压电式骨传导听觉装置振动器结构设计与试验研究
摘要
骨传导听觉装置是解决气导听力障碍及特种环境作业人员声音信号传输的重要设备,同时也可以替代对听力有损伤的一些气传导听觉装置。由于压电元件具有无电磁辐射、电能损耗小、响应特性好、重量轻、结构精巧等优点,本文结合国家教育部高等学校科技创新工程重大项目培育资金项目《驱动测试控制功能一体化新型压电驱动机构研究》(No.708028)和吉林省科技发展计划项目《压电驱动式骨传导助听装置作用机理与关键技术研究》(No.20070538),以压电式骨传导听觉装置为研究对象,采用压电双晶片振子为振动膜片,将音讯信号转为振动信号,对这种新型骨传导听觉装置开展理论及实验研究。
主要的研究工作如下:
采用有限元分析方法,选择适合作为骨传导听觉装置振动膜片的压电振子金属基板。对矩形压电振子与圆形压电振子进行仿真分析与实验测试,得出两种不同压电振子在不同支撑方式下的静态与动态特性结果,根据结果确定了压电振子在结构中最适合的支撑方式。分析两种不同压电振子的结构尺寸对其振动性能影响,选定结构样机中采用的矩形与圆形压电振子元件的结构参数。
设计矩形与圆形单膜片骨传导振动器试验样机结构,分析结构传导柱直径与覆盖胶板厚度参数对压电振子振动性能的影响,选定结构传导柱直径与覆盖胶板的厚度参数。建立单膜片振动器动力学模型和仿真模型,应用Matlab进行动态仿真,分析单膜片骨传导振动器机构动态特性,为样机实验提供依据。对两种试验样机在静态参数、时域响应、频域响应进行实验测试比较,分析两种结构振动特性的区别,确定两种振动器样机的频率响应特性。
在单膜片振动器基础上,提出双膜片分频振动的骨传导振动器试验样机结构,与电磁式骨传导听觉装置进行对比实验测试分析,确定分频点。结果表明,双膜片分频振动的压电式骨传导听觉装置,在灵敏度、响应速度、频率响应等性能参数较优。
Bone conduction auditory device carry the wave signal to inner ear through the skull which gains it a wide application to patients with auditory impairment and normal human since it conquers the masking effect in the noise to ensure clear listening and protects ears from hearing loss by replacing the air conduction earphone.
The piezoelectric bone conduction aditory device produces hearing by the vibration of a vibrator driven by electric signal with certain frequencies. The key vibrator of this device has superiorities in small energy loss, light weight, thin surface, none electromagnetic radiation, radio resistance, etc. The frequency band and deformation of common piezoelectric ceramic materials are not large enough for bone conduction auditory device due to its inherent properties. Nevertheless, a piezoelectric ceramic vibrator with the deformation amplified might meet the requirement of bone conduction auditory device.
The research in this paper is combined with the Ministry of Education in Colleges and Universities Technology Innovation Program fund major cultivating Project (Research on the new piezoelectric drive structure for universal measurement and control, No.708028) and Scientific and Technological Development Project of Jilin Province (Study on the working theory and key technologies of piezoelectric bone conduction auditory device).
1.Basic theory of piezoelectric bone conduction auditory device The study on piezoelectric bone conduction auditory device is the integration of bone conduction auditory theory and the converse piezoelectric effect including the analysis on the physical properties of sound, the function of auditory organ, the transmission pathway of sound and the auditory parameters which provides evidence to the design of the key vibrator. Being the key vocal element of bone conduction auditory device, the piezoelectric materials have a direct impact on the performance of the vibrator via its inherent performance and parameters. Based on the analysis of the performance and parameter index of piezoelectric materials, PZT is selected as the vocal element to meet the strong and static converse piezoelectric effect requirement of the vibration membrane. As an elastomer with piezoelectric effect, the piezoelectric materials has special parameters such as dielectric constant d , elastic constant s , piezoelectric constant d , electromagnetic coupling coefficient K , mechanical quality coefficient Qm , etc. There are four piezoelectric equations considering the different boundary conditions and independent variables, two of which related to the PZT are analyzed in this paper.
2.Theoretical analysis on the basic performance of piezoelectric vibrator Piezoelectric bimorphs are selected and the vibration membrane based on the analysis of the performance of piezoelectric vibrator. The power is connected in parallel to increase the displacement and force of the piezoelectric vibrator. The sensitive zone of bone conduction is 800Hz to 2000Hz, where the low frequency signal is usually too small to be perceived. As the key performance parameters of bone conduction auditory device, the fundamental frequency and displacement of piezoelectric vibrator can be determined by configuring the resonance frequency to the low frequency. This configuration may increase the displacement of the vibrator in the low frequency area so as to improve the low frequency response. The hysteresis characteristic of piezoelectric materials is analyzed as it determines the stationarity of the sound loudness. The mechanical model of rectangular and circular piezoelectric bimorph is established. The vibration equation and surface deformation equation are solved to find the formula of stiffness and amplitude of the piezoelectric vibrator. The relationship between the piezoelectric bimorph and the dimensions and materials of the metal substrate is analyzed.
3. Analysis on the performance of the piezoelectric vibrator structure With the PZT-5 piezoelectric ceramic is chosen as the bone conduction auditory device vibration membrane material, beryllium bronze is selected as the substrate of piezoelectric vibrator on the finite element simulation analysis of the displacement and fundamental frequency of different substrate. Finite element simulation analysis of the rectangular piezoelectric vibrator fixed on one end and two ends and circular piezoelectric vibrator fixed on the centre and edge gives the displacement and fundamental frequency of them. Experiments on different supporting ways of the two piezoelectric vibrators are conducted to determine the major parameters such as the output force, hysteresis, step response. A conclusion can be made from the experiment that the rectangular piezoelectric vibrator in bone conduction application should be fixed on the two ends and the circular one should be fixed on the edge. The influence of the structure parameters of the piezoelectric vibrator—length, width, and thickness of the substrate and bimorph to the rectangular one and diameter, width, thickness of the substrate and bimorph to the circular one—on the displacement and fundamental frequency is simulating analyzed, which provides evidence to the determination of these parameters. Experiment is conducted on the selected piezoelectric vibrator to prove the feasibility of the vibrator. The experiments involve the test of the relationship between the driven voltage and displacement, the deformation displacement test, the fundamental frequency test, the step response test, the sine signal response test, and the amplitude-frequency test.
4.Study on the vibrator structure design of single membrane bone conduction auditory device
Prototypes of the rectangular and circular membrane bone conduction vibrator are designed with a conduction column and a rubber plate to transmit the sound vibration to the skull. Experiments on the relationship between the diameter of the conduction column and the displacement and fundamental frequency of the piezoelectric vibrator and the relationship between the thickness of the rubber plate and the displacement and fundamental frequency of the piezoelectric vibrator are conducted to determine the diameter of the conduction column and the thickness of the rubber plate. The dynamic model and simulation model of the rectangular piezoelectric vibrator are established. The simulation analysis shows the dynamic characteristic of the vibrator. The static test of the two prototypes on the relationship between the displacement and voltage and fundamental frequency shows that the rectangular piezoelectric vibrator has a lower fundamental frequency and consequently a larger displacement in the low frequency response compared with the circular piezoelectric vibrator. The dynamic test of the dynamic response of the circular and rectangular piezoelectric vibrator shows that the rectangular one gives better response in the low frequency area and the circular one excels in other frequency area.
5.Study on the vibrator structure design of double membranes bone conduction hearing device A double membrane frequency based piezoelectric bone conduction auditory
device prototype is design with a rectangular piezoelectric vibrator working in the low frequency area and a circular piezoelectric vibrator working in the medium and high frequency area. Simulation and experiment on the rectangular vibrator with a hole in the centre are conducted to analyze the influence of the hole diameter on the performance of the vibrator. The appropriate hole diameter is given. The dynamic model of the double membrane bone conduction auditory device is established to analyze the coupling characteristics of the two membranes. Rubber damping material is added to the fixed point of the piezoelectric vibrator to decrease the influence of the membrane on the structure and the coupling interference between the two membranes. A comparison test is conducted between the piezoelectric vibrator and the electromagnetic bone conduction earphone. The voltage-displacement test and fundamental frequency test show that the piezoelectric bone conduction vibrator has a lower fundamental frequency and consequently larger amplitude in the low frequency area. The sine wave and step signal test demonstrate that the piezoelectric vibrator has a faster step response and better sine wave response than its counterpart. The voltage-displacement test of both the piezoelectric vibrator and the electromagnetic one under different frequency is conducted to determine the frequency division point. The dynamic performance of the piezoelectric vibrator with the rectangular membrane working in the low frequency area and the circular membrane working in the medium and high frequency area is proved to be better than the electromagnetic one in the whole frequency zone.
主要的研究工作如下:
采用有限元分析方法,选择适合作为骨传导听觉装置振动膜片的压电振子金属基板。对矩形压电振子与圆形压电振子进行仿真分析与实验测试,得出两种不同压电振子在不同支撑方式下的静态与动态特性结果,根据结果确定了压电振子在结构中最适合的支撑方式。分析两种不同压电振子的结构尺寸对其振动性能影响,选定结构样机中采用的矩形与圆形压电振子元件的结构参数。
设计矩形与圆形单膜片骨传导振动器试验样机结构,分析结构传导柱直径与覆盖胶板厚度参数对压电振子振动性能的影响,选定结构传导柱直径与覆盖胶板的厚度参数。建立单膜片振动器动力学模型和仿真模型,应用Matlab进行动态仿真,分析单膜片骨传导振动器机构动态特性,为样机实验提供依据。对两种试验样机在静态参数、时域响应、频域响应进行实验测试比较,分析两种结构振动特性的区别,确定两种振动器样机的频率响应特性。
在单膜片振动器基础上,提出双膜片分频振动的骨传导振动器试验样机结构,与电磁式骨传导听觉装置进行对比实验测试分析,确定分频点。结果表明,双膜片分频振动的压电式骨传导听觉装置,在灵敏度、响应速度、频率响应等性能参数较优。
Bone conduction auditory device carry the wave signal to inner ear through the skull which gains it a wide application to patients with auditory impairment and normal human since it conquers the masking effect in the noise to ensure clear listening and protects ears from hearing loss by replacing the air conduction earphone.
The piezoelectric bone conduction aditory device produces hearing by the vibration of a vibrator driven by electric signal with certain frequencies. The key vibrator of this device has superiorities in small energy loss, light weight, thin surface, none electromagnetic radiation, radio resistance, etc. The frequency band and deformation of common piezoelectric ceramic materials are not large enough for bone conduction auditory device due to its inherent properties. Nevertheless, a piezoelectric ceramic vibrator with the deformation amplified might meet the requirement of bone conduction auditory device.
The research in this paper is combined with the Ministry of Education in Colleges and Universities Technology Innovation Program fund major cultivating Project (Research on the new piezoelectric drive structure for universal measurement and control, No.708028) and Scientific and Technological Development Project of Jilin Province (Study on the working theory and key technologies of piezoelectric bone conduction auditory device).
1.Basic theory of piezoelectric bone conduction auditory device The study on piezoelectric bone conduction auditory device is the integration of bone conduction auditory theory and the converse piezoelectric effect including the analysis on the physical properties of sound, the function of auditory organ, the transmission pathway of sound and the auditory parameters which provides evidence to the design of the key vibrator. Being the key vocal element of bone conduction auditory device, the piezoelectric materials have a direct impact on the performance of the vibrator via its inherent performance and parameters. Based on the analysis of the performance and parameter index of piezoelectric materials, PZT is selected as the vocal element to meet the strong and static converse piezoelectric effect requirement of the vibration membrane. As an elastomer with piezoelectric effect, the piezoelectric materials has special parameters such as dielectric constant d , elastic constant s , piezoelectric constant d , electromagnetic coupling coefficient K , mechanical quality coefficient Qm , etc. There are four piezoelectric equations considering the different boundary conditions and independent variables, two of which related to the PZT are analyzed in this paper.
2.Theoretical analysis on the basic performance of piezoelectric vibrator Piezoelectric bimorphs are selected and the vibration membrane based on the analysis of the performance of piezoelectric vibrator. The power is connected in parallel to increase the displacement and force of the piezoelectric vibrator. The sensitive zone of bone conduction is 800Hz to 2000Hz, where the low frequency signal is usually too small to be perceived. As the key performance parameters of bone conduction auditory device, the fundamental frequency and displacement of piezoelectric vibrator can be determined by configuring the resonance frequency to the low frequency. This configuration may increase the displacement of the vibrator in the low frequency area so as to improve the low frequency response. The hysteresis characteristic of piezoelectric materials is analyzed as it determines the stationarity of the sound loudness. The mechanical model of rectangular and circular piezoelectric bimorph is established. The vibration equation and surface deformation equation are solved to find the formula of stiffness and amplitude of the piezoelectric vibrator. The relationship between the piezoelectric bimorph and the dimensions and materials of the metal substrate is analyzed.
3. Analysis on the performance of the piezoelectric vibrator structure With the PZT-5 piezoelectric ceramic is chosen as the bone conduction auditory device vibration membrane material, beryllium bronze is selected as the substrate of piezoelectric vibrator on the finite element simulation analysis of the displacement and fundamental frequency of different substrate. Finite element simulation analysis of the rectangular piezoelectric vibrator fixed on one end and two ends and circular piezoelectric vibrator fixed on the centre and edge gives the displacement and fundamental frequency of them. Experiments on different supporting ways of the two piezoelectric vibrators are conducted to determine the major parameters such as the output force, hysteresis, step response. A conclusion can be made from the experiment that the rectangular piezoelectric vibrator in bone conduction application should be fixed on the two ends and the circular one should be fixed on the edge. The influence of the structure parameters of the piezoelectric vibrator—length, width, and thickness of the substrate and bimorph to the rectangular one and diameter, width, thickness of the substrate and bimorph to the circular one—on the displacement and fundamental frequency is simulating analyzed, which provides evidence to the determination of these parameters. Experiment is conducted on the selected piezoelectric vibrator to prove the feasibility of the vibrator. The experiments involve the test of the relationship between the driven voltage and displacement, the deformation displacement test, the fundamental frequency test, the step response test, the sine signal response test, and the amplitude-frequency test.
4.Study on the vibrator structure design of single membrane bone conduction auditory device
Prototypes of the rectangular and circular membrane bone conduction vibrator are designed with a conduction column and a rubber plate to transmit the sound vibration to the skull. Experiments on the relationship between the diameter of the conduction column and the displacement and fundamental frequency of the piezoelectric vibrator and the relationship between the thickness of the rubber plate and the displacement and fundamental frequency of the piezoelectric vibrator are conducted to determine the diameter of the conduction column and the thickness of the rubber plate. The dynamic model and simulation model of the rectangular piezoelectric vibrator are established. The simulation analysis shows the dynamic characteristic of the vibrator. The static test of the two prototypes on the relationship between the displacement and voltage and fundamental frequency shows that the rectangular piezoelectric vibrator has a lower fundamental frequency and consequently a larger displacement in the low frequency response compared with the circular piezoelectric vibrator. The dynamic test of the dynamic response of the circular and rectangular piezoelectric vibrator shows that the rectangular one gives better response in the low frequency area and the circular one excels in other frequency area.
5.Study on the vibrator structure design of double membranes bone conduction hearing device A double membrane frequency based piezoelectric bone conduction auditory
device prototype is design with a rectangular piezoelectric vibrator working in the low frequency area and a circular piezoelectric vibrator working in the medium and high frequency area. Simulation and experiment on the rectangular vibrator with a hole in the centre are conducted to analyze the influence of the hole diameter on the performance of the vibrator. The appropriate hole diameter is given. The dynamic model of the double membrane bone conduction auditory device is established to analyze the coupling characteristics of the two membranes. Rubber damping material is added to the fixed point of the piezoelectric vibrator to decrease the influence of the membrane on the structure and the coupling interference between the two membranes. A comparison test is conducted between the piezoelectric vibrator and the electromagnetic bone conduction earphone. The voltage-displacement test and fundamental frequency test show that the piezoelectric bone conduction vibrator has a lower fundamental frequency and consequently larger amplitude in the low frequency area. The sine wave and step signal test demonstrate that the piezoelectric vibrator has a faster step response and better sine wave response than its counterpart. The voltage-displacement test of both the piezoelectric vibrator and the electromagnetic one under different frequency is conducted to determine the frequency division point. The dynamic performance of the piezoelectric vibrator with the rectangular membrane working in the low frequency area and the circular membrane working in the medium and high frequency area is proved to be better than the electromagnetic one in the whole frequency zone.
引文
[1]姚守拙.压电化学与生物传感[M].长沙:湖南师范大学出版社,1997.
[2] Abdelhafid OMARI, et al. Development of a high precision mounting robot system with fine motion mechanism (3rd Report)[J]. JSPE, 2001, 67 (7): 1101-1107.
[3] Hisayuki Aoyama. Flexible micro-processing by multiple microrobots in SEM[C]. Proc of international Conference on Robotics & Automation 2001.
[4]赵宏伟,刘建芳,华顺明,刘国嵩,程光明,吴博达.压电型步进精密旋转驱动器[J].光学精密工程,Vol.13 No.3 Jun.2005.
[5] Hiromichi Morita et al. Electical discharge device with direct drive method for thin wire electrode[C]. IEEE International Conference on Robotics and Automation,1995.
[6] Ralph Hollis et al. Miniature factories for precision assembly[C]. Proc.Intternational Workshop on Micro-Factories,Tsukuba,Japan,December 7-8,1998: 1-6.
[7] S Roundy, P K Wright. A piezoelectric vibration based generator for wireless electronics[J]. Institute of Physics Publishing. Samrt Mater. Struct.13(2004)1131-1142.
[8]日本工业技术振兴协会固体アクチュエ-タ研究部会编.精密制御用ニュ-アクチュエ-タ便览[M].东京:フヅテクノツステム,1994.
[9]内野研二.压电アクチュエ-タ[M].东京:森北出版株式会社,1991.
[10]上羽贞行,富川义郎.新版超音波モ-タ[M].东京:トリヮップスス,1991.
[11]张福学,王丽坤.现代压电学[M].北京:科学出版社,2002.
[12]电子陶瓷情报网编.压电陶瓷应用[M].山东:山东大学出版社,1985.
[13]栾桂冬,张金铎,王仁乾.压电换能器和换能器阵[M].北京:北京大学出版社,2004.
[14]田中哲郎(日)等.压电陶瓷材料.陈俊彦,王余君译[M].北京:科学出版社,1982.
[15]张沛霖,钟维烈.压电材料与器件物理[M].济南:山东科学技术出版社,1997.
[16]林声和,王裕斌.压电陶瓷[M].北京:国防工业出版社,1980.
[17]山东大学压电铁电物理教研室.压电陶瓷及其应用[M].济南:山东人民出版社,1974.
[18]电子陶瓷情报网.压电陶瓷应用[M].济南:山东大学出版社,1985.
[19]徐锡林.压电型微驱动器[J].上海交通大学学报,1997,31(1):67-70.
[20]韩德民.临床听力学[M].北京:人民卫生出版社,2006.9.
[21]彭玉成.耳聋与助听器选配[M].北京:人民军医出版社,2001.
[22] Mylanus et al. Intraindividual Comparison of the Bone-Anchored Hearing Aid andAir-Conduction Hearing Aids[J]. Arch Otolaryngol Head Neck Surg,1998,124:271-276.
[23] Mariano Belinky, Natalie Jeremijenko. Sound through bone conduction in public interfaces[C]. Conference on Human Factors in Computing Systems,2001.181-182.
[24] M.L.Oenhardt, R.Skellett, P.Wang,et al. Human ultrasonic speech perception[J]. Science,1991,253(5015):82-85.
[25] Haeff, Knox. Perception of Ultrasound[J]. Science,1963 ,139:590-592.
[26] Peder Carlsson, BoHakansson. Force threshold for hearing by direct bone conduction[J]. J.Acoust.Soc.Am.97(2),February 1995:1124-1129.
[27]龚文,邵斌.双导式聋哑人听力器:中国,02266851.1989-09-10.
[28]温大鹏,郑建晖.骨传导式耳机:中国,02802599.2002-07-15.
[29]严建敏.骨传导助听器:中国,02266851. 2003-09-11.
[30]陈奚平.骨传导扬声器:中国,200620033506. 2007-03-14.
[31]修翔凤.头卡式骨传导助听器:中国,2790089Y.2006-06-21.
[32]郁令友.手表式蓝牙耳机结构:中国,2800681Y.2006-07-26.
[33]严世熙.整合式骨传导技术眼镜:中国,201035260Y.2008-03-12.
[34]许必亮.骨传导运动眼镜:中国,201156128Y.2008-11-26.
[35]王舜清.鼻骨传导助听装置:中国台湾,200420120237.2005-05-24.
[36]王舜清.鼻骨传导活体声纹辨识装置:中国台湾,101042869A.2007-09-12.
[37]王舜清.鼻骨传导影音传输装置:中国台湾,101022681A.2007-08-23.
[38]福田干夫.骨传导扬声器:日本,1406449A.2003-03-12.
[39]小林一二.骨传导扬声器:日本,1656849A.2005-08-17.
[40]落合浩一郎.骨传导扬声器装置:日本,1723733A.2006-01-18.
[41]姜京玉.带有能引起骨传导和空气传导听觉的接收器的电话:韩国,1276142A.2000-12-17.
[42]李亿基.使用振动膜的超小型骨振动扬声器和具有它的移动电话:韩国,1675846A.2005-09-28.
[43]田中正智.耳部安装型的通话装置:日本,1742476A.2006-03-01.
[44]藤田柾彦.耳部佩戴式声音信息传达器:日本,1625189A.2005-06-08.
[45]渥美智也.骨传导耳机:日本,1465204A.2003-12-31.
[46]武田猛.骨传导受话装置:日本,1984505A.2007-06-20.
[47] Yoshiyasu, Yamada. Study on voice recognition utilizing bone-conducted voice[C]. IEEJTrans. SM, Vol.124,No.8,2004.
[48]冀飞.植入式助听装置简介[J].《中国医疗器械信息》,2009年第15卷第1期Vol.15 No.1.
[49] Bo E.V.Hakansson. The balanced electromagnetic separation transducer:A new bone conduction transducer[J]. J.acoust.soc.Am.113(2).February 2003.
[50] E.G.里查孙,马大猷猷,关定华.声学技术概要(中)[M].北京:科学技术出版社,1965.
[51]徐锡林.压电型微驱动器[J].上海交通大学学报,1997,31(1):67-70.
[52]刘德忠.双指微动操作器开发与研究[D].北京:北京工业大学,2002.
[53]章句才.基础听力学[M].北京:中国计量出版社,1993.
[54]谢鼎华.基础与应用听力学[M].长沙:湖南科学技术出版社,2003.
[55]何永照.听力学概论[M].上海:上海科学技术出版社,1964.
[56] E.G.里查孙,章启馥,声学技术概要(上)[M].北京:科学技术出版社,1961.
[57]李学佩.耳鼻咽喉科学[M].北京:北京大学医学出版社,2003.
[58]王永华.耳聋[M].合肥:安徽科学技术出版社,2001.
[59]李东亮,许继田,关宿东.临床生理学[M].郑州:郑州大学出版社,2004.
[60]岳利民.生理学[M].北京:科学出版社,2003.
[61]刘国艺.生理学[M].北京:人民军医出版社,2006.
[62]朱妙章.大学生理学[M].北京:高等教育出版社,2002.
[63]宋道仁.压电效应与应用[M].北京:科学普及出版社,1987年第一版.
[64]张福学,王丽坤.现代压电学(上册)[M].北京:科学出版社,2001.
[65]李远,秦自楷,周志刚.压电材料与铁电材料的测量[M].北京:科学出版社, 1984.
[66]李尚平,徐永利,苏建华等.驱动器用陶瓷材料与展望[J].压电与声光,1999,21(6):483-487.
[67]林声和,叶至碧,王裕斌.压电陶瓷[M].北京:国防工业出版社,1980.
[68]电子陶瓷情报网.压电陶瓷应用[M].济南:山东大学出版社,1985.
[69]胡德昌,胡滨.新型材料特性及其应用[M].广州:广东科技出版社,1995.
[70]张沛霖,张仲渊.压电测量[M].北京:国防工业出版社,1983.
[71]岛村招治著蔡克芬译.日开拓未来的尖端材料[M].北京:冶金工业出版社,1988.
[72]李尚平,徐永利,苏建华等.驱动器用陶瓷材料与展望[J].压电与声光,1999,21(6):483-487
[73]张涛,孙立宁,蔡鹤皋.压电陶瓷基本特性研究[J].光学精密工程,1998,6(5):40-47.
[74]高乔贞行.驱动器用压电陶瓷[J].压电与声光,1986,50-56.
[75]蔡鹤皋,孙立宁,安辉.压电/电致伸缩微位移器件与应用(下)[J].高技术通讯.1994.
[76]小西良弘.电子陶瓷基础和应用[M].北京:机械工业出版社,1983.
[77]许小红,武海顺.压电薄膜的制备、结构与应用[M].北京:科学出版社,2002.
[78]沈传亮.压电型直动式电液伺服阀的基本理论与试验研究[D].吉林大学博士学位论文, 2006.
[79]栾桂冬,张金铎,王仁乾.压电换能器和换能器阵[M].北京:北京大学出版社,2005:103-126.
[80]刘一声.压电双晶片致动元件的应用[J].压电与声光,1985(1):35-46.
[81] T . Higuchi. Precise Positioning Mechanism Utilizing Rapid Deformations of Plezoelectric Elements[C]. Proceeding of IEEE Micro Electro Mechanical System Workshop,1990, 203.
[82] Yoshida, Ryuichi, Okamoto, Yasuhiro, Higuchi, Toshiro, etc. Development of smooth impact drive mechanism (SIDM) - proposal of driving mechanism and basic performance[J]. Journal of the Japan Society for Precision Engineering,1999, 65 (1): 111-115.
[83] Binnig G, Rohrer H. Scanning tunneling microscope[J]. Helv Phys Acta,1982,55: 726-730.
[84] Binnig G, Quate CF. Atomic force microscope[J]. Phys Rev Lett, 1986, 56: 930-936.
[85]朱健国,骆英.压电驱动器性能的有限元分析[J].压电与声光,2006,28 (1):27-29.
[86] Jeong-Du Kim, Dong-Sik Kim. Waviness compensation of precision machining by piezoelectric micro cutting device[J]. International Journal of Machine Tools & Manufacture, 1998, 38: 1305-1322.
[87] R. Caracciolo, D. Richiedei, et al. Design and experimental validation of piecewise-linear state observers for flexible link mechanisms[J]. Meccanica , 2006,41:623–637.
[88] Donald E. Croft. High-Speed High-Precision Piezoactuators with Application to Scanning Probe Microscopy[D]. The University of Utah, Doctoral thesis. 2003.
[89]向毅,王亚君,任晓东等.压电陶瓷的谐振特性研究[J].中国科技信息,2006,(2):61-70.
[90]杨志刚.双弯曲压电超声波驱动器的理论与试验研究[D].吉林工业大学博士学位论文,1998.
[91]刘永刚,沈星,赵东标.交叉指型电极压电振子的谐振特性研究[J].压电与声.Vol.30 NO.e Jun.2008.
[92]鲍善惠,王艳东.压电换能器在并联谐振频率附近特性的研究[J].声学技术.Vol.25 No.2:165-168. apr.2006.
[93]李黎,刘向东,王伟.压电陶瓷执行器迟滞特性的广义非线性Preisach模型及其数值实现[J].光学精密工程.Vol.15 No.5 May 2007.
[94]张凯,党选举,曹凤金.基于小波变换的压电陶瓷动态特性迟滞性建模[J].微电子学与计算机.Vol.26 No.June 2009.
[95] P. Muralt, A. Kholkin, M. Kohli, et al. Piezoelectric actuation of PZT thin-film diaphragms at static and resonant conditions[J]. Sensors and Actuators A: Physical, 1996, 53(1-3): 398-404.
[96] M. Koch, C. G. J. Schabmueller, A. G. R. Evans, et al. Micromachined chemical reaction system[J]. Sensors and Actuators A: Physical, 1999, 74(1-3): 207-210.
[97] C. H. J. Fox, X. Chen, S. McWilliam. Analysis of the deflection of a circular plate with an annular piezoelectric actuator[J]. Sensors and Actuators A: Physical, 2007, 133(1): 180-194.
[98] Qifeng Cui, Chengliang Liu, Xuan F. Zha. Simulation and optimization of a piezoelectric micropump for medical applications[J]. International Journal of Advanced Manufacturing Technology, 2008, 36(5-6): 516-524.
[99] A. B. Dobrucki, P. Pruchnicki. Theory of piezoelectric axisymmetric bimorph[J]. Sensors and Actuators, A: Physical, 1997, 58(3): 203-212.
[100] D. Accoto, O. T. Nedelcu, M. C. Carrozza, et al. Theoretical analysis and experimental testing of a miniature piezoelectric pump[C]. 1998. Piscataway, NJ, USA: IEEE.
[101] Christopher J. Morris, Fred K. Forster. Optimization of a circular piezoelectric bimorph for a micropump driver[J]. Journal of Micromechanics and Microengineering, 2000, 10(3): 459-465.
[102] Q. Wang, S. T. Quek, C. T. Sun, et al.. Analysis of piezoelectric coupled circular plate[J]. Smart Materials and Structures, 2001, 10(2): 229-239.
[103]刘品宽,孙立宁,祝宇虹等.双压电复合薄圆板驱动器的理论分析[J].压电与声光,2002,24(02): 111-115.
[104] Michel Brissaud, Sarah Ledren, P. Gonnard. Modelling of a cantilever non-symmetric piezoelectric bimorph[J]. Journal of Micromechanics and Microengineering,2003,13(6):832-844.
[105] Minqiang Bu, Tracy Melvin, Graham Ensell, et al. Design and theoretical evaluation of a novel microfluidic device to be used for PCR[J]. Journal of Micromechanics and Microengineering,2003,13(4):125-130.
[106] Sunghwan Kim, William W. Clark, Qing-Ming Wang. Piezoelectric energy harvesting using a diaphragm structure[C]. The International Society for Optical Engineering,2003.
[107] Shifeng Li, Shaochen Chen. Analytical analysis of a circular PZT actuator for valveless micropumps[J]. Sensors and Actuators,A: Physical,2003,104(2):151-161.
[108]范国滨,王卫东,贾建援.压电致动式圆片驱动装置结构分析与设计[J].西安电子科技大学学报,2003,30(01):42-46.
[109] Michel Brissaud. Modelling of non-symmetric piezoelectric bimorphs[J]. Journal of Micromechanics and Microengineering,2004,14(11): 1507-1518.
[110] Michel Brissaud. Theoretical modelling of non-symmetric circular piezoelectric bimorphs[J]. Journal of Micromechanics and Microengineering,2006,16(5): 875-885.
[111] Baowei Wang,Xiangcheng Chu,Enzhu Li, et al.Simulations and analysis of a piezoelectric micropump[J]. Ultrasonics,2006,44(SUPPL):643-646.
[112] B. L. Wang, J. C. Han. A circular indenter on a piezoelectric layer[J]. Archive of Applied Mechanics,2006,76(7-8): 67-379.
[113] Mandar Deshpande, Laxman Saggere. An analytical model and working equations for static deflections of a circular multi-layered diaphragm-type piezoelectric actuator[J]. Sensors and Actuators, A: Physical,2007,136(2):673-689.
[114] Tao Li, Y. H. Chen, J. Ma. Frequency dependence of piezoelectric vibration velocity[J]. Sensors and Actuators, A: Physical,2007,138(2):404-410.
[115] Shuyu Lin. Study on the radial composite piezoelectric ceramic transducer in radial vibration[J]. Ultrasonics,2007,46(1):51-59.
[116] Poorna Mane, Karla Mossi, Christopher Green, et al. Studying the effects of temperature on energy harvesting using prestressed piezoelectric diaphragms[C]. Behavior and Mechanics of Multifunctional and Composite Materials 2007. Proceedings of the SPIE, Volume 6526, pp. 65260K (2007).
[117] Shuyu Lin. The radial composite piezoelectric ceramic transducer[J]. Sensors and Actuators, A: Physical,2008,141(1):136-143.
[118] Melih Papila, Mark Sheplak, Louis N. Cattafesta Iii. Optimization of clamped circular piezoelectric composite actuators[J]. Sensors and Actuators,A: Physical,2008,147(1):310-323.
[119] Tao Zhang, Qing-Ming Wang. Valveless piezoelectric micropump for fuel delivery in direct methanol fuel cell (DMFC) devices[J]. Journal of Power Sources,2005,140(1):72-80.
[120]曹志远.板壳振动理论[M].北京:中国铁道出版社,1989.
[121]黄克智等.板壳理论[M].北京:清华大学出版社,1987.
[122]寿南椿.弹性薄板弯曲[M].北京:高等教育出版社, 1986.
[123]吕恩琳.复合材料力学[M].重庆:重庆大学出版社. 1992.
[124]铁摩辛柯等.板壳理论[M].北京:科学出版社,1977.
[125] J.L.Pons, H. Rodr′guez, F. Seco, R. Ceres, L. Calderón. Modelling of piezoelectric transducers applied to piezoelectric. motors: a comparative study and new perspective Institutode[J]. Sensors and Actuators A:Physical Volume 110,Issues 1-3,1 February 2004,Pages 336-343.
[126] E. Taciroglu, C.W. Liu, S.B. Dong, C.K. Chun. Analysis of laminated piezoelectric circular cylinders unde axisymmetric mechanical and electrical loads with a semi-analytic finite element method[J]. International Journal of Solids and Structures Volume 41,Issues 18-19,September 2004,Pages 5185-5208.
[127] Zan Zhang, C. Feng, K.M. Liew. Three-dimensional vibration analysis of multilayered piezoelectric composite plates[J]. International Journal of Engineering Science,v 44,n 7,p 397-408,April 2006.
[128] M. Shakeri, M.R. Eslami, A. Daneshmehr. Dynamic analysis of thick laminated shell panel with piezoelectric layer based on three dimensional elasticity solution[J]. Computers & Structures Volume 84,Issues 22-23,September 2006,Pages 1519-1526.
[129] R. C. Batra, X. Q. Liang. the vibration of a rectangular laminated elastic plate with embedded piezoelectric sensors and actuators[J]. Computers & Structures Volume 63,Issue 2,April 1997,Pages 203-216.
[130] Michel Brissaud. Theoretical modelling of non-symmetric circular piezoelectric bimorphs[J]. Journal of Micromech and Microeng,2006(16):875-885.
[131]程昌钧,朱媛媛.弹性力学[M].上海:上海大学出版社,2005.
[132]徐芝纶.弹性力学[M].北京:高等教育出版社,2005.
[133]刘孝敏.工程材料的微细观结构和力学性能[M].合肥:中国科技大学出版社,2003.
[134]张义民.机械振动力学[M].长春:吉林科学技术出版社,2002.
[135]田村光男.声振动发生元件:日本,1627864A.2005.6.
[136]杨志刚,孙海涛,陈亚元.矩形压电振子振动有限元分析[J].压电与声光.Vol.18 No.4:244-248. Aug.1996.
[137]朴林华,栾桂冬,张福学.压电泵振动模态的有限元分析[J].压电与声光.Vol.26 No.6 :503-505.Dec.2004.
[138]葛杨翔,王东生,李玉和.压电双晶片的静动态特性分析与测量[J].压电与声光. Vol.28 No.5 :621-623.Oct.2006.
[139]任露泉,杨志刚,佟金.双弯曲型压电振子的振动解析[J].压电与声光.Vol.20 No.3 : 162-165.June.1998.
[140]范兰德拉特J,塞德林顿R E,彭浩波,马乐山,胡邦豪.压电陶瓷[M].北京:科学出版社,1981.
[141]马海峰,周桃生.压电陶瓷机械品质因数Qm及其温度稳定性[J].长沙:湖北大学学报,2003,25(1): 49-52.
[142] Moulson A J, Herbert J M,李世普,陈晓明,樊东辉.电子陶瓷材料性能应用[M].武汉:武汉工业大学出版社,1993.
[143]许煜寰.铁电与压电材料[M].北京:科学出版社,1978.
[144]刘梅冬,许毓春.压电与铁电材料与器件[M].武汉:华中理工大学出版社,1992.
[145] N. Snis, U. Simu, S. Johannson. Piezoelectric drive platform for cm3-sized autonomous robot[C]. Actuator 2004,9th International conference on new actuators,14-16 June 2004,Bremen, Germany.
[146] Wang Q.M., Cross L.E. Performance analysis of piezoelectric cantilever bending actuators[J]. Ferroelectrics, 1998(215):187-213.
[147] Jan G. Smits, Susan I, Dalke, Thomas IL Cooney. The constituent equations of piezoelectric bimorphs[J]. Sensors and Acntators A:1991,28:41-61.
[148]华顺明.压电式粘滑精密运动机构驱动理论与试验研究[D].长春:吉林大学机械科学与工程学院,2005.
[149]温熙森,陈循.机械系统动态分析理论与应用[M].北京:国防科技大学出版社,1997.
[150]声学校准测听设备的基准零级.第3部分骨振器纯音基准等效阈级.北京:中华人民共和国国家标准. GB/T 4854.3-1998 eqv ISO 389-3:1994(E).
[151]俞锦元.音箱原理及制作[M].北京:电子工业出版社出版,1997.
[152]早坂寿雄.电声学[M].北京:电子工业出版社出版,1987.
[153]成天龙. LC二分频器与电子分频器的性能比较[J].科技情报开发与经济,2002,12卷,第2期91-92.
[154]张春生,常青.特殊分频电路设计[J].现代电子技术.2006年第6期,总第221期112-116.
[155]陈凤霞,默立冬,吴思汉.微波宽带单片集成电路二分频器的设计与实现[J].半导体技术. 2008(2),第33卷,第2期164-166.
[2] Abdelhafid OMARI, et al. Development of a high precision mounting robot system with fine motion mechanism (3rd Report)[J]. JSPE, 2001, 67 (7): 1101-1107.
[3] Hisayuki Aoyama. Flexible micro-processing by multiple microrobots in SEM[C]. Proc of international Conference on Robotics & Automation 2001.
[4]赵宏伟,刘建芳,华顺明,刘国嵩,程光明,吴博达.压电型步进精密旋转驱动器[J].光学精密工程,Vol.13 No.3 Jun.2005.
[5] Hiromichi Morita et al. Electical discharge device with direct drive method for thin wire electrode[C]. IEEE International Conference on Robotics and Automation,1995.
[6] Ralph Hollis et al. Miniature factories for precision assembly[C]. Proc.Intternational Workshop on Micro-Factories,Tsukuba,Japan,December 7-8,1998: 1-6.
[7] S Roundy, P K Wright. A piezoelectric vibration based generator for wireless electronics[J]. Institute of Physics Publishing. Samrt Mater. Struct.13(2004)1131-1142.
[8]日本工业技术振兴协会固体アクチュエ-タ研究部会编.精密制御用ニュ-アクチュエ-タ便览[M].东京:フヅテクノツステム,1994.
[9]内野研二.压电アクチュエ-タ[M].东京:森北出版株式会社,1991.
[10]上羽贞行,富川义郎.新版超音波モ-タ[M].东京:トリヮップスス,1991.
[11]张福学,王丽坤.现代压电学[M].北京:科学出版社,2002.
[12]电子陶瓷情报网编.压电陶瓷应用[M].山东:山东大学出版社,1985.
[13]栾桂冬,张金铎,王仁乾.压电换能器和换能器阵[M].北京:北京大学出版社,2004.
[14]田中哲郎(日)等.压电陶瓷材料.陈俊彦,王余君译[M].北京:科学出版社,1982.
[15]张沛霖,钟维烈.压电材料与器件物理[M].济南:山东科学技术出版社,1997.
[16]林声和,王裕斌.压电陶瓷[M].北京:国防工业出版社,1980.
[17]山东大学压电铁电物理教研室.压电陶瓷及其应用[M].济南:山东人民出版社,1974.
[18]电子陶瓷情报网.压电陶瓷应用[M].济南:山东大学出版社,1985.
[19]徐锡林.压电型微驱动器[J].上海交通大学学报,1997,31(1):67-70.
[20]韩德民.临床听力学[M].北京:人民卫生出版社,2006.9.
[21]彭玉成.耳聋与助听器选配[M].北京:人民军医出版社,2001.
[22] Mylanus et al. Intraindividual Comparison of the Bone-Anchored Hearing Aid andAir-Conduction Hearing Aids[J]. Arch Otolaryngol Head Neck Surg,1998,124:271-276.
[23] Mariano Belinky, Natalie Jeremijenko. Sound through bone conduction in public interfaces[C]. Conference on Human Factors in Computing Systems,2001.181-182.
[24] M.L.Oenhardt, R.Skellett, P.Wang,et al. Human ultrasonic speech perception[J]. Science,1991,253(5015):82-85.
[25] Haeff, Knox. Perception of Ultrasound[J]. Science,1963 ,139:590-592.
[26] Peder Carlsson, BoHakansson. Force threshold for hearing by direct bone conduction[J]. J.Acoust.Soc.Am.97(2),February 1995:1124-1129.
[27]龚文,邵斌.双导式聋哑人听力器:中国,02266851.1989-09-10.
[28]温大鹏,郑建晖.骨传导式耳机:中国,02802599.2002-07-15.
[29]严建敏.骨传导助听器:中国,02266851. 2003-09-11.
[30]陈奚平.骨传导扬声器:中国,200620033506. 2007-03-14.
[31]修翔凤.头卡式骨传导助听器:中国,2790089Y.2006-06-21.
[32]郁令友.手表式蓝牙耳机结构:中国,2800681Y.2006-07-26.
[33]严世熙.整合式骨传导技术眼镜:中国,201035260Y.2008-03-12.
[34]许必亮.骨传导运动眼镜:中国,201156128Y.2008-11-26.
[35]王舜清.鼻骨传导助听装置:中国台湾,200420120237.2005-05-24.
[36]王舜清.鼻骨传导活体声纹辨识装置:中国台湾,101042869A.2007-09-12.
[37]王舜清.鼻骨传导影音传输装置:中国台湾,101022681A.2007-08-23.
[38]福田干夫.骨传导扬声器:日本,1406449A.2003-03-12.
[39]小林一二.骨传导扬声器:日本,1656849A.2005-08-17.
[40]落合浩一郎.骨传导扬声器装置:日本,1723733A.2006-01-18.
[41]姜京玉.带有能引起骨传导和空气传导听觉的接收器的电话:韩国,1276142A.2000-12-17.
[42]李亿基.使用振动膜的超小型骨振动扬声器和具有它的移动电话:韩国,1675846A.2005-09-28.
[43]田中正智.耳部安装型的通话装置:日本,1742476A.2006-03-01.
[44]藤田柾彦.耳部佩戴式声音信息传达器:日本,1625189A.2005-06-08.
[45]渥美智也.骨传导耳机:日本,1465204A.2003-12-31.
[46]武田猛.骨传导受话装置:日本,1984505A.2007-06-20.
[47] Yoshiyasu, Yamada. Study on voice recognition utilizing bone-conducted voice[C]. IEEJTrans. SM, Vol.124,No.8,2004.
[48]冀飞.植入式助听装置简介[J].《中国医疗器械信息》,2009年第15卷第1期Vol.15 No.1.
[49] Bo E.V.Hakansson. The balanced electromagnetic separation transducer:A new bone conduction transducer[J]. J.acoust.soc.Am.113(2).February 2003.
[50] E.G.里查孙,马大猷猷,关定华.声学技术概要(中)[M].北京:科学技术出版社,1965.
[51]徐锡林.压电型微驱动器[J].上海交通大学学报,1997,31(1):67-70.
[52]刘德忠.双指微动操作器开发与研究[D].北京:北京工业大学,2002.
[53]章句才.基础听力学[M].北京:中国计量出版社,1993.
[54]谢鼎华.基础与应用听力学[M].长沙:湖南科学技术出版社,2003.
[55]何永照.听力学概论[M].上海:上海科学技术出版社,1964.
[56] E.G.里查孙,章启馥,声学技术概要(上)[M].北京:科学技术出版社,1961.
[57]李学佩.耳鼻咽喉科学[M].北京:北京大学医学出版社,2003.
[58]王永华.耳聋[M].合肥:安徽科学技术出版社,2001.
[59]李东亮,许继田,关宿东.临床生理学[M].郑州:郑州大学出版社,2004.
[60]岳利民.生理学[M].北京:科学出版社,2003.
[61]刘国艺.生理学[M].北京:人民军医出版社,2006.
[62]朱妙章.大学生理学[M].北京:高等教育出版社,2002.
[63]宋道仁.压电效应与应用[M].北京:科学普及出版社,1987年第一版.
[64]张福学,王丽坤.现代压电学(上册)[M].北京:科学出版社,2001.
[65]李远,秦自楷,周志刚.压电材料与铁电材料的测量[M].北京:科学出版社, 1984.
[66]李尚平,徐永利,苏建华等.驱动器用陶瓷材料与展望[J].压电与声光,1999,21(6):483-487.
[67]林声和,叶至碧,王裕斌.压电陶瓷[M].北京:国防工业出版社,1980.
[68]电子陶瓷情报网.压电陶瓷应用[M].济南:山东大学出版社,1985.
[69]胡德昌,胡滨.新型材料特性及其应用[M].广州:广东科技出版社,1995.
[70]张沛霖,张仲渊.压电测量[M].北京:国防工业出版社,1983.
[71]岛村招治著蔡克芬译.日开拓未来的尖端材料[M].北京:冶金工业出版社,1988.
[72]李尚平,徐永利,苏建华等.驱动器用陶瓷材料与展望[J].压电与声光,1999,21(6):483-487
[73]张涛,孙立宁,蔡鹤皋.压电陶瓷基本特性研究[J].光学精密工程,1998,6(5):40-47.
[74]高乔贞行.驱动器用压电陶瓷[J].压电与声光,1986,50-56.
[75]蔡鹤皋,孙立宁,安辉.压电/电致伸缩微位移器件与应用(下)[J].高技术通讯.1994.
[76]小西良弘.电子陶瓷基础和应用[M].北京:机械工业出版社,1983.
[77]许小红,武海顺.压电薄膜的制备、结构与应用[M].北京:科学出版社,2002.
[78]沈传亮.压电型直动式电液伺服阀的基本理论与试验研究[D].吉林大学博士学位论文, 2006.
[79]栾桂冬,张金铎,王仁乾.压电换能器和换能器阵[M].北京:北京大学出版社,2005:103-126.
[80]刘一声.压电双晶片致动元件的应用[J].压电与声光,1985(1):35-46.
[81] T . Higuchi. Precise Positioning Mechanism Utilizing Rapid Deformations of Plezoelectric Elements[C]. Proceeding of IEEE Micro Electro Mechanical System Workshop,1990, 203.
[82] Yoshida, Ryuichi, Okamoto, Yasuhiro, Higuchi, Toshiro, etc. Development of smooth impact drive mechanism (SIDM) - proposal of driving mechanism and basic performance[J]. Journal of the Japan Society for Precision Engineering,1999, 65 (1): 111-115.
[83] Binnig G, Rohrer H. Scanning tunneling microscope[J]. Helv Phys Acta,1982,55: 726-730.
[84] Binnig G, Quate CF. Atomic force microscope[J]. Phys Rev Lett, 1986, 56: 930-936.
[85]朱健国,骆英.压电驱动器性能的有限元分析[J].压电与声光,2006,28 (1):27-29.
[86] Jeong-Du Kim, Dong-Sik Kim. Waviness compensation of precision machining by piezoelectric micro cutting device[J]. International Journal of Machine Tools & Manufacture, 1998, 38: 1305-1322.
[87] R. Caracciolo, D. Richiedei, et al. Design and experimental validation of piecewise-linear state observers for flexible link mechanisms[J]. Meccanica , 2006,41:623–637.
[88] Donald E. Croft. High-Speed High-Precision Piezoactuators with Application to Scanning Probe Microscopy[D]. The University of Utah, Doctoral thesis. 2003.
[89]向毅,王亚君,任晓东等.压电陶瓷的谐振特性研究[J].中国科技信息,2006,(2):61-70.
[90]杨志刚.双弯曲压电超声波驱动器的理论与试验研究[D].吉林工业大学博士学位论文,1998.
[91]刘永刚,沈星,赵东标.交叉指型电极压电振子的谐振特性研究[J].压电与声.Vol.30 NO.e Jun.2008.
[92]鲍善惠,王艳东.压电换能器在并联谐振频率附近特性的研究[J].声学技术.Vol.25 No.2:165-168. apr.2006.
[93]李黎,刘向东,王伟.压电陶瓷执行器迟滞特性的广义非线性Preisach模型及其数值实现[J].光学精密工程.Vol.15 No.5 May 2007.
[94]张凯,党选举,曹凤金.基于小波变换的压电陶瓷动态特性迟滞性建模[J].微电子学与计算机.Vol.26 No.June 2009.
[95] P. Muralt, A. Kholkin, M. Kohli, et al. Piezoelectric actuation of PZT thin-film diaphragms at static and resonant conditions[J]. Sensors and Actuators A: Physical, 1996, 53(1-3): 398-404.
[96] M. Koch, C. G. J. Schabmueller, A. G. R. Evans, et al. Micromachined chemical reaction system[J]. Sensors and Actuators A: Physical, 1999, 74(1-3): 207-210.
[97] C. H. J. Fox, X. Chen, S. McWilliam. Analysis of the deflection of a circular plate with an annular piezoelectric actuator[J]. Sensors and Actuators A: Physical, 2007, 133(1): 180-194.
[98] Qifeng Cui, Chengliang Liu, Xuan F. Zha. Simulation and optimization of a piezoelectric micropump for medical applications[J]. International Journal of Advanced Manufacturing Technology, 2008, 36(5-6): 516-524.
[99] A. B. Dobrucki, P. Pruchnicki. Theory of piezoelectric axisymmetric bimorph[J]. Sensors and Actuators, A: Physical, 1997, 58(3): 203-212.
[100] D. Accoto, O. T. Nedelcu, M. C. Carrozza, et al. Theoretical analysis and experimental testing of a miniature piezoelectric pump[C]. 1998. Piscataway, NJ, USA: IEEE.
[101] Christopher J. Morris, Fred K. Forster. Optimization of a circular piezoelectric bimorph for a micropump driver[J]. Journal of Micromechanics and Microengineering, 2000, 10(3): 459-465.
[102] Q. Wang, S. T. Quek, C. T. Sun, et al.. Analysis of piezoelectric coupled circular plate[J]. Smart Materials and Structures, 2001, 10(2): 229-239.
[103]刘品宽,孙立宁,祝宇虹等.双压电复合薄圆板驱动器的理论分析[J].压电与声光,2002,24(02): 111-115.
[104] Michel Brissaud, Sarah Ledren, P. Gonnard. Modelling of a cantilever non-symmetric piezoelectric bimorph[J]. Journal of Micromechanics and Microengineering,2003,13(6):832-844.
[105] Minqiang Bu, Tracy Melvin, Graham Ensell, et al. Design and theoretical evaluation of a novel microfluidic device to be used for PCR[J]. Journal of Micromechanics and Microengineering,2003,13(4):125-130.
[106] Sunghwan Kim, William W. Clark, Qing-Ming Wang. Piezoelectric energy harvesting using a diaphragm structure[C]. The International Society for Optical Engineering,2003.
[107] Shifeng Li, Shaochen Chen. Analytical analysis of a circular PZT actuator for valveless micropumps[J]. Sensors and Actuators,A: Physical,2003,104(2):151-161.
[108]范国滨,王卫东,贾建援.压电致动式圆片驱动装置结构分析与设计[J].西安电子科技大学学报,2003,30(01):42-46.
