
28 Kamada T, Fujita T, Hatayama T, et al. Active Vibration Control of Frame Structure with Smart Structures Using Piezoelectric Actuators(Vibration Control by Control of Bending Moments of Columns) [J]. Smart Materials and Structures, 1997, No.6: 448-456.
29欧进萍.结构振动控制—主动、半主动和智能控制[M].北京:科学出版社,2003.
30 John W Ayres, Frederic Lalande, Zaffir Chaudhry, et al. Qualitative impedance-based health monitoring of civil infrastructures [J]. Smart Mater Struct, 1998, 7: 599-605.
31 Sun F, Chaudhry Z, Liang C, Rogers C A. Truss structure integrity identification using PZT sensor-actuator [J]. J of Intelligent Material Systems and Structures, 1995, 16(2): 134-139.
32 Park G, Cudney H H, Inman D J. Impedance-based health monitoring of civil structural componsents [J]. Journal of Infrastructure Systems, 2000(4): 353-354.
33赵晓燕,李宏男.基于压电陶瓷的混凝土裂缝损伤监测[J].压电与声光,2009,31(3):437-443.
34 Song G, Mo Y L, Otero K. Health monitoring and rehabilitation of a concrete structyre using intelligent materials [J]. Smart Mater Struct, 2006, 15(2): 309-314.
35文玉梅,李平,刘双临等.压电机敏混凝土原理[J].压电与声光,2002,24(3):196-198.
36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.
37 Saravanos D A, Heyliger P R. Mechanics and computational models for laminated piezoelectic beams, plates, and shells [J]. Applied Mechanics Review, 1999, 52(10): 305-319.
38 Yang J S, Batra R C, Liang X Q. The cylindrical bending vibration of a laminated elastic plate due to piezoelectric actuators [J]. Smart Material and Structures, 1994, (3): 485-493.
39 Vel S S, Batra R C. Cylindrical bending of laminated plates with distributed and segmented piezoelectric actuators / sensors [J]. AIAA Journal, 2000, 38(5): 857-867.
40 Heyliger P. Exact solutions for simply supported laminated piezoelectric plates [J]. Journal ofapplied mechanics, 1997, 64: 299-306.
41丁皓江,陈伟球,徐荣桥.压电板壳自由振动的三维精确分析[J].力学季刊,2001,22(1):1-9.
42蔡金标,叶贵如,陈伟球等.横观各向同性层合压电矩形板稳定问题的三维精确分析[J].复合材料学报,2002,19(1):69-73.
43盛宏玉,张伟林,高荣誉.一般边界条件下压电层合厚板的精确解[J].安徽建筑工业学院学报.2002,10(4):1-6.
44高坚新,沈亚鹏,王子昆.压电层合板的结构特性及优化分析[J].西安交通大学学报,1998,32(9):76-80.
45 Padma Akella. Modeling, analysis, control of flexible and smart structures [D]. Rensselaer Polytechnic Institue, 1997.
46 Crawley E F, J de Luis. Use Piezoelectric Actuator as Elements of Intelligent Structures [J]. AIAA Journal 1987(10): 1373-1385.
47孙东昌,王大均.梁振动控制的分布压电单元法[J].北京大学学报:自然科学版,1996,32(5):585-593.
48 Lines M.E. and Glass A.M. Principles and Applications of Ferroelectrics and Related Materials [M]. Oxford: Clarendon Press, 1977.中译本:钟维烈译,王华馥校.铁电体及有关材料的原理和应用[M].北京:科学出版社,1989.
49崔玉国.压电陶瓷自感知执行器及其驱动微动工作台控制方法的研究[D].大连:大连理工大学,2003.
50 Griffiths R B. Dependence of critical indices on a parameter [C]. Phys. Rev. Lett, 1970, 24(26): 1479-1482.
51张建雄.自感知二维微动工作台及其控制方法的研究[D].[硕士学位论文]大连:大连理工大学,2005.
52张福学,王丽坤.现代压电学(上)[M].北京:科学出版社,2001.
53 Wickramasinghe V K, Hagood N W. Durability Characterization of Active Fiber Composite Actuators for Helicopter Rotor Blade Applications [C]. 44thAIAA/ASME/ASCE/AHS Structures, Structural Dynamics, and Materials Con, 2003, 4:7-10.
54 W P Mason. Piezoelectric Crystals and Their Application to Ultrasonics [M]. D Van Nostrand Company Inc, New York, 1955.
55 W P Mason. Physical Acoustics-Principles and Methods. Vol.I, New York and London, 1964.
56 Landau L D, Lifshits E M. Statistical Physics [M]. Oxford: Pergamon Press, 1980.
57杨大智.智能材料与智能系统[M].天津:天津大学出版社,2000.
58王矜奉,姜祖桐,石瑞大.压电振动[M].北京:科学出版社,1989.
59吴克恭.埋入压电材料的智能复合材料结构振动主动控制理论和实验研究[D].西安:西北工业大学,2003.
60盛宏玉.结构动力学(第二版)[M].合肥:合肥工业大学出版社,2007.
61胡海岩.机械振动基础[M].北京:北京航空航天大学出版社,2005.
62隋华.压电效应的有限元分析及压电悬置控制方法的研究[D].[硕士学位论文]长春:吉林大学,2003.
63李俊宝,吕刚.智能桁架结构振动控制中压电主动构件的研究:(三)压电主动构件动力学建模[J].压电与声光,1998,20(5):237-241.
64张奔牛,张俊乾,黄尚廉.层合机敏结构的变形传递和层间应力分析[J].重庆大学学报:自然科学版,2002,25(2):134-138.
65孙威.基于波动法的压电智能混凝土结构主动健康监测技术[D].[博士学位论文]大连:大连理工大学,2009.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |