金属-压电陶瓷双迭片弯曲型压电传感器谐振频率半解析求解方法
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- 英文论文题名：Semi analytical solution to the resonant frequency of the bending piezoelectric sensor with metal piezoelectric ceramics bimorph
- 论文作者：吉德三 ; 杨琳
- 英文论文作者：JI De-san ; YANG Lin ; College of Science ; Wuhan University of Science and Technology
- 年：2016
- 作者机构：武汉科技大学理学院;
- 论文关键词：双迭片 ; 双迭片弯曲型压电传感器 ; 谐振频率 ; 边界固支 ; 半解析方法
- 英文论文关键词：bimorph ; bimorph flexural piezoelectric ceramic transducer ; resonant frequency ; fixed boundary ; general solution of displace ; half analytic solution
- 会议召开时间：2016-09-17
- 会议录名称：2016年度声学技术学术会议论文集
- 语种：中文
- 分类号：TB552;TP212
- 学会代码：SXJS
- 会议名称：2016年度声学技术学术会议
- 会议地点：中国湖北武汉
- 主办单位：船舶振动噪声重点实验室、湖北省声学学会
- 学会名称：《声学技术》编辑部
- 页数：6
- 文件大小：449k
- 原文格式：D
- 会议级别：全国
摘要
本文从金属-压电陶瓷双迭片压电振子的力学特性出发,在忽略辐射阻尼和损耗的条件下,将边缘固定的金属-压电陶瓷双迭片压电振子视为边缘固定的、中间部分为金属-压电陶瓷双迭片的薄圆板,导出在满足薄板小挠度变形和轴对称的条件下压电振子弯曲位移的一般解。由薄板小挠度变形和轴对称的条件下压电振子弯曲位移的一般解求得金属-压电陶瓷双迭片弯曲型压电传感器的谐振频率。借助于Matlab强大的符号计算功能,将此法应用于金属-压电陶瓷双迭片弯曲型压电传感器的谐振频率的求解并计算结果与Ansys模拟运算结果进行对照,可以认为求解的结果与有限元模拟所得的结果比较接近。
According to the mechanic characteristic of the piezoelectricity oscillator, the metal-piezoceramics bimorph flexural piezoelectric ceramic transducer clamped along boundary is considered as a circular thin plate with a fixed boundary and a metal-piezoceramic bimorph in the central section. Then a general solution of displace of piezoelectricity oscillator with the assumption the small deflection and the axial symmetry conditions are satisfied is presented. According to the general solution, the resonant frequencies of metal-piezoceramics bimorph flexural piezoelectric ceramic transducer are approached. The method has been applied to the calculation of the resonant frequency of the bending piezoelectric sensor with metal piezoelectric ceramics bimorph and the results are compared with the results of Ansys simulation. It can be considered that the results obtained from the solution are close to the results of finite element simulation.
According to the mechanic characteristic of the piezoelectricity oscillator, the metal-piezoceramics bimorph flexural piezoelectric ceramic transducer clamped along boundary is considered as a circular thin plate with a fixed boundary and a metal-piezoceramic bimorph in the central section. Then a general solution of displace of piezoelectricity oscillator with the assumption the small deflection and the axial symmetry conditions are satisfied is presented. According to the general solution, the resonant frequencies of metal-piezoceramics bimorph flexural piezoelectric ceramic transducer are approached. The method has been applied to the calculation of the resonant frequency of the bending piezoelectric sensor with metal piezoelectric ceramics bimorph and the results are compared with the results of Ansys simulation. It can be considered that the results obtained from the solution are close to the results of finite element simulation.
引文
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[25]丁皓江,池毓蔚,国凤林等.压电材料轴对称有限元分析[J].计算力学学报,2000,17(1):1-7.DING Haojiang,CHI Yuwei,GUO Fenglin.Axisymmetric finite element analysis of piezoelectric media[J].Chinese Journal of Computational Mechanics,2000,17(1):1-7.
[26]姜德义,郑拯宇,李林等.压电陶瓷片耦合振动模态的ANSYS模拟分析[J].传感技术学报,2003,16(4):452-456.JIANG Deyi,ZHENG Zhengyu,LI Lin.The Analyses of the Vibration Model of Piezoelectric Ceramic Piece Based on ANSYS[J].Journal of Transcluction Technology,2003,16(4):452-456.
[2]N.F.Ivina.Analysis of Natural Vibrations of Round Bimorph Piezoelectric Ceramic Plates of Arbitrary Dimensions.II.Rigidly Fixed Piezoelectric Plate[J].Russian Journal of Nondestructive Testing,2001;37(8):561-564.
[3]胡晓冰,李龙士,任飞.双迭片弯曲压电陶瓷换能器及振动模态分析测量[J].功能材料,2002,33(6):661-663.HU Xiaobing,LI Longtu,REN Fei,GUI Zhilun.Bimorph flexural piezoelectric ceramic transducer and measurement of its resonance modes[J].Journal of Functional Materials,2002,33(6):661-663.
[4]Fernandes A.Analytical and numerical approaches to piezoelectric bimorph[J].International Journal of Solids&Structures,2003,40(17):4331-4352.
[5]Chi-Hung Huang,Yu-Chih Lin,Chien-Ching Ma.Theoretical Analysis and Experimental Measurement for Resonant Vibration of Piezoceramic Circular Plates[J].Transactions on Ultrasonics Ferroelectrics&Frequency Control,2004,51(1):12-24.
[6]袁易全.超声换能器[M].北京:南京大学出版社,1992.YUAN Yiquan.Ultrasonic Transducer[M].Beijing:Nanjing University Press,1992.
[7]应崇福.超声学.北京:科学出版社,1990.YING Chongfu.Ultrasonics.Beijing:Science Press,1990.
[8]王矜奉,姜祖桐,石瑞大.压电振动[M].北京:科学出版社,1989.WANG Jinfeng,JIANG Zutong,SHI Rui.Piezoelectric Vibration[M].Beijing:Science Press,1989.
[9]张沛霖,张仲渊.压电测量[M].北京:国防工业出版社,1983.ZHANG Peilin,ZHANG Zhongyuan.Piezoelectric Measurement[M].Beijing:National Defence Industry Press,1983.
[10]Hu Xiao Bing,Li Long Tu,Chu,Xiang Cheng et al.The resonance vibration properties of a bimorph flexural piezoelectric ultrasonic transducer for distance measurement[J].Materials Science&Engineering B,2003,99(1-3):316-320.
[11]Lee,Peter C.Y.,Huang Rui.Vibrations and Static Responses of Asymmetric Bimorph Disks of Piezoelectric Ceramics[J].Transactions on Ultrasonics Ferroelectrics&Frequency Control,2000,47(3):706-715.
[12]Christopher J.T.,Gregory N.W.A Comprehensive Piezoceramic Actuator Review[J].Intelligent Structures&Systems Laboratory,Proc SPIE,2002,4701:443-454.
[13]林书玉.弯曲振动超声换能器的振动特性及辐射声场研究[J].陕西师范大学学报(自然科学版),2003,31(3):32-39.LIN Shuyu.Vibration and radiation characteristics of air-coupled flexural ultrasonic transducers[J].Journal of Shaanxi Normal University(Natural Science Edition),2003,31(3):32-39.
[14]林书玉.弯曲振动气介式超声换能器的振动特性及辐射声场研究[J].声学与电子工程,2004,3:1-7.LIN Shuyu.Vibration and radiation characteristics of air-coupled flexural ultrasonic transducers[J].Acoustics and Eleclrical Engineering,2004,3:1-7.
[15]Sung K.H..Analysis of the asymmetric triple-layered piezoelectric bimorph using equivalent circuit models[J].Smart Structures and Materials Laboratory,Analysis of the asymmetric triple-layered piezoelectric bimorph using equivalent circuit models[J].Journal of the Acoustical Society of America,2001,110:856-864.
[16]Wang,C.Y.Vibration of a circular plate with an attached core[J].Journal of Sound&Vibration,2005,280(3-5):1075-1082.
[17]Zhen-Qiang Cheng,Reddy J.N..An Asymptotic Theory for Vibrations of Inhomogeneous/Laminated Piezoelectric Plates[J].Journal of Sound&Vibration,2003,266(4):723-735.
[18]Wang,C.Y.Vibration of a circular plate with an attached core[J].Journal of Sound&Vibration,2005,280(3-5):1075-1082
[19]Bambill D.V.,La M S.,Rossit C.A.et al.Analytical and experimental investigation on transverse vibrations of solid circular and annular plates carrying a concentrated mass at an arbitrary position with marine applications[J].Ocean Engineering,2004,31(2):127-138.
[20]陈滨.动力学、振动与控制的研究[M].北京:北京大学出版社,1994CHEN Bin.Study on Dynamics Vibration and Control[M].Beijing:Peking University Press,1994.
[21]吴福光,蔡承武,徐兆.振动理论[M].北京:高等教育出版社,1987.WU Fuguang,CAI Chengwu,Xu Zhao.Vibration Theory[M].Beijing:Higher Education Press,1987.
[22]郑兆昌.机械振动[M].北京:机械工业出版社,1986.ZHENG Zhaochang.Mechanical Vibration[M].Beijing:China Machine Press,1986.
[23]荣现志,张顺忠译.标准数学手册[M].北京:化学工业出版社,1988RONG Xianzhi,ZHANG Shunzhong.Standard Mathematical Manual[M].Beijing:Chemical Industry Press,1988.
[24]张志涌.精通MATLAB(6.5版)[M].北京:北京航空航天大学出版社,2003.ZHANG Zhiyong.MATLAB applacation(V6.5)[M].Beijing:Beijing University of Aeronautics Press.2003.
[25]丁皓江,池毓蔚,国凤林等.压电材料轴对称有限元分析[J].计算力学学报,2000,17(1):1-7.DING Haojiang,CHI Yuwei,GUO Fenglin.Axisymmetric finite element analysis of piezoelectric media[J].Chinese Journal of Computational Mechanics,2000,17(1):1-7.
[26]姜德义,郑拯宇,李林等.压电陶瓷片耦合振动模态的ANSYS模拟分析[J].传感技术学报,2003,16(4):452-456.JIANG Deyi,ZHENG Zhengyu,LI Lin.The Analyses of the Vibration Model of Piezoelectric Ceramic Piece Based on ANSYS[J].Journal of Transcluction Technology,2003,16(4):452-456.