[109] Michel Brissaud. Modelling of non-symmetric piezoelectric bimorphs[J]. Journal of Micromechanics and Microengineering,2004,14(11): 1507-1518.
[110] Michel Brissaud. Theoretical modelling of non-symmetric circular piezoelectric bimorphs[J]. Journal of Micromechanics and Microengineering,2006,16(5): 875-885.
[111] Baowei Wang,Xiangcheng Chu,Enzhu Li, et al.Simulations and analysis of a piezoelectric micropump[J]. Ultrasonics,2006,44(SUPPL):643-646.
[112] B. L. Wang, J. C. Han. A circular indenter on a piezoelectric layer[J]. Archive of Applied Mechanics,2006,76(7-8): 67-379.
[113] Mandar Deshpande, Laxman Saggere. An analytical model and working equations for static deflections of a circular multi-layered diaphragm-type piezoelectric actuator[J]. Sensors and Actuators, A: Physical,2007,136(2):673-689.
[114] Tao Li, Y. H. Chen, J. Ma. Frequency dependence of piezoelectric vibration velocity[J]. Sensors and Actuators, A: Physical,2007,138(2):404-410.
[115] Shuyu Lin. Study on the radial composite piezoelectric ceramic transducer in radial vibration[J]. Ultrasonics,2007,46(1):51-59.
[116] Poorna Mane, Karla Mossi, Christopher Green, et al. Studying the effects of temperature on energy harvesting using prestressed piezoelectric diaphragms[C]. Behavior and Mechanics of Multifunctional and Composite Materials 2007. Proceedings of the SPIE, Volume 6526, pp. 65260K (2007).
[117] Shuyu Lin. The radial composite piezoelectric ceramic transducer[J]. Sensors and Actuators, A: Physical,2008,141(1):136-143.
[118] Melih Papila, Mark Sheplak, Louis N. Cattafesta Iii. Optimization of clamped circular piezoelectric composite actuators[J]. Sensors and Actuators,A: Physical,2008,147(1):310-323.
[119] Tao Zhang, Qing-Ming Wang. Valveless piezoelectric micropump for fuel delivery in direct methanol fuel cell (DMFC) devices[J]. Journal of Power Sources,2005,140(1):72-80.
[120]曹志远.板壳振动理论[M].北京:中国铁道出版社,1989.
[121]黄克智等.板壳理论[M].北京:清华大学出版社,1987.
[122]寿南椿.弹性薄板弯曲[M].北京:高等教育出版社, 1986.
[123]吕恩琳.复合材料力学[M].重庆:重庆大学出版社. 1992.
[124]铁摩辛柯等.板壳理论[M].北京:科学出版社,1977.
[125] J.L.Pons, H. Rodr′guez, F. Seco, R. Ceres, L. Calderón. Modelling of piezoelectric transducers applied to piezoelectric. motors: a comparative study and new perspective Institutode[J]. Sensors and Actuators A:Physical Volume 110,Issues 1-3,1 February 2004,Pages 336-343.
[126] E. Taciroglu, C.W. Liu, S.B. Dong, C.K. Chun. Analysis of laminated piezoelectric circular cylinders unde axisymmetric mechanical and electrical loads with a semi-analytic finite element method[J]. International Journal of Solids and Structures Volume 41,Issues 18-19,September 2004,Pages 5185-5208.
[127] Zan Zhang, C. Feng, K.M. Liew. Three-dimensional vibration analysis of multilayered piezoelectric composite plates[J]. International Journal of Engineering Science,v 44,n 7,p 397-408,April 2006.
[128] M. Shakeri, M.R. Eslami, A. Daneshmehr. Dynamic analysis of thick laminated shell panel with piezoelectric layer based on three dimensional elasticity solution[J]. Computers & Structures Volume 84,Issues 22-23,September 2006,Pages 1519-1526.
[129] R. C. Batra, X. Q. Liang. the vibration of a rectangular laminated elastic plate with embedded piezoelectric sensors and actuators[J]. Computers & Structures Volume 63,Issue 2,April 1997,Pages 203-216.
[130] Michel Brissaud. Theoretical modelling of non-symmetric circular piezoelectric bimorphs[J]. Journal of Micromech and Microeng,2006(16):875-885.
[131]程昌钧,朱媛媛.弹性力学[M].上海:上海大学出版社,2005.
[132]徐芝纶.弹性力学[M].北京:高等教育出版社,2005.
[133]刘孝敏.工程材料的微细观结构和力学性能[M].合肥:中国科技大学出版社,2003.
[134]张义民.机械振动力学[M].长春:吉林科学技术出版社,2002.
[135]田村光男.声振动发生元件:日本,1627864A.2005.6.
[136]杨志刚,孙海涛,陈亚元.矩形压电振子振动有限元分析[J].压电与声光.Vol.18 No.4:244-248. Aug.1996.
[137]朴林华,栾桂冬,张福学.压电泵振动模态的有限元分析[J].压电与声光.Vol.26 No.6 :503-505.Dec.2004.
[138]葛杨翔,王东生,李玉和.压电双晶片的静动态特性分析与测量[J].压电与声光. Vol.28 No.5 :621-623.Oct.2006.
[139]任露泉,杨志刚,佟金.双弯曲型压电振子的振动解析[J].压电与声光.Vol.20 No.3 : 162-165.June.1998.
[140]范兰德拉特J,塞德林顿R E,彭浩波,马乐山,胡邦豪.压电陶瓷[M].北京:科学出版社,1981.
[141]马海峰,周桃生.压电陶瓷机械品质因数Qm及其温度稳定性[J].长沙:湖北大学学报,2003,25(1): 49-52.
[142] Moulson A J, Herbert J M,李世普,陈晓明,樊东辉.电子陶瓷材料性能应用[M].武汉:武汉工业大学出版社,1993.
[143]许煜寰.铁电与压电材料[M].北京:科学出版社,1978.
[144]刘梅冬,许毓春.压电与铁电材料与器件[M].武汉:华中理工大学出版社,1992.
[145] N. Snis, U. Simu, S. Johannson. Piezoelectric drive platform for cm3-sized autonomous robot[C]. Actuator 2004,9th International conference on new actuators,14-16 June 2004,Bremen, Germany.
[146] Wang Q.M., Cross L.E. Performance analysis of piezoelectric cantilever bending actuators[J]. Ferroelectrics, 1998(215):187-213.
[147] Jan G. Smits, Susan I, Dalke, Thomas IL Cooney. The constituent equations of piezoelectric bimorphs[J]. Sensors and Acntators A:1991,28:41-61.
[148]华顺明.压电式粘滑精密运动机构驱动理论与试验研究[D].长春:吉林大学机械科学与工程学院,2005.
[149]温熙森,陈循.机械系统动态分析理论与应用[M].北京:国防科技大学出版社,1997.
[150]声学校准测听设备的基准零级.第3部分骨振器纯音基准等效阈级.北京:中华人民共和国国家标准. GB/T 4854.3-1998 eqv ISO 389-3:1994(E).
[151]俞锦元.音箱原理及制作[M].北京:电子工业出版社出版,1997.
[152]早坂寿雄.电声学[M].北京:电子工业出版社出版,1987.
[153]成天龙. LC二分频器与电子分频器的性能比较[J].科技情报开发与经济,2002,12卷,第2期91-92.
[154]张春生,常青.特殊分频电路设计[J].现代电子技术.2006年第6期,总第221期112-116.
[155]陈凤霞,默立冬,吴思汉.微波宽带单片集成电路二分频器的设计与实现[J].半导体技术. 2008(2),第33卷,第2期164-166